The W Charge Asymmetry: Measurement of the Proton ......The W Charge Asymmetry: Measurement of the Proton Structure with the ATLAS Detector Kristin Lohwasser St. Catherine’s College,

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The W Charge Asymmetry:Measurement of the ProtonStructure with the ATLAS

Detector

Kristin LohwasserDepartment of Physics

Oxford University

St. Catherine’s College

Thesis submitted in fulfilment of the requirements for the

degree of

Doctor of Philosophy

October 2009

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c©Kristin Lohwasser, 2009. All rights reserved.

The author hereby grants to Oxford University permission to reproduce and distributepublicly paper and electronic copies of this thesis document in whole or in part.

This thesis was supported by a stipend from the German Academic Exchange Ser-vice – Deutscher Akademischer Austauschdienst (DAAD) – and by a Michael-Foster-Fellowship awarded by the University of Oxford

The W Charge Asymmetry:

Measurement of the Proton Structurewith the ATLAS Detector

Kristin LohwasserSt. Catherine’s College, Oxford

Thesis submitted in fulfilment of the requirementsfor the degree of Doctor of Philosophy.

October 2009

Abstract

The charge asymmetry in the production of W± bosons in pp collisions is depen-dent on the momenta of the partons participating in the Drell-Yan process. It is asensitive probe in particular to the u and d valence quark distributions, that are onlyloosely constrained in the kinematic range of the LHC pp collider. A measurement ofthe W charge asymmetry will be crucial to understand the initial states of pp collisionsat the LHC centre of mass energy of

√s =14 TeV.

In this thesis a weighting technique to measure the W charge asymmetry at theLHC is evaluated and discarded as not sound in the kinematic range of the collider.Therefore, the prospects of a measurement of the lepton charge asymmetry at

√s = 14

TeV with 100 pb−1 as a function of the pseudorapidity of the lepton are investigatedusing simulated data of the ATLAS detector. This includes a full and thoroughanalysis of the systematical errors. For 100 pb−1, the expected total percentage errorsare found to be between 5-10%. These relative errors are a factor of 0.5-0.8 below thePDF uncertainties, which are about 15% in the kinematic range of the LHC. Hencean early measurement of the W asymmetry will be crucial to put constraints on thePDFs.

Fur Karl Lang und Gerald Karl Lohwasser

We shall not cease from explorationAnd the end of all our exploring

Will be to arrive where we startedAnd know the place for the first time.

T.S. Eliot,Little Gidding,Four Quartets

Acknowledgements

This work would not have been possible without the help, support and love of a lotof people, whom I would like to thank here (hopefully not missing out on anyone):

First of all, I would like to thank my supervisor, Cigdem Issever, who has beengiving me good guidance and is a great physicist and mentor. I would also like tothank the other people in the Oxford Physics department, who I have worked closelywith and who have helped me in various software and physics matters: Tony Wei-dberg, Amanda Cooper-Sarkar, James Ferrando, Pierre-Hugues Beauchemin, MugeKaragoz, Farrukh Azfar, Claire Gwenlan and Robin Devenish, who has been my in-ternal examiner. I thank also the Oxford IT and secretariat support staff, with specialregards to Sue Geddes!

I would also like to thank, people elsewhere than Oxford, who have contributedto this thesis by giving me their help and advise, setting interesting challenges andproviding helpful discussions. These are in no particular order: Kerstin Jon-And,Peter Loch, Sven Menke, Iacopo Vivarelli, Teresa Barilla, Gennadi Pospelov, TancrediCarli, Daniel Froidevaux, Maarten Boonekamp, Matthias Schott and Lucia DiCiaccio.

I am also deeply indebted to various theorists, who have enlightened me withregards to W s and PDFs: Giulia Zanderighi, Robert Thorne and James Stirling, whohas been my external examiner – thank you very much!

Special thanks should also go to the various ATLAS students (be it at Oxford orelsewhere), with whom I have collaborated over the years, who have shared code ortaken over work or a project: Maria Fiascaris (thank you so much for everything!),Florian Heinemann, Guillaume Kirsch, Oleg Brandt, Simon Ward (whose Master’sThesis I supervised and with whom I worked on the ” 6ET vs. Iso” method), Cate-rina Doglioni (the Jetting star!), Sam Whitehead, Ryan Buckingham (who peekedinto the W+jets with Cigdem, James and me), Markus Ahlers, Stephen West, EllieDobson and Erik Devetak (all Oxford), Elin Bergeaas-Kuutmann, Andreas Jantsch,Paola Giovannini (the LC-crew), Florent Fayette, Pavel Weber, Victor Lendermann,Martina Hurwitz, Frederik Ruhe and lots of others!!

A word of thanks should also be given to Prof. Dietrich Wegener, put me in contactwith Cigdem and who supervised my diploma thesis. With nostalgic feeling I wouldalso like to thank all the people at DESY and my old group in Dortmund/Heidelberg,who have introducted me particle physics, evil ROOT and the joys of shell scripts.

Apart from all my collaborators and mentors I should also thank my friends andfamily, who have kept me sane and happy.

Before switching to my German mother tongue, I would like to thank all myfriends on ’ze island’ as opposed to ’ze continent’. First of all, my thanks go to myhousemates, the first one (in order of appearance) is Katherine Allen (and her crew)– thanks so much for taking me on trips, teaching me cricket (a little bit) and visiting

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me in Geneva!! Then, lots of thanks to Anders and Julliette, who will probably nevercollect her mail. Last but not least, biggest thanks to my latest housemates, someof the best, I ever had: Eileen, Cath and Bobbidy! Thanks for teaching me Irish,cooking for me when I was writing up and sharing a organic veg box with me. Youare always welcome!

Thanks also go to my friends from college. Special thanks to the Sking crew,Meabh, Stephen, Yuki, Offir, Eileen, Xiaodon and Derek, as also listed in [1]. Irelandand Israel are indeed still on the list, be warned! Many thanks to Tiina and Sarah!

Zum Schluss kommen meine deutschen Freunde: Franziska, Nicola, Chris, Nadine,Jana, Sonja, Rita, Dani K., Dani A., Ingo, Lena, Dirk, Markus S. – Vielen Dank furnicht nur telefonische Unterstutzung und Besuche in Genf und Oxford!

Ich danke meinen Eltern, meinem Bruder Bjorn und meinen Großeltern, meinenTanten und Onkeln, sowie meinen (Groß)cousinen und meinem Cousin von Herzenfur ihre Unterstutzung.

I am sure, I have forgotten someone, so please fill your name here: / Ich bin mirsicher, ich habe Menschen, die mir wichtig sind, vergessen, bitte tragen Sie IhrenNamen hier ein:. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

[1] Eileen Nugent, Novel Traps for Bose-Einstein Condensates, DPhil Thesis, Ox-ford, 2009

Contents

1 Introduction 11.1 The Aim of this Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Theoretical Framework 32.1 The Structure of the Proton . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Physics at Proton Colliders . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2.1 Event Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Parton Distribution Functions . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Determination of PDFs from Experimental Data . . . . . . . . . 62.3.2 Effects of PDF Uncertainties on Measurements at Proton Colliders 10

2.4 Constraining PDFs using the W Asymmetry . . . . . . . . . . . . . . . 112.4.1 Drell-Yan Production of W Bosons . . . . . . . . . . . . . . . . 112.4.2 W Charge Asymmetry . . . . . . . . . . . . . . . . . . . . . . . 122.4.3 Kinematic Phase Space of the W Charge Asymmetry . . . . . . 12

2.5 Measuring the W Asymmetry at Hadron Colliders . . . . . . . . . . . . 142.5.1 Decay of W Bosons . . . . . . . . . . . . . . . . . . . . . . . . . 142.5.2 The Lepton Asymmetry . . . . . . . . . . . . . . . . . . . . . . 172.5.3 Previous Measurements . . . . . . . . . . . . . . . . . . . . . . . 19

3 Direct W Asymmetry Measurement 203.1 Reconstruction of the W Asymmetry . . . . . . . . . . . . . . . . . . . 203.2 Performance of the Iterative Weighting Procedure . . . . . . . . . . . . 26

3.2.1 Performance of the Iterative Weighting Procedure at the TeVatron 263.2.2 Performance of the Iterative Weighting Procedure at the LHC . 303.2.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4 Detector and Experimental Setup 414.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 The Atlas Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.2.1 Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2.2 Tracking Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.3 Calorimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5 Reconstruction 515.1 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1.1 EM Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.1.2 Reconstruction of Electrons . . . . . . . . . . . . . . . . . . . . 525.1.3 Electron Identification . . . . . . . . . . . . . . . . . . . . . . . 53

V

VI

5.1.4 Photon Identification . . . . . . . . . . . . . . . . . . . . . . . . 535.2 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

5.2.1 Inputs to jet reconstruction . . . . . . . . . . . . . . . . . . . . 535.2.2 Jet Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.2.3 Jet Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.2.4 Performance of the Jet Reconstruction . . . . . . . . . . . . . . 58

5.3 6ET Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6 W → eν Candidate Event Selection: Signal and Backgrounds 606.1 Investigated Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . 606.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

7 Determination of QCD Backgrounds in the W Candidate Event Sam-ple 647.1 MC Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7.1.1 Origin of the Reconstructed Electron . . . . . . . . . . . . . . . 657.2 The ” 6ET vs. Iso” Method . . . . . . . . . . . . . . . . . . . . . . . . . 667.3 The Photon Extrapolation Fit Method . . . . . . . . . . . . . . . . . . 737.4 Template Fit Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

7.4.1 Template Fit with Photon Selection and 6ET . . . . . . . . . . . 827.4.2 Failed ID Cut Selection to select Background Control Samples . 867.4.3 Template Fit with calo-based Failed ID Cut Selection and 6ET . 877.4.4 Template Fit with calo-based Failed ID Cut Selection and ET,iso

frac 887.4.5 Template Fit with track-based Failed ID Cut Selection and ET,iso

frac 907.4.6 Effect of Statistics on the Systematic Error Estimation . . . . . 91

7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

8 Experimental Prospects for the Lepton Asymmetry Measurement 968.1 Systematic Uncertainties on the Measurement . . . . . . . . . . . . . . 96

8.1.1 Systematic Effect of Backgrounds . . . . . . . . . . . . . . . . . 968.1.2 Influence of Scales and Resolutions . . . . . . . . . . . . . . . . 1038.1.3 Trigger and Lepton Identification Biases . . . . . . . . . . . . . 1048.1.4 Charge misidentification . . . . . . . . . . . . . . . . . . . . . . 1108.1.5 Effects of Electroweak Corrections . . . . . . . . . . . . . . . . . 114

8.2 Expected Uncertainties and Implications for PDFs at the LHC . . . . . 1208.2.1 Expected Uncertainties on Lepton Asymmetry . . . . . . . . . . 1208.2.2 Comparison of Experimental with PDF Uncertainties . . . . . . 125

8.3 Presentation of Results of the Lepton Asymmetry Measurement . . . . 1308.3.1 Relation between True and Reconstructed Lepton Asymmetry . 1308.3.2 Resolution Functions of the Atlas Detector . . . . . . . . . . . 1308.3.3 Restoring the True Asymmetry . . . . . . . . . . . . . . . . . . 133

8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

9 Conclusions 137

A W Charge Asymmetry in the Presence of Jets 139

VII

B Electron and Photon Identification Cuts 143B.1 Electron Identification Cuts . . . . . . . . . . . . . . . . . . . . . . . . 143B.2 Photon Identification Cuts . . . . . . . . . . . . . . . . . . . . . . . . . 143

C Distorted Material 150

D Derivation of the Misidentification Correction 153

Bibliography 158

Chapter 1

Introduction

The objective of particle physics is to understand the fundamental forces and particlesof nature and to describe their behaviour consistently and comprehensively from thebeginning of our cosmos to the present day. The approach which is at present themost successful in doing so is referred to as the standard model(SM) [1], [2]. Thismodel describes the building blocks of nature as excitations of quantum fields [3] andtraces the fundamental phenomena back to the exchange of three fundamental forceparticles between twelve different fundamental particles, six quarks and six leptons,and their respective antiparticles.

Despite the tremendous success of this model, there still remain questions andproblems not solved yet: How can one incorporate gravity, the fourth fundamentalforce that still lacks a convincing description as a quantum field? What is the ori-gin of mass and mass difference between the different particles? Can the forces beunified above a certain energy threshold? There are several theoretical explanationswithin and beyond the standard model that try to answer these and other problems.Beside the Higgs mechanism, which is part of the standard model and one of theapproaches meant to explain the origin of mass, currently prominent theories beyondthe standard model (BSM) are Supersymmetry and Extra Dimension models. SMand BSM models are to be addressed from an experimental point of view at the LargeHadron Collider (LHC) which is scheduled to start collisions at the end of 2009 orbeginning of 2010. The machine will collide two proton beams at

√s = 14 TeV. This

would be the highest terrestrial centre of mass energy ever achieved. Two general pur-pose detectors, Atlas and CMS, and one specialised b-physics experiment, LHCb,will look for phenomena beyond the standard model and hope to clarify some of thequestions left open by the standard model.

A correct description of the proton structure is crucial to all analyses at the LHC.Protons are made up of partons, two u quarks and one d quark, which are the ini-tial states of any scattering at the LHC. The momentum distribution of the partonsconfined inside the proton is parametrised using the so-called parton distributionfunctions (PDFs), which describe the dynamical structure of the proton. PDFs can-not be calculated analytically and need to be determined experimentally. The LHCoperates in a kinematic region not yet covered by any previous experiments. Thismeans, the proton substructure will have to be ‘re-discovered’ in this kinematic re-gion. Only a measurement of the PDFs at the LHC will give accurate informationon the proton initial states in pp collisions at

√s = 14 TeV. Examples from the past

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2

show that data could be misinterpreted as evidence for new physics due to inaccu-rate knowledge of PDFs and proton substructure. This happened at the TeVatron ppcollider, where the first measurements of the high ET dijet production cross sectionreported a significant excess over what was predicted by next-to-leading order (NLO)calculations, [4], [5]. It is therefore important to include LHC data in PDF fits in anattempt to validate and to improve the PDFs, reducing theoretical uncertainties andenhancing the discovery prospects of the LHC.

The measurement of the asymmetry in the rapidity distributions of W± bosons isone of the first measurements that will help to constrain the PDFs. This measurementis sensitive in particular to u and d valence quarks inside the proton. For low valuesof the parton momentum fraction x, these valence quark momentum distributionsare not well constrained by the current precision data obtained at HERA. Previousmeasurements of theW charge asymmetry were carried out at the SPS collider and theTeVatron. The TeVatron measurements constrain only partons with x values that areroughly one order of magnitude larger compared to the x values of colliding partonsat the LHC. In fact, the main PDF parametrisations, MSTW and CTEQ, differ intheir prediction of the W charge asymmetry at the LHC by up to 40%. Thereforea measurement of the asymmetry at the LHC is a vital and in fact indispensablecontribution to the Atlas physics programme.

1.1 The Aim of this Thesis

In this thesis the feasibility of a measurement of the W charge asymmetry at theAtlas detector will be evaluated using fully simulated Atlas events. The thesis isorganised as follows: Chapter 2, Theoretical Framework, introduces the protonand its structure in the context of collisions at the LHC. Emphasis is given to the phe-nomenological description of hadron collisions and of their initial states using PDFs.The charge asymmetry of W bosons produced in Drell-Yan processes is introducedas a possible way to constrain PDFs. A method recently developed at the TeVatronto measure the direct W asymmetry is reviewed in chapter 3, Direct W Asym-metry Measurement in the context of its applicability at the Atlas experiment. In Chapter 4, Detector and Experimental Setup, the LHC and the Atlas

detector are described with an emphasis on the detector components most crucial tothe asymmetry measurement, the inner tracking detectors as well as the calorimeters.Chapter 5, Reconstruction, describes how physics objects are reconstructed fromwhat is measured in the detector. The emphasis of this chapter lies on the reconstruc-tion of electrons and jets. The data-driven determination of the QCD background toa W → eν signal is described in Chapter 7, Determination of the QCD Back-ground to W Measurements. Three methods to determine this background andits corresponding uncertainties are presented in this chapter. The prospects of theW asymmetry measurement are detailed in Chapter 8, Prospects of an EarlyMeasurement of the W Charge Asymmetry. Here, the steps of the analysis asit would be carried out with real Atlas data are described and results are obtainedusing fully simulated Atlas events. Appendix A, W Charge Asymmetry in thePresence of Jets describes a possible extension of the measurement to a differentialmeasurement of the asymmetry as a function of jet multiplicity and explains why thisis useful.

Chapter 2

Theoretical Framework

2.1 The Structure of the Proton

The proton is not a fundamental but a composite particle. Its structure can beinvestigated using a point-like probe, whose resolution power is usually expressed interms of the energy scale Q2, the squared momentum transfer between the probe andthe proton.

The proton consists of quarks and gluons, whose interactions are described byQuantum Chromodynamics (QCD), the SU(3) gauge theory of strong interactions[6, 7]. Due to the non-Abelian nature of QCD the strength of the interaction increaseswith the distance between the interacting quarks and gluons. Hence, they usually existonly in bound states such as the proton. This is called confinement. For probes withan energy scale of Q2 . 1 GeV2, the proton’s substructure cannot be resolved, itappears to be a fundamental particle. The static properties of the proton are fullydescribed by the characteristics of three so-called valence quarks (uud), that determineits charge, isospin and its place amongst the other baryons forming the SU(3) flavourgroup [8].

The larger the scale Q2, the smaller are the distances that are probed and thereforethe strength of the QCD interactions decreases. This is referred to as asymptoticfreedom, and allows the treatment of the quarks and gluons inside the proton asquasi-free particles above energy scales of Q2 ∼ 1 GeV2. The first evidence for theexistence of point-like constituents in the proton was obtained in the 60s and 70sby experiments in which of leptons were scattered off protons [9, 10]. In the quarkparton model (QPM) these so-called partons were originally identified with the valencequarks [11, 12, 13]. This model was adapted and became the improved QPM whenit emerged that a large fraction of the proton momentum is carried by gluons and byquark-antiquark pairs of sea quarks that the gluons can fluctuate into. The dynamicsof proton collisions is determined by how the momentum of the proton is distributedamongst the individual partons.

2.2 Physics at Proton Colliders

The substructure of the proton has profound consequences for collider experimentsusing proton beams. For a large transfer of momentum between the two colliding pro-tons, their substructures are resolved. The actual interaction is between two partons,

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one from each proton. For this interaction, no information is exchanged between thosepartons that interact and those that don’t. Therefore, the partons that take part inthe scattering can be regarded as a free, pointlike particle, which allows the applica-tion of pertubative QCD (pQCD) and the calculation of the cross section of two-bodyparton-parton interaction via the resonant state X, σparton−parton → X, where X canbe e.g. a Z or a W boson. This class of parton-parton interactions is called hardscattering.

2.2.1 Event Kinematics

A schematic sketch of hard scattering processes at the LHC and other proton collidersis shown in figure 2.1: The incoming protons carry a momentum P = Pi, which isgiven by the beam energy of the collider. They contain partons, two of which enterthe hard scatter. Each of these partons carries a momentum pi, which is a fraction ofthe momentum of its parent proton. This momentum fraction x is given by

xi =pi

Pi

, with 0 < x < 1. (2.1)

The energy scale of the process, Q2, is given by the sum of the four vectors of thepartons entering the scatter. In case of resonant scattering, the mass of the resonanceand the sum of the four momenta of its decay products, (pµ

3 + pµ4), are directly related

to the scale of the process Q2

Q2 = (pµ1 + pµ

2)2 = M2

X = (pµ3 + pµ

4)2 = sx1x2. (2.2)

Here,√s is the centre of mass energy between the two proton beams,

√s = 2P .

The probability to find a parton inside the proton with a given momentum fractionx depends on x and Q2

PDF = f(xi, Q2). (2.3)

This parton distribution function does not have an analytical form and willbe discussed in more detail in section 2.3.

To first approximation, the partons can be assumed to be massless and to collideexactly head-on, i.e. not to carry any transverse momentum. Therefore, the boostof the produced resonance X along the z axis directly depends on the differencebetween x1 and x2 of the incoming partons. A measure of the longitudinal boost isthe rapidity y. It is defined as

yX =1

2lnEX + pX

z

EX − pXz

(2.4)

=1

2lnx1

x2

. (2.5)

The two partons enter the hard scattering and scatter with a process-dependentcross-section σparton−parton, that describes the probability for that process to occur.It can be analytically calculated as a function of the coupling strength of the specificinteraction, α, and the energy scale at which the process happens, Q2

5

f(x2 = p2P2, Q2)

f(x1 = p1P1, Q2)P1

P2

p1

p2

σXQ2 = (p1 + p2)

2

Q2 = M 2X

p3

p4

Figure 2.1: In interactions of protons with momentum P1 = P2 = Pi at the LHC, thehard-scattering cross-section is given in terms of the partonic cross section, σ. Partondistribution functions, f(xi, Q

2) define the probability to find a parton of a certainmomentum fraction xi in the proton which takes part in the hard scattering.

σparton−parton = σ(α,Q2). (2.6)

As a result of the hard scatter, the protons break up, the remaining partons nottaking part in the hard scatter rearrange themselves into colourless hadrons, whichcan be detected as hadronic activity in these events alongside the produced resonanceX or its decay products. This additional hadronic activity from the beam remnantsis usually referred to as the underlying event. In proton-proton collisions, only thefour vectors of the final states are known. For theoretical calculations of proton-proton scattering, the initial states are input parameters that in principle need to beknown to make any predictions of cross sections and the like. The initial states aredescribed by the PDFs and the only way to gain information about them is to conductmeasurements with special sensitivity to the PDFs.

Factorisation Theorem

According to the Drell-Yan factorisation theorem, the cross section of proton collisionsfor hard scatters, σPP→X , can be separated into two different independent contribu-tions [14]. These two contributions are the cross section of the parton interaction,σparton−parton, and the PDFs, fq(x2, Q

2). Using this separation, the cross section,σPP→X, for quark-antiquark, qq, processes can be written as follows

σPP→X = PDF ⊗ σhardscatter =∑

q

∫

dx1dx2fq(x1, Q2)fq(x2, Q

2) ⊗ σqq→X(α,Q2)

(2.7)

6

The final state X can be any final state produced in hard parton scatterings. Thenumber N of produced events of type X is given by

N = σPP→X × L. (2.8)

where L, the integrated luminosity of the collider, is a measure of the amount ofdata taken. It is obvious from equation 2.7, that the rate at which any final state willbe observed depends on the PDFs, since they enter in the calculation of σPP→X (seeeq. 2.7).

2.3 Parton Distribution Functions

The PDFs, f(xi, Q2), describe how the momentum of the proton is shared between

the individual partons. This is not trivial, because the different partons (i.e. valencequarks, sea quarks and gluons) inside the proton do not carry the same fractionof the proton’s momentum, x. Also, the momentum fractions x of the respectiveparton flavours depend strongly on the Q2 scale of the process in question. Figure 2.2illustrates the PDFs for the valence quarks, uv(x) and dv(x), the sea quarks, u(x), d(x),ss(x), cc(x) and bb(x), and the gluon, g(x) for two different scales, Q2 = 10 GeV2

and Q2 = 104 GeV2. While the valence quarks dominate at low Q2, other partonflavours grow in importance when going to higher scales. In particular, the gluondistribution becomes dominant for x values less than 0.01 and increases steeply forhigher values of Q2. The difference between the valence quarks diminishes with risingscale. The evolution of the PDFs with Q2 can, in contrast to the actual functionalform, be described analytically using pQCD. The basis of the PDF evolution in Q2 arethe so-called DGLAP1 equations, a set of coupled equations [15], [16], which describehow the PDFs change with ln(Q2).

2.3.1 Determination of PDFs from Experimental Data

The PDFs which are not calculable analytically and also not directly accessible ex-perimentally, must be obtained if one wants to calculate production cross sections forproton collisions in a particular kinematic region defined by Q2 and x. Therefore,PDFs are usually parametrised functions of Q2 and x for the different parton flavours(or linear combinations of them). The parameters are obtained using global analysisof data sensitive to PDFs, such as ep and νp scattering, pp collisions and specialisedfixed target experiments. The use of different processes in the fits is possible, becausePDFs are universal, i.e. the proton structure is independent of the process used toprobe it.

Competing PDF global fit collaborations have used using different approachesand parametrisations to find the functional form of the PDFs. The most prominentcollaborations are MSTW [17], CTEQ [18], NNPDF [19] and Alekhin [20]. The H1and the ZEUS collaborations conducting deep-inelastic ep scattering experiments atthe HERA collider [21] have also performed fits and recently published combined fits(see [22] for H1 fits, [23, 24] for ZEUS and for the combined analysis [25]). They are

1Dokshitzer-Gribov-Lipatov-Altarelli-Parisi

7

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

g/10

d

d

u

uss,

cc,

2 = 10 GeV2Q

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

g/10

d

d

u

u

ss,

cc,

bb,

2 GeV4 = 102Q

x-410 -310 -210 -110 1

)2xf

(x,Q

0

0.2

0.4

0.6

0.8

1

1.2

MSTW 2008 NLO PDFs (68% C.L.)

Figure 2.2: PDFs for gluons and all quark flavours except tt as a function of x shownfor two different scales of Q2 =10 and 104 GeV2 as predicted by the MSTW PDFfitting group with 68% confidence level [17].

collectively available with the actual numerical values given over a grid in (Q2,x) inthe LHAPDF library [26].

In general, the process of global PDF analysis begins with a parametrisation ofthe parton distributions, e.g. the valence quark distributions, uv(x) and dv(x), thegluon distributions, g(x) and the sea quark distributions, qsea(x)

2. Next, a global fit toexperimental data is performed at the scale Q2

0, which determines the initial choice forthe numerical values of the parameters. Using DGLAP evolution in leading or next-to-leading order in pQCD, the initial PDFs are evolved to different scales Q2

1, Q22, ...

Q2n, where the agreement of PDF prediction and data is evaluated. The accuracy of

the extrapolation is dependent on the precision of the data measurement, the αs(Q2)

uncertainty and the uncertainty of the evolution code itself. In a global fit, a set ofvariables is determined such that they minimise the global χ2/N between the PDFprediction and all the data points. Errors on the PDFs are usually estimated usinga Hessian technique, where an eigenvector basis for the matrix of all free parametersin the fit is formed [27]. The PDFs are varied for each eigenvector along its positiveand negative axes. Each of these variations give rise to new PDFs, referred to asPDF error sets [28]. These PDF error sets come in pairs, each pair corresponding tothe variation of one eigenvector along the positive and negative axes. The pairs oferror sets are PDF2n−1 (variation along the positive axis) and PDF2n (variation alongthe negative axis), where n=1,2,3,....,N=number of eigenvectors. PDF0 denotes the

2It is a matter of choice, which parton distributions are explicitly parametrised, here only the mostbasic examples are given. It is also common to additionally parametrise s(x) and s(x) distributionsto account for a possible asymmetry in the strange sea.

8

nominal PDF set 0, which is used to calculated the central value for the observableX(PDF0). When using PDF error sets to predict a given observable X, then theusage of a PDF error set PDF2n−1 from a variation along a positive axis should giverise to a positive variation of the resulting prediction for X(PDF2n−1) compared tothe nominal prediction X(PDF0). Therefore, in theory, positive PDF uncertaintiesare calculated as the quadratic sum of the deviations of X(PDF2n−1) − X(PDF0),while negative uncertainties are calculated from the negative variations of along eacheigenvector, that is using PDF2n. In practise however, in some cases the deviationsfrom X(PDF0) are either both positive or negative for the same PDF error set. Then,the most positive (or most negative) deviation from the nominal prediction is includedin the quadratic sum for the positive (or negative) error. The least positive (or leastnegative) deviation is included in the quadratic sum for the negative (or positive) PDFuncertainty. The uncertainty ∆± on a given observable X(PDF0) is thus calculatedas

∆+ =

√

√

√

√

NPDF∑

n=1

max (+(X(PDF2n−1) −X(PDF0)),+(X(PDF2n) −X(PDF0)), 0)2

∆− =

√

√

√

√

NPDF∑

n=1

max (−(X(PDF2n−1) −X(PDF0)),−(X(PDF2n) −X(PDF0)), 0)2(2.9)

Figure 2.3 gives a graphical overview over the kinematic phase space relevant forPDF fits and collisions at the LHC. Shown in terms of Q2 and x is the kinematicphase space of the parton collisions at the LHC (grey area). It is compared to thekinematic region of previous experiments, the ep collider HERA and various fixedtarget experiments, both indicated by green lines. The kinematic phase space of theTeVatron, a pp machine with a centre of mass energy of

√s =1.96 TeV, covers the

upper part of the HERA kinematic region at high x and high Q2 and is indicatedusing black lines. Experimental data from HERA, the fixed target experiments andto a lesser extent from the TeVatron has been used to determine the PDF global fitsthat are used to constrain the initial states at the LHC.

Figure 2.3 gives the impression that the partons are well measured for lower Q2

over most of the x range relevant for LHC at previous experiments and that all thatis needed for the LHC is to evolve them to higher Q2 using the DGLAP equations.This however is not exactly true. Indeed, data is available over most of the x phasespace, but a measurement in a specific part of the kinematic phase space providesinformation only on the parton distribution function of a certain parton flavour ora combination of flavours. If there is no information available on a flavour PDF ina specific kinematic region, then no DGLAP extrapolation can be started from thiskinematic region for this parton flavour. As an example, table 2.3 lists the processesused in the latest MSTW global fit together with the (combination of) PDFs flavoursand the x range probed. The lowest x values probed are of the order of 10−4, butthese measurements only provide information about the general q and q PDFs as wellas on the c and g content of the proton. However, there is no specific information onvalence quarks available for x < 10−2. Thus, the data acquired to date may not besufficient to fully describe the initial states at the LHC and fully constrain the PDFs

9

Figure 2.3: The kinematic phase space of the parton collisions at the LHC is shown asa shaded area in terms of Q2 and x and compared to the kinematic region of previousexperiments, the pp collider TeVatron, the ep collider HERA and various fixed targetexperiments. Since the scale of the process Q2 is commonly identified with the massof a produced resonance, M , selected masses, 0.1 1 and 10 TeV, are indicated on theplots. [28].

and their uncertainties.Another problem is the low x regime. In the DGLAP formalism, the PDF evolu-

tion is evaluated using the leading log approximation, where only terms of the n-thorder αn

s (lnQ2)n (the so-called leading logs) are included. However, some of thenon-leading terms give a large contribution at low values of x, but are neglectedin the calculation of the DGLAP PDF evolution. One approach developed for thelow x region is the BFKL3 [29], [30] approximation. The BKFL approach involvesre-summing the leading logs αs ln 1

xand in doing so tries to describe multiple gluon

emissions at low x, where the gluon density is very high. Hints of additional radiationpredicted by BFKL were observed at HERA in the form of an excess of forward jetproduction as compared to the DGLAP predictions [31], [32], [33], [34].

It would not be possible to describe both high-x and low-x data, where thesenon-leading terms give a sizable contribution, consistently by a global PDF fit using

3Balitski-Fadin-Kuraev-Lipatov

10

Process Subprocess Partons x rangeℓ± p (orn or 2H) → ℓ±X γ∗q → q q, q, g x & 0.01ℓ± n/p ratio → ℓ±X γ∗ d/u→ d/u d/u x & 0.01pp→ µ+µ−X uu, dd→ γ∗ q 0.015 . x . 0.35pn/pp→ µ+µ−X (ud)/(uu) → γ∗ d/u 0.015 . x . 0.35ν(ν)N → µ−(µ+)X W ∗q → q′ q, q 0.01 . x . 0.5ν N → µ−µ+X W ∗s→ c s 0.01 . x . 0.2ν N → µ+µ−X W ∗s→ c s 0.01 . x . 0.2e± p→ e±X γ∗q → q g, q, q 0.0001 . x . 0.1e+ p→ ν X W+ {d, s} → {u, c} d, s x & 0.01e±p→ e± cc X γ∗c→ c, γ∗g → cc c, g 0.0001 . x . 0.01e±p→ jet +X γ∗g → qq g 0.01 . x . 0.1pp→ jet +X gg, qg, qq→ 2j g, q 0.01 . x . 0.5pp→ (Z → ℓ+ℓ−)X uu, dd→ Z d x & 0.05pp→ (W± → ℓ±ν)X ud→W, ud→W u, d, u, d x & 0.05

Table 2.1: A list of the main processes included in the current global PDF analysis ofthe MSTW group, ordered in three groups: fixed-target experiments, HERA and theTeVatron. For each process the dominant partonic subprocesses, the primary partonswhich are probed and the approximate range of x constrained by the data is given.Taken from [17].

only DGLAP evolution. Indeed, the MRST/MSTW collaboration reported markedlyworsened χ2/N values in their global PDF fit, when including very low-x data (x <0.005) [35]. This is an indication, that there are theoretical challenges connected withthe inclusion as well as with the prediction of the low-x data, that might play a roleat the LHC.

2.3.2 Effects of PDF Uncertainties on Measurements at Pro-ton Colliders

The PDFs play a substantial part in calculating the measurable cross section at hadroncolliders. They have an impact on the theoretical uncertainty on the predictions ofcross sections at the LHC and other hadron colliders. Djouadi and Ferrag investigatedthe uncertainties on Higgs production cross sections due to PDF uncertainties at theTeVatron and at the LHC [36] in the processes qq → HW , gg → H , qq → Hqq andqq/gg → Htt. They found differences in the prediction of the Higgs production crosssection of the order of up to 15% at both colliders, when comparing different PDFparametrizations. Another study by Ferrag [37] discusses the impact of PDF uncer-tainties on the discovery potential for extra-dimensions. The compactification scaleof extra dimensions that could be discovered with 5σ, was about twice as large whenonly theoretical uncertainties without considering PDF uncertainties were accountedfor.

An underestimation of the PDF errors could not only lead to later discoveries butalso result in false alarms like at the TeVatron. The first measurements of the high ET

dijet production cross section reported a significant excess over what was predicted

11

W (Q2 = M2W )

q(x)

q(x) e

νe

Figure 2.4: Annihilation diagram for Drell-Yan production of W bosons at the LHC.

from NLO calculations, [4], [5], in principle a sign for compositeness of quarks and newphysics. The excess was however ultimately explained by an underestimation of theuncertainty of the gluon PDF. At the time of the measurement there was precise datato constrain the parton distributions in the x range of interest for dijet productionat the TeVatron. However, this data mainly constrained the quark distributions,but not the gluon distributions. Also, the methods for PDF error estimation werejust being developed and the errors on the gluon PDFs were underestimated. Afterimprovements to the error estimation procedure and the inclusion of the CDF datainto the global fits, the high ET dijet excess was in good agreement with the theoreticalprediction within its uncertainty.

2.4 Constraining PDFs using the W Asymmetry

Considering that for most of the LHC kinematic region, one relies on extrapolationsof the PDFs fitted to data obtained at lower centre of mass energies, there is a needto investigate measurements to constrain PDFs with data taken at the LHC. Oneof these measurements is the charge asymmetry of W bosons produced in Drell-Yanprocesses.

2.4.1 Drell-Yan Production of W Bosons

W bosons at the LHC are at lowest order exclusively produced in Drell-Yan annihila-tion processes as shown in figure 2.4. An incoming quark-antiquark pair annihilatesinto a W boson, which subsequently decays. In this thesis, only the decay into leptonsof the first generation, i.e. electrons and νe or positrons and νe

4, will be considered.Analogously to what has been discussed in section 2.2, the cross section of W

production in pp collisions can be factorised into a partonic cross section and into acontribution from the PDFs, depending on x and Q2. The scale, Q2, the momentum

4In the following the term ‘lepton’ is used to denote specifically a lepton of the first generation,that is an electron or a positron. The more general application to µ or τ is not used unless other-wise specified. Correspondingly the terms ‘electron’ and ‘positron’ refer specifically to e− and e+

respectively.

12

transfer squared, is for these types of processes identified as the mass of the resonance,thus for W production, Q2 is fixed at a value of Q2= M2

W = (80.4 GeV)2 [1].

2.4.2 W Charge Asymmetry

W+ production depends mainly on the u(x) and d(x) distributions, while W− pro-duction however is dependent on the d(x) and u(x) distributions5. This allows theconstruction of a observable that is very sensitive to the difference of u(x) and d(x)distributions. This observable is the so-called W charge asymmetry. It is defined as:

AW =dσ(W+)/dyW+ − dσ(W−)/dyW−

dσ(W+)/dyW+ + dσ(W−)/dyW−

(2.10)

AW is very sensitive to the relative shapes of u(x) and d(x) distributions [7]. Ameasurement of the W charge asymmetry can therefore be used to constrain PDFsin the novel kinematic regime of the LHC.

2.4.3 Kinematic Phase Space of the W Charge Asymmetry

For leading order Drell-Yan annihilation processes, the product x1x2 of the annihilat-ing quarks is restricted according to equation 2.2. Also the ratio x1

x2(see equation 2.5)

is limited to certain values, allowing the Q2 and x phase space covered by measure-ments of the W asymmetry to be calculated. Combining these equations gives therelation between the minimal and maximal values xmin,max of a parton taking part inW production and the maximal and minimal W rapidity yW , that can be observed inthe detector

xmin =MW√se−ymax

W (2.11)

xmax =MW√se+ymin

W (2.12)

The values of xmin and xmax are listed numerically in table 2.2 for three differentrapidities yW and for three different collider centre of mass energies,

√s = 7 TeV,√

s = 10 TeV and√s = 14 TeV. These centre of mass energies represent different

possible scenarios for LHC running. The x-values of the partons participating inDrell-Yan production of W bosons span from 3×10−4 to 1×10−1 at a collider centreof mass energy of

√s = 14 TeV for a rapidity of yW = 3.0, the maximum rapidity

that can be observed at the Atlas detector at the LHC. For a centre of mass energyof

√s = 7 TeV, the x-value range increases to xmin = 6 × 10−4 and xmax = 2 × 10−1.

The calculated values for xmin are also shown over the whole yW range accessiblewith a multi-purpose detector at the LHC and at the TeVatron in figure 2.5. Thekinematic x phase accessible at the LHC is for

√s = 14 TeV about an order of

magnitude lower than at the TeVatron and even for√s = 7 TeV it is still much lower

than at the TeVatron.

5There are other contributions, some are suppressed by the electroweak couplings of the CKMmatrix [38, 1], e.g. us → W+, others could be larger, e.g. cs → W+, which could be a 20%contribution [39].

13

Rapidity yW xmin xmax√s =14 TeV

0.0 0.006 0.0061.5 0.001 0.033.0 0.0003 0.1√

s =10 TeV0.0 0.008 0.0081.5 0.002 0.0343.0 0.0004 0.2√

s =7 TeV0.0 0.011 0.0111.5 0.003 0.053.0 0.0006 0.2

Table 2.2: Parton-x values for W production at various rapidities yW and for threedifferent collider centre of mass energies,

√s = 7 TeV,

√s = 10 TeV and

√s = 14

TeV.

W

y Rapidity 0 0.5 1 1.5 2 2.5 3

min

x

-310

-210

=1.96 TeVsTeVatron, =7 TeVsLHC, =10 TeVsLHC, =14 TeVsLHC,

=7 TeVs

=1.96 TeVs

=10 TeVs=14 TeVs

Figure 2.5: Accessible xmin compared for the TeVatron and three centre of massenergies

√s at the LHC – The kinematic x phase accessible at the LHC is about an

order of magnitude lower than at the TeVatron.

14

It should be noted, that these values are really just the extreme values – on averagethe x values accessed at the TeVatron are about x & 0.05 (cf. table 2.1, data usedin MSTW08 fits, last column). The differences between the x values sampled at theTeVatron and the LHC are about an order of magnitude in size, leaving the averagex values to be accessed at the LHC at around x & 0.005. Thus, a measurement ofthe W asymmetry will access the u(x) and d(x) distribution at the lowest x evermeasured at these Q2 values. Indeed, it will be one of the lowest x measurements everperformed, apart from deep-inelastic scattering at HERA, which delivers informationon g(x), q(x), q(x), c(x) and c(x) for x & 0.0001. It should be noted, that HERAcan only very loosely constrain the ratio between u and d quarks by using so-calledcharged current events, where a W is exchanged between the incoming lepton and theproton. These events take place at high Q2 and high x, in a kinematic region differentfrom the LHC kinematic regime for W production. Measuring the W asymmetry atthe LHC will contribute greatly to the understanding of the valence PDFs at low x.

It is very instructive to also look at what the different collaborations predict forthe kinematic region of the LHC. Figure 2.6 compares on the upper plot the latestglobal PDFs from MSTW and CTEQ at Q2=10 TeV2 with error bands indicating the68% confidence level. In particular for x values around ∼ 10−2 there are significantdifferences between the valence quark PDFs of the the two collaborations. On thelower plot the consequences of these differences for the W asymmetry is shown. TheW asymmetry is shown as calculated in NLO order using the CTEQ6.6 PDF data setand its uncertainty depicted as blue error band. It is compared to the central valueof the distribution as calculated in NLO with the MSTW 08 PDF (red line). Below,the W asymmetries normalized to the CTEQ6.6 PDF central values are shown. Thepredictions for the W asymmetry differ by up to 40% in the central region |yW | < 1and still differ up significantly up to |yW | = 2.5. This indicates to some degree apossible underestimation of the PDF errors [40] and highlights the importance togain access to PDF data in the kinematic range of the LHC. In appendix A, theasymmetry of W±+jet events is described. This is an interesting measurement totarget some regions of kinematic phase space or a certain parton flavour more closely.

2.5 Measuring the W Asymmetry at Hadron Col-

liders

In the decay W → eνe, the neutrino cannot be detected experimentally. Only itstransverse energy can be inferred indirectly by requiring that the vector sum of themeasured energies in an event needs to be equal to zero, because the pp collision havein first order no transverse component. The missing transverse energy in the detector,6ET , can then be attributed to the escaped neutrino, and used to select W events.

2.5.1 Decay of W Bosons

W decays are governed by V −A couplings [2, 42, 43]. The angular distribution of theW decay products is therefore not random and causes a correlation between leptonand W variables [1, 3]. The angular dependency is

15

Figure 2.6: Comparison of MSTW08 and CTEQ6.5M PDFs for gluon, sea and valencequarks at Q2 = 10 TeV2 (upper plots). There are differences between the uV and thedV distributions almost over the entire x range. These differences are significant with68% confidence level [41]. On the lower plot, the consequences of the differencesbetween the u and d valence quarks are shown: The W asymmetry as calculated inNLO order using the CTEQ6.6 PDF data set and its uncertainty depicted as blueerror band is compared to the central value of the distribution as calculated in NLOwith the MSTW 08 PDF (red line). Below, the W asymmetries normalized to theCTEQ6.6 PDF central values are shown [41].

16

qq

νe

e−

θ∗W,e− qq

νe

e−

θ∗W,e−

1) xq > xq

(1 − cos θ∗l,W )2(1 + cos θ∗l,W )2

2) xq < xq

W− W−

Figure 2.7: W− production in qq collisions and the subsequent decay into e−νe. Thespin and momentum vectors are indicated by large grey and small black arrows. Theleft hand side depicts W− production for a leading quark, xq > xq. The helicity of theW is thus approximately -1, the helicity of the electron is -1, thus yielding a decaydistributions of (1+cos θ∗l,W )2 or the indicated angle θ∗l,W . On the right hand side, thecase xq < xq, leading anti-quark production is shown.

dN

d cos θ∗W,l

∝ (1 + sgn(hl × hW ) cos θ∗l,W )2 = (1 ± cos θ∗l,W )2 (2.13)

Here, the decay angle θ∗l,W is defined between the lepton and the W boson, whichis boosted along one of the beam directions. For W bosons produced in Drell-Yanprocesses, the sign in equation 2.13 is determined by the product of the helicity ofthe lepton6 and the helicity of the W . The helicity of the W in turn depends on theincoming partons. The incoming leading, that is higher x, parton gives a longitudinalboost to the W boson and defines its direction of motion. The spin direction isalready fixed to point in the direction of motion of the incoming anti-quark. This isschematically shown in figure 2.7.

Due to the decay angle distribution of (1±cos θ∗l,W )2, a strong correlation betweenthe W direction and the direction of the decay lepton exists. It is primarily emittedparallel (or anti-parallel) to the W− (W+) in case the W is boosted along the directionof the incoming quark.

The W decay thus only smears the momentum of the lepton with regard to the ini-tial momentum, pz of the W and therefore of the reconstructed rapidity as illustratedin figure 2.8. Here, the composition of the momentum of the lepton along the z-axis,pl

z into its two fundamental components is shown. Firstly, the initial z-momentum ofthe W , pW

z , that would be parallel to the plz if the decay angle would be 0. Secondly,

it is the additional lepton z-momentum, pl∗z , that results from the W decay and gives

a positive contribution if cos θ∗W,e < 0 and a negative contribution if cos θ∗W,e > 0, so

6Helicity is defined as the normalised projection of a particle’s spin, −→s , onto it’s momentum, −→p :

h ≡ −→s ·−→p|−→s ||−→p |

. For massless particles, there are two orthogonal helicity states: -1 (left-handed fermions,

e.g. quarks) and +1 (right-handed fermions, e.g. anti-quarks).

17

that e.g. in this latter case plz < pW

z . So the reconstructed plz and as a result also the

yl of the lepton can be decomposed as

plz = pW

z + pl∗z

yl = yW + y∗l (2.14)

y∗l can be expressed as a function of cos θ∗W,e, if one starts out with

y∗l =1

2ln

|−→pl | + pz

|−→pl | − pz

=1

2ln

|−→pl ||−→pl |

(

1 + pz|pWz |

|−→pl ||pW

z |

)

(

1 − plz|pW

z ||−→pl ||pW

z |

)

=1

2ln

1 + cos θ∗W,l

1 − cos θ∗W,l

(2.15)

Here the fact that E2 = |−→p |2 for massless particles was used. Nothing is assumedabout the actual average size of cos θ∗W,e, which depends on the V − A decay and isdistributed ∝ (1 ± cos θ∗e∓,W )2. The average values of < cos θ∗W,l > can be used tocalculate the average offset < y∗l > of the lepton with regard to yW . The average< cos θ∗W,l > can be estimated by using the median, M – the value of cos θ∗W,l, at which50% of events exhibit a higher cos θ∗W,l and 50% exhibit a smaller decay angle.

Using this approximation, it is possible to calculate the average < cos θ∗W,l > andthe average < cos θ∗W,l > to be < cos θ∗W,l >≈ 0.5875 and | < y∗l > | = 0.677. Here,

| < y∗l > | is the average offset of the lepton yl with regard to the W rapidity yW

as defined in equation 2.14. The calculation therefore indicates, that we can expectto be sensitive to |ymax

W | ≈ 3.0 with full statistics if we measure |ymaxl | =2.4, which is

why the previous discussions considered only W production up to |ymaxW | ≈ 3.0.

It should be noted, that these considerations are only valid if no cuts on theleptons are applied. The situation changes, if one applies pl

T cuts on the leptons.This is because, in the W rest frame, the total momentum of the lepton is given by|pl| = MW/2, from which follows sin θ∗ = 2pl

T/MW . Thus cos θ∗ = 1 − 4pl,2T /M

2W .

The higher the transverse momentum of the lepton, the smaller is cos θ∗ on average.Selecting only leptons with a minimum pT will therefore imply a maximum cos θ∗W,l

and therefore ultimately reduce < cos θ∗W,l > and therefore the range of |yW | valuessampled by a measurement, where the W events are selected using leptons of a specificrapidity |yl|. This can help to get a better handle on the PDFs in measurements, wherethe W asymmetry is not directly measured, but where instead the lepton asymmetryis used as discussed in the next section.

2.5.2 The Lepton Asymmetry

Since it is not possible to directly reconstruct the four-momentum of the W dueto the missing neutrino z-momentum component, the lepton quantities are usuallymeasured instead and together with the 6ET used to form the observables to measure

7These values do not depend on the centre of mass energy.

18

pWz

pl∗z

plz

−→p l

θ∗W,l

−→p l∗

plz

pl∗z

θ∗W,l

−→p l∗

pWz

−→p l

cos θ < 0 cos θ > 0

Figure 2.8: This figure demonstrates how the reconstructed lepton rapidity receivescontributions from both, the W rapidity and the decay angle cos θ∗W,e by consideringthe z-component of the momenta. Here, pl

z is the reconstructed z-momentum ofthe decay lepton: It is the sum of the z-momentum of the W , pW

z , and pl∗z , the

additional z-momentum that results from the decay W → eνe and is pl∗z =

−→pW ·

−→pl =

|−→pW ||

−→pl | cos θ∗W,e, where |

−→pW | = pW

z . While for cos θ∗W,e = 0, pWz = pl

z, the reconstructedlepton pl

z gets smaller for cos θ∗W,e > 0, plz < pW

z and larger for cos θ∗W,e < 0, plz > pW

z .Here nothing is assumed about the actual values of cos θ∗W,e, which depend on theV −A decay and follow the distributions specified in equation 2.13.

characteristics ofW boson production. The observable lepton asymmetry Al is definedanalogue to the W asymmetry

Al =dσ(l+)/dy(l+) − dσ(l−)/dy(l−)

dσ(l+)/dy(l+) + dσ(l−)/dy(l−). (2.16)

Figure 2.9 compares the lepton asymmetry (light markers) to the W asymmetry(dark markers) and shows the effects of the smearing due to the W decay at

√s = 14

TeV, that was discussed in the previous section. The W charge asymmetry is smallerthan the lepton charge asymmetry in the very central region, |y| < 0.5. The slope ofthe W charge asymmetry is however steeper and for |y| > 2, the W charge asymmetryis slightly larger. The maximal values of the lepton rapidity that can be observedare |ηl| = |y| <2.4, due to the acceptance cuts. The W rapidities of these selectedevents extend to values of |yW | ∼ 3.5 with the asymmetry being as large as 0.8 at themaximal rapidities of |yW | ∼ 3.5.

The right hand side of the figure depicts the ratios of the lepton charge asymmetriesat different centre of mass energies,

√s = 7 and 10 TeV, to the lepton charge asym-

metry at√s = 14 TeV. The lepton charge asymmetry in the central region, y <1.8,

is up to 40% larger at√s=10 TeV and up to 80% larger at

√s=7 TeV compared to

the asymmetry at√s=14 TeV. Thus each measurement of the lepton asymmetry at

a different center of mass energies will provide additional input for the PDF fits.For these plots, 107 events were used, generated with Pythia 8.120 [44] using the

leading order MSTW2008 PDF. Acceptance cuts, plT >25 GeV, pν

T > 25 GeV, |yl| <2.4, are applied to all events.

19

yRapidity 0 0.5 1 1.5 2 2.5 3 3.5

Asy

mm

etry

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8=14 TeVsW asymmetry,

=14 TeVslepton asymmetry,

rapidity y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

l L

epto

n A

sym

met

ry A

1

1.2

1.4

1.6

1.8

2=14 TeV)s (l=10 TeV) / As (lA

=14 TeV)s (l=7 TeV) / As (lA

Figure 2.9: The W (in black circles) and the lepton asymmetries (in red triangles)are compared for a centre of mass energy of 14 TeV on the left hand side. Thedifference between the lepton asymmetries at centre of mass energies of

√s = 7, 10

and 14 TeV are of the order of 30% percent as shown on the right hand side, where thelepton charge asymmetry are compared normalized to the lepton charge asymmetry at√s=14 TeV. For each of the curves 107 events were generated using Pythia 8.120 with

the leading order MSTW2008 PDF and evaluated at MC truth level. For conveniencea line is drawn at 1.

2.5.3 Previous Measurements

The measurement of the lepton asymmetry and its subsequent use in global PDF fitshas a long tradition at the hadron collider TeVatron with the measurements datingback to 1992 [45], where this first measurement used a data sample of 4.05 pb−1,taken during a TeVatron engineering run 1988-1989. Electron and muon samples wereanalysed yielding a lepton asymmetry in several bins for |y| < 1.7 with percentageerrors between 25-100%.

Subsequent measurements, such as [46], which provided the latest data includedin global PDF analysis, used differential bins in the lepton transverse energy, 25<El

T <35 GeV and ElT > 35 GeV, and 170 pb−1 of data. As explained above, there

is a correlation between cos θ∗e,W and ElT = pl

T , so that in the higher ElT bin, smaller

maximal values of cos θ∗e,W are observed. < yl − yW >=< y∗l > is then ∼ 0.2 which issmaller than 0.67, so that a narrower region in yW is sampled by measuring a certainvalue of yl.

The latest lepton asymmetry measurements were performed by the D∅ experimentat the TeVatron for the electron asymmetry [47] (0.75 fb−1) and the muon asymme-try [48] (0.3 fb−1). For the electron measurement, a slight undershoot of the datacompared to the prediction could be observed, while the predictions for the muonasymmetry showed good agreement to the muon asymmetry measured in data.

A different approach has been used by the CDF Collaboration [49], who extractthe W asymmetry at the CDF experiment by an iterative weighting procedure for1 fb−1 of data. The applicability of the iterative weighting procedure to the Atlas

environment will be discussed in the next chapter, where also the basic principles ofthe method will be described in more detail.

Chapter 3

Direct W AsymmetryMeasurement

The CDF collaboration has recently published a direct measurement of the W pro-duction charge asymmetry [49]. This measurement uses a technique proposed byBodek et al. [50] for use at the TeVatron pp collider. In this measurement the Wboson rapidity is reconstructed event-by-event from the charge lepton and the missingtransverse energy.

The PDF sensitivity of the W boson asymmetry and the W± boson rapiditydistributions is caused by the fact that the boost of the W boson, measured byyW , is directly proportional to the PDFs. The lepton asymmetry and the leptonrapidity distributions on the other hand are not directly proportional to the PDFs,because this relation is distorted due to the W decay. Therefore the PDF sensitivityof the W boson asymmetry is in general larger than the PDF sensitivity of the leptonasymmetry. Hence, a direct measurement of the W asymmetry should have a largerlever arm in global PDF fits, if the direct measurement is precise and accurate.

Bodek et al.’s approach makes use of the angular correlations of the W decay aswell as of the theoretical prediction of the cross section dσ(W )/dyW . The uncertaintyon the direct W asymmetry measurement is smaller than the uncertainty on theW asymmetry due to PDFs. This indicates that a direct measurement of the Wasymmetry is beneficial for PDF global fits.

It should be noted that the CDF measurement was not the first measurement of thedirect W asymmetry at a pp collider. The UA1 collaboration also fully reconstructedW s in studies of W properties at the CERN SPS collider with

√s = 0.546 and 0.630

TeV [51, 52] using a similar but less sophisticated technique. In the following sections,firstly the iterative MC reweighting procedure as used by Bodek et al. is described,then its performance at the TeVatron is investigated. Finally, the applicability of themeasurement to the LHC environment is discussed.

3.1 Reconstruction of the W Asymmetry

TheW rapidity can be reconstructed by using the constraint on theW mass, MW =80.398GeV [1], to determine the longitudinal momentum of the neutrino, pν

z

(pµe + pµ

ν )2 = M2W (3.1)

20

21

Starting from this equation, pνz can be calculated to be

pνz = +

apez

c±√

(

apez

c

)2

+(a2 − b)

c(3.2)

with a,b and c being defined as

a =1

2M2

W + pexp

νx + pe

ypνy

b = E2e (p

2x,ν + p2

y,ν)

c = E2e − p2

z,e.

In this calculation, either pνx and pν

y (for MC studies) or the x and y components ofthe reconstructed 6ET (for studies involving detector simulation and reconstruction)can be used. To first approximation, only pure Drell-Yan W production is considered,initial and final state radiation are neglected. Therefore, the longitudinal momentumof the neutrino cannot exceed the beam energy, and neither can the longitudinalmomentum of the W boson

|pz,ν| <√s/2

|pz,ν + pz,e| <√s/2. (3.3)

Solutions of equation 3.2 not fulfilling these inequalities are discarded. For mostevents however, the quadratic equation still yields a twofold ambiguity for pν

z and thusfor yW . This ambiguity can be resolved statistically with the help of MC predictions.

1. Expected cross section dσ/dyW : The cross sections dσ/dyW have a dis-tinct behaviour as a function of yW . Two different rapidity solutions can becompared as to which is more probable, using as probability density func-tions the expected cross section dσ/dyW predicted by Monte Carlo. Theseexpected cross sections depend strongly on the MC input PDFs, since e.g.dσ/dy+

W ∼ 2π3

GF√2

[

u(xp)d(xp)]

.

2. Expected decay angle cos θ∗W,e and anti-quark/quark ratios: As detailedin section 2.5.1 the angular distribution in W decays follows a (1 ± cos θ∗l,W )2

distribution (cf. eq. 2.13), which can be used as another probability densityfunction to weight the two rapidity solutions. The sign of the (1±cos θ∗l,W )2 dis-tribution depends on the helicity of the lepton and the helicity of the incominghigher-x parton. The former can be measured, while the latter cannot. There-fore in the cos θ∗W,e weighting, the probability density function is build from thecontributions of events with higher-x quarks ((1±cos θ∗l,W∓)2) and of events withhigher-x anti-quarks ((1 ∓ cos θ∗l,W±)2) as also demonstrated in figure 3.1. Theprobability density function for the weighting is constructed as the sum of thetwo decay distributions. The contribution of the higher-x anti-quark events isadjusted using the parameter q

q, which is defined as

22

+,W+lθ cos

-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1

+ ,l+

W* θd

cosd N

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

=0.6l,W1θcos =0.75l,W

2θcos

higher-x quark2)θP=(1-cos

=0.6)=0.64l,W1θP(cos

=0.75)=0.77l,W2θP(cos

higher-x anti-quark

2)θP=(1+cos=0.6)=0.16l,W

1θP(cos=0.75)=0.06l,W

2θP(cos total

Figure 3.1: This figure shows, how the weighting of solution 1 and solution 2 accordingto the expected decay angle cos θ∗W+,e+ distributions works. Here, only W productionboosted in the direction of the proton beam is considered. In case the higher-xparton is a quark this distribution is (1− cos θ∗W+,e+)2, shown as a red solid line. Theprobabilities for the solutions 1 (cos θ∗W+,e+ = 0.6) and solution 2 (cos θ∗W+,e+ = 0.75)can be read off directly as 0.16 and 0.06. It is a reasonable assumption, that thehigher-x parton is a quark, because the proton predominantly consists of valencequarks. However, there is a sizeable amount of events, where the higher-x partonis an anti-quark or a sea quark. These events make up at most q

q= 25% of the

quark initiated events at the TeVatron and they are accounted for by the dotted blueline, 0.25(1 + cos θ∗W+,e+)2. For these anti-quark initiated events, the probabilitiescan be read off as P(cos θ∗W+,e+ = 0.6) = 0.64 and P(cos θ∗W+,e+ = 0.75) = 0.77. Inthe weighting of the solutions 1 and 2, both these cos θ∗W+,e+ distributions need tobe taken into account with their appropriate contribution. The effective probabilitydensity function is therefore the sum of the two contributions, shown as black line.

q

q(pW

T , yW ) =# higher- x anti-quarks from proton

# higher-x quarks from proton(pW

T , yW ) (3.4)

This definition of the ratio qq

restricts the probability density function to bevalid only for W bosons produced with a boost along the proton beam direction.Other cases will be discussed later. The ratio q

qis a function of pW

T and yW . It isdetermined from Monte Carlo simulations and therefore also depends on PDFpredictions. Using q

q, we can build the total probability density function from

the sum of the two possible angular distributions for the LHC

P (cos θ∗l,W ) = (1 ∓ cos θ∗l±,W )2 +q

q(pW

T , yW )(1 ± cos θ∗l±,W )2 (3.5)

23

And for the TeVatron

P (cos θ∗l,W , yW > 0) = (1 ∓ cos θ∗l±,W )2 +q

q(pW

T , yW )(1 ± cos θ∗l±,W )2 (3.6)

P (cos θ∗l,W , yW < 0) =q

q(pW

T , yW )(1 ∓ cos θ∗l±,W )2 + (1 ± cos θ∗l±,W )2 (3.7)

As can be seen from the equations, at the pp collider LHC equation 3.5 holds forall rapidity regions, at the TeVatron there are two distinct functions for negativeand positive rapidities yW , accounting also for cases, where the W is producedwith a boost along the anti-proton beam direction.

In the positive rapidity regime yW > 0, the probability density function P (cos θ∗l,W )is the same for LHC and TeVatron. For negative rapidities the W is boostedalong the direction of the incoming anti-proton at the TeVatron, implying thatthe higher-x parton is more likely an anti-quark. Therefore, q

q(from proton) in

equation 3.6 is replaced by qq(from anti-proton) in the equation or negative ra-

pidities, eq. 3.7. Since qq(from anti − proton) is still connected with the higher-x

quarks, it is associated with the (1∓ cos θ∗l±,W )2 term in equation 3.7. It should

be noted, that qq

(from proton)(yW > 0) = qq(from anti-proton)(yW < 0), so that

either of these terms can be used in place of the other.

Figure 3.2 clarifies, how P (cos θ∗l,W ) is defined at the TeVatron. At the LHC,only the functions on the right hand side, on the positive axis are used, becauseat the LHC only proton-beams are collided. In any case, q

qhas to be determined

from MC input and is thus dependent on the theoretical PDF predictions.

We can combine the probability density function for the cross section and thedecay angle to calculate weighting factors, w1 and w2, for each of the solutions 1 and2 of equation 3.2, depending on the charge of the W±

w1,2(W±) =

P (cos θ∗l±,W±) × (dσ/dyW±1,2

)

∑2i=1

(

P (cos θ∗l±,W±) × (dσ/dyW±i)) (3.8)

In a reconstructed event each of the solutions 1 and 2 is weighted by w1,2 and filledwith that weight into histograms of y±W . The fact that the weights w1,2 are normalisedto their sum preserves the statistics of the used data sample.

The weights depends on MC input and therefore on PDF predictions. Bodek etal. propose, that this dependence can be removed using an iterative procedure. Thisiterative procedure of the direct measurement of the W asymmetry is described inthe following.

1. Calculation of the W rapidity: For each reconstructed event, the two solu-tions of the W rapidity are calculated using equation 3.2.

2. Weighting of the W rapidity solutions: In each event, the solutions arefilled into yW histograms with a weight calculated using equation 3.8. If only onephysical solution is found, the event is filled with a weight of 1. For the weightingprocedure, MC predictions of dσ/dyW as well as q

q(p

W1,2

T , yW1,2) must be used,

they are calculated as weighting tables from a MC input. Step 1 (Calculation

24

p direction

directionp

production+W

production-

W

2)θ(1-cosqq

+ 2)θ(1+cos 2)θ(1+cosqq

+ 2)θ(1-cos

2)θ(1-cosqq

+ 2)θ(1+cos 2)θ(1+cosqq

+ 2)θ(1-cos

Figure 3.2: The cos θ∗W,e probability density functions used at the TeVatron.

of the solutions) and step 2 (weighting of the solutions) are hereafter referredto as full kinematic W reconstruction.

3. Acceptance corrections: The rapidities of the kinematically fully recon-structed W bosons are corrected in each bin i of yW for the detector acceptance,detector resolution and, as will be shown below, also for biases of the full kine-matic W reconstruction introduced by the weighting procedure. The acceptancecorrections are calculated bin-by-bin as the ratio between MC generated W dis-tributions after acceptances cuts, detector simulation and W reconstruction andthe MC generated W distributions without any cuts:

Acc(bin i) =MC events (with detector simulation) with acceptance cuts with W reco(bin i)

MC events without any cuts(bin i)

(3.9)

In case only a MC study using ‘pseudo data’ is conducted, the detector sim-ulation can be omitted. The acceptance correction is applied by multiplying1/Acc(bin i) with content of bin i of the yW distributions of the kinematicallyfully reconstructed W bosons. Step 3 yields the experimentally determinedyW distributions, extrapolated to the whole phase space.

4. Compare experimentally determined yW distributions and MC inputyW distributions: In this step the decision is taken whether to stop the iter-ation or not. If the experimentally determined yW distributions and the MC

25

1. Calculation of W rapidity solutions 1 and 2

a) Input: - Quark / Antiquark ratio - Normalized W rapidity distributions

2. Weight solutions (Step 1+2: y(W) reco)

5. Feedback measured W rapidity distributions:Reweighting MC without cuts to reproduce

measured W rapditiy after acceptance correction

3. Correct for acceptance: # events (MC + cuts [ + sim] + W rapidity reconstruction)

Acc = # events (MC - no cuts)

b) Input: - (MC with cuts [ with sim] with y(W) reco ) - (MC - without cuts)

4. Compare measured W rapidity distribution and MC generator W rapidity distribution used as input

Do they agree within uncertainties?

7. Calculation of W asymmetry

YESNO

y(W) Reconstruction

Corrections Final Check

MC Input

6. Re-calculate MC Input from reweighted MC

Iterative Loop

Final Result

Figure 3.3: Flow chart of the reconstruction of the W rapidities in the weightingprocedure

input yW distributions agree, the iterations stops. If they disagree, the proce-dure needs to be iterated.

5. Reweight input MC to reproduce experimentally determined yW dis-tributions: The input MC yW distributions without any cuts and the yW dis-tributions experimentally determined in step 1-3 are compared. A reweightingfactor is extracted bin-by-bin:

r(bin i) =experimentally determined yW (bin i)

Input MC ytrueW (bin i)

(3.10)

Each event in the input MC is re-weighted with the event weight r (ytrueW (MC

input)).

6. Recalculation of weighting tables: The weighting tables for dσ/dyW , qq(pW

T , yW )and the acceptance corrections are recalculated from the reweighted MC inputand the steps 1-4 are repeated until convergence.

7. Measurement of the W asymmetry: When the experimentally determinedand the used input MC yW distributions are found to agree within statisticaluncertainty, the W asymmetry is calculated.

26

Figure 3.3 summarises this procedure, that was developed for the TeVatron, in aflow chart. In the next section the application of the reweighting technique at theTeVatron and crucial differences to the LHC environment are discussed.

3.2 Performance of the Iterative Weighting Proce-

dure

In the following the weighting procedure is investigated for the TeVatron and theLHC environments using MC data samples generated using the Monte Carlo gener-ators Pythia 8.120 [44] and Herwig++ 2.4.0 [53] with either MSTW08 or CTEQ66PDFs. The positive weight NLO matching scheme (POWHEG) [54] was used inthe generation of the Herwig++ sample. This approach consistently combines theNLO calculation and parton shower simulation and was implemented in Herwig++by Hamilton et al. [55]. The MC samples are either used as input MC or as ‘pseudodata’. No detector simulation is applied. The following acceptance cuts are used inthe event selection in order simulate the detector acceptance:

• P lT > 25 GeV

• P νT > 25 GeV

• |ηl| < 2.4

3.2.1 Performance of the Iterative Weighting Procedure atthe TeVatron

Bodek et al. examine the workings of the weighting procedure in [50]. They concen-trate on two main issues. Firstly, they examine systematic uncertainties due to thedetector resolution and the modelling of the acceptance correction. Secondly, theyinvestigate systematic uncertainties due to PDF uncertainties in the MC input. Theyconclude that the weighting procedure works very well at the TeVatron, yielding totalsystematic uncertainties of the measurement well below the uncertainties of the PDFprediction. Their investigations were not repeated in detail in this study. This sectiononly points out important features of the weighting procedure at the TeVatron whichwill make it easier to understand the problems that are encountered at the LHC.

For the following plots, 8×106 events were produced using Pythia 8.120 and theMSTW08 PDF set. As a sanity check of the procedure, the same MC sample is usedas MC input and as ‘pseudo-data’. In the calculation of the two W rapidity solutions,pν

x and pνy of the neutrino are directly used. Figure 3.4 shows the weight of the solution

that was closest to the true rapidity out of the two solutions of equation 3.2 calculatedin step 1. The figure shows the normalised distribution only for W− events but looksexactly the same for W+ events. The weight peaks at 1 and is mostly above 0.5,indicating that in the weighting procedure indeed the solution closest to the true yW

value is given the larger weight.Figure 3.5 compares the true yW− distributions (with acceptance cuts applied, grey

open circles) from the MC to the calculated yW− distribution (blue open squares),for which only the yW− solution closest to the true yW− value is used. For this

27

weight 0 0.2 0.4 0.6 0.8 1

nor

mal

ized

num

ber

of e

ntrie

s

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Figure 3.4: Normalised distributions of weights given to the solution to equation 3.2which is closest to true W− rapidity at the TeVatron.

and for the following TeVatron plots, the yW+ distributions are not shown, becauseNW−

(−yW−) = NW+

(+yW+) at the TeVatron. Deviations of the calculated and thetrue yW distributions would stem from resolution effects due to the finite width ofMW used in the calculation (cf. eq. 3.1 and 3.2). On the right hand side, the ratioof these distributions, ycalculated

W− /ytrueW−, is shown as open markers. Additionally the

respective ratio for W+ bosons is shown as full markers. Up to |yW | ∼ 2.2, the ratiosare 1+0.01

−0.03. For larger values, there are large deviations. This indicates a bias in thecalculation which is probably due the vanishing statistics and skewed distributions ofthe W bosons for values of |yW | > 2.2, because of the lepton acceptance cuts. Thisshows, that the maximal reconstructed values of |yW | need to be chosen carefully inorder not to be biased due to the lepton |ηl| acceptance cut.

Figure 3.6 compares the true yW− distribution (with acceptance cuts applied, greyopen circles) to the fully kinematically reconstructed yW− (full red triangles). This isa check on how well the yW distributions can be kinematically reconstructed, whenno MC information is used to determine the best solution, but when a weighting as instep 1+2 is a applied. There is some overshoot of the reconstructed yW (red triangles)around yW = 0 and some undershoot in the very low and very high yW region. Thisindicates that the weighting procedure works in principle. This is also evident fromfigure 3.6, where on the right hand side the ratio of the fully kinematically recon-structed yW distributions to the true yW distribution (with acceptance cuts applied)is shown for W+ and yW− in full and open markers. This ratio is unity in the centralregion, with only a slight overshoot (∼ 4%) for yW = 0. Beyond |yW | = 2.0, the ratiofalls of to values of about 0.1-0.4%, indicating an undershoot of the full kinematic re-construction with regard to the true yW distribution. This overshoot and undershoot

28

-3 -2 -1 0 1 2 30

10000

20000

30000

40000

50000

60000

70000

80000

True W (with acceptance cuts)

Calculated W (using best solution)

Wrapidity y

-2 -1 0 1 2

ratio

0

0.5

1

1.5

2

2.5

3

3.5

(with acceptance cuts) W

(best solution) / true yW

ratio calculated y+W

(with acceptance cuts) W


ratio calculated y-W

Figure 3.5: The calculated (blue open squares) and true (with acceptance cuts,grey open circles) yW− distributions are shown for the TeVatron on the left –the yW+ distributions, reflected about yW = 0, look exactly the same, they fulfilN(yW+) = N(−yW−) and therefore not shown. On the right, the ratios of the calcu-lated and the true yW distributions are shown for positive and negative W bosons.The calculated rapidity distributions refers to the yW distributions, where only thesolution to equation 3.2 which is closest to true yW value is used. Acceptance cutsare applied to the MC in order to obtain the true yW distributions.

Wrapidity y

-3 -2 -1 0 1 2 3

Num

ber

of e

vent

s

0

10000

20000

30000

40000

50000

60000

70000

80000


Reweighted W (using both solutions, weighted)

Wrapidity y

-3 -2 -1 0 1 2 3

ratio

0.2

0.4

0.6

0.8

1

1.2

1.4 W+ ratio

W- ratio

(with acceptance cuts)W

/ true yW

kinematically reconstructed y

Figure 3.6: The fully kinematically reconstructed (red full triangles) and true yW−

(with acceptance cuts, grey open circles) yW− distributions are shown for the at theTeVatron on the left. On the right, the ratios of the fully kinematically reconstructedand the true yW distributions are shown for positive and negative W bosons. Thefully kinematically reconstructed refers the weighting of both solutions to equation3.2 (step 1 + 2). Acceptance cuts are applied to the MC in order to obtain the trueyW distributions.

need to be corrected for.The corrections for biases of the full kinematic Reconstruction of the W are im-

plicitly included in the acceptance corrections (step 3) correcting for the acceptancecuts applied to select the events [56, 57]. The acceptance corrections are obtainedusing the distributions shown in figure 3.7, left hand side. In the figure, the fullykinematically reconstructed yW− are shown as full red triangles. The true yW− distri-bution from MC is shown as full black circles. The acceptance correction is calculated

29

Wrapidity y

-3 -2 -1 0 1 2 3

Num

ber

of e

vent

s

0

20

40

60

80

100

120

140

160

310×True W (without cuts)


Wrapidity y

-3 -2 -1 0 1 2 3

acce

ptan

ce

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 W+ acceptance

W- acceptance (without acc. cuts)

W / true y

Wkinematically reconstructed y

Figure 3.7: The fully kinematically reconstructed (red full triangles) and true yW−

(without acceptance cuts, black full circles) yW− distributions are shown for the at theTeVatron on the left. On the right, the ratios of the fully kinematically reconstructedand the true yW distributions (without cuts) are shown for positive and negative Wbosons. The fully kinematically reconstructed refers the weighting of both solutionsto equation 3.2 (step 1 + 2). The true yW distributions are obtained from MC for thewhole kinematic phase space.

from these distributions as the ratio of the fully kinematically reconstructed yW dis-tributions to true yW distributions, where no acceptance cuts are applied. The fullacceptance corrections are around 0.6 and drop to lower values beyond |yW | > 2. Itshould be noted, that if we take the mirror reflections of the W+ acceptances aboutzero we recover the W− acceptances. Comparing figures 3.6 and 3.7, shows that thebias of the fully reconstructed yW distributions due to the acceptance cuts is muchlarger than the bias due to the weighting applied in step 1+2.

After evaluating the yW distributions, it is also interesting to examine how theweighting procedure affects the asymmetry distribution, which is directly calculatedfrom the yW distributions. Figure 3.8 a) shows the asymmetry distributions for theTeVatron. Shown are the true W asymmetry (without cuts, full black circles) andtrue W asymmetry (with acceptance cuts applied, grey open circles) distributionsfrom the MC. Also depicted is the calculated W (blue open squares), where only theW solution closest to the true yW value is used. The W asymmetry based on the fullkinematic reconstruction (step 1+2) is shown in red triangles. They all agree quitewell up to yW = 1.5, beyond that there is some disagreement for the reconstructedand the true W asymmetry. This can be better seen in figure 3.8 b), which shows theratio of the kinematically fully reconstructed W asymmetry and the true asymmetry,the latter either with acceptance cuts applied (open circles) or without acceptancecuts (full circles). The difference between the reconstructed and the true asymmetrywith the acceptance cuts applied is only around 20%. The true asymmetry withoutacceptance cuts is at most 80% to 100% larger than the reconstructed asymmetry.This shows, that the corrections for the detector acceptance cuts are larger and moreimportant than the bias from the full kinematic reconstruction (step 1+2).

30

WRapidity y

-3 -2 -1 0 1 2 3

Asy

mm

etry

-1

-0.5

0

0.5

1 True W (without cuts)




a) W asymmetry

W

Rapidity y-3 -2 -1 0 1 2 3

Rat

io A

sym

met

ries

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

(without cuts)trueA (reweighted) / A

(with acceptance cuts)trueA (reweighted) / A

b) Ratio of reconstructed asymmetry and trueasymmetries (with and without cuts)

Figure 3.8: This figure shows the asymmetry as evaluated at various stages of theiterative weighting procedure (a). In b) the ratios of reconstructed asymmetry andtrue asymmetries (with and without cuts) are depicted.

3.2.2 Performance of the Iterative Weighting Procedure atthe LHC

It is not clear, whether it is possible to transfer the above described technique to theLHC because of crucial differences between the TeVatron and LHC environments. TheTeVatron is a pp collider operating at

√s =1.96 TeV, while the LHC is due to collide

pp beams at√s =14 TeV. These differences pose a major challenge when applying

the weighting method to the LHC environment. Colliding pp beams, will break themirror symmetry between W+ and W−, which are produced at the TeVatron in equalnumbers and with the same characteristics albeit with opposite rapidity. At the LHCthis symmetry is broken: W+ are produced almost twice as often than W− and alsowith a larger boost. This tells us already in advance, that the iterative weightingprocedure will behave differently for W+ and W−.

First of all, we examine the full kinematic reconstruction and the weights usedin this reconstruction (step 1+2 of the iterative procedure) using a Pythia MCwith a MSTW08 PDF. As already described above, the two solutions to equation 3.2calculated in step 1, are weighted in step 2 using two basic considerations.

• Shape of cross section as function of yW : At the LHC the cross sectionfor W production is much flatter and extends over a much larger range of yW

compared to the TeVatron. This is shown in figure 3.2.2 obtained with 8×106

events and MSTW08 PDFs at√s =14 TeV. There is no peak in the yW dis-

tributions for central rapidities and only above yW > 1.5 − 2.0 there is a falloffof the yW distributions. Therefore, if both reconstructed solutions are within−1.5 < yW < 1.5, both are equally probable. In particular, the reconstruction ofW+ rapidities suffers from this fact, since the longitudinal boost of W+ bosonsis in general larger than the boost of W−, and therefore flatter up to highervalues of yW .

• Ratios of leading q versus leading q: Another problem is the contribution ofW s produced with a higher-x anti-quark. If the higher-x parton participating inthe Drell-Yan W production is an anti-quark, the W is no longer produced with

31

W rapidity y

-3 -2 -1 0 1 2 3

nor

mal

ized

num

ber

of e

ntrie

s

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

W minus (TeVatron)W plus (TeVatron)W minus (LHC)W plus (LHC)

a) Normalised yW± distributions

Figure 3.9: Problems of theweighting procedure at the LHC:a) The normalised yW± distribu-tions are flatter at the LHC (fullmarkers) compared to the TeVa-tron (open markers). The ratiosq/q used in the weighting proce-dure at the LHC are shown forW− in b) and for W+ in c). Forboth charges, the ratio is consider-able larger than 0.25, which is themaximal value of this ratio at theTeVatron.

W

yRapidity 0 0.5 1 1.5 2 2.5 3

[GeV

]T

P

1

10

210 /qq r

atio

0

0.2

0.4

0.6

0.8

1

1.2

b) q/q ratio for W−

W

yRapidity 0 0.5 1 1.5 2 2.5 3

[GeV

] T

P

1

10

210 /qq r

atio

0.2

0.4

0.6

0.8

1

1.2

c) q/q ratio for W+

a boost parallel to the incoming quark, but antiparallel to the incoming quark.This introduces a change of sign in the expected cos θ∗e,W decay angle. In theweighting procedure this is accounted for by constructing the cos θ∗e,W weightsuch that it combines a weight for leading quark and leading anti-quark Wproduction according to their relative contributions by using the ratio q/q as afunction of pW

T and yW , cf. eq. 3.8. At TeVatron centre of mass energies, leadingquark production is indeed the most probable process, with q/q=0.25 at most.At the LHC however, the ratio q/q becomes even larger than 1 as shown in figure3.2.2. This basically destroys the unambiguity of the cos θ∗e,W weighting. Thisis in particular problematic for W− production, where the ratio of anti-quarkinduced processes is higher than for W+ production. This is also shown in figure3.10, where the actual cos θ∗e,W distributions of W− (left) and W+ (right) bosonsare shown for W production at the LHC. The cos θ∗e,W distributions for eventswith a higher-x quark are shown as red dotted line, the distributions for eventswith higher-x anti-quarks is shown as blue dashed line. The total of the two isshown as black line. In particular for the W− distributions, the contribution ofhigher-x anti-quarks is large and two solutions with cos θ∗,1e,W ∼ − cos θ∗,2e,W cannot

be distinguished. Solutions with cos θ∗,2e,W ∼ − cos θ∗,1e,W or cos θ∗,2e,W ∼ cos θ∗,1e,W arein fact most common and in these cases each of the solutions 1 and 2 will beweighted with factors of about 0.5.

The conclusion from this is, that at the LHC the full kinematic reconstruction

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Figure 3.10: cos θ∗e,W distributions at the LHC. The contribution of higher-x anti-quark events is larger than at the TeVatron, where the rate is at most 25%. Thetotal of the higher-x quark (red dotted line) and higher-x anti-quark (blue dashedline) distributions is shown as black line. When using the cos θ∗e,W distributions at theLHC, the weighting is far more ambiguous for two very different solutions of cos θ∗e,W1 and 2 than at the TeVatron (cf. figure 3.1).

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Figure 3.11: This figure shows the weight given to reconstructed rapidity solutionclosest to the true value of yW for W− and W+ at the LHC. The same data set wasused to create the weighting tables and to test the weighting procedure (Pythia MCwith MSTW08 PDF).

suffers, because in the kinematic region of the LHC it is inherently less possible todistinguish the two solutions from one another. The consequences for the iterativeweighting procedure are investigated in the following using a Pythia MC samplegenerated using the MSTW08 PDF set. This sample is used both as ‘pseudo-data’and as MC input.

Iterative Weighting Procedure using Perfect MC Input

Figure 3.11 displays the weight given to the rapidity solution that was closest to theactual right rapidity at the LHC. While at the TeVatron, this distribution peaks at1 and is mostly larger than 0.5 (cf. fig. 3.4), at the LHC most weights are around0.5. For W− production the weights given to the right solution are on average at leastmarginally larger than 0.5, however the for W+ rapidities it is symmetric around 0.5,thus reducing the weighting procedure to pure guess work.

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Figure 3.12: The calculated (blueopen squares) and true (with ac-ceptance cuts, grey open circles)yW± distributions are shown forLHC. Also shown are the ratios ofthe calculated and the true yW dis-tributions. The calculated rapid-ity distributions refers to the yW

distributions, where only the solu-tion to equation 3.2 which is clos-est to true yW value is used. Ac-ceptance cuts are applied to theMC in order to obtain the true yW

distributions.

Figure 3.12 compares for the LHC the true yW distributions (with acceptance cutsapplied, grey open circles) from the MC to the calculated yW distribution (blue opensquares), for which only the yW solution closest to the true yW value is used. Thesedistributions are shown for W− on the left (a), for W+ on the right (b). Also shownis the ratio of these distributions, ycalculated

W /ytrueW as open markers for W− and as full

markers for W+ (c). Up to |yW | = 2.0, the ratios are 1+0.02−0.04. For larger values, there

are large deviations, possibly indicating edge effects from the acceptance cuts. All inall, the calculation of the yW asymmetry using equation 3.2 works well also at theLHC.

Figure 3.13 compares the true yW distribution (with acceptance cuts applied, greyopen circles) to the fully kinematically reconstructed yW (full red triangles). This isa check on how well the yW distributions can be kinematically reconstructed, whenno MC information is used to determine the best solution, but when a weighting asin step 1+2 is a applied. On the right, the distribution is shown for W−, on the leftfor W+. For the W− distribution, there is some overshoot of the fully kinematicallyreconstructed yW− distribution over the true yW− distribution around |yW | = 0. Inthe region of 1.0 < |yW | < 2.0, the fully kinematically reconstructed yW− undershootthe true distribution. However, the agreement between the two is still quite goodin comparison to the agreement between the fully kinematically reconstructed yW+

distribution and the true yW+ distribution. Around 1.0 < |yW | < 2.0 there is about

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Figure 3.13: The kinematicallyfully reconstructed (red triangles)and true (with acceptance cuts,grey open circles) yW± distribu-tions are shown for LHC. Alsoshown are the ratios of the kine-matically fully reconstructed andthe true yW distributions. Fullkinematic reconstruction refers tothe weighting of both solutions ofequation 3.2 (step 1 + 2). Accep-tance cuts are applied to the MCin order to obtain the true yW dis-tributions.

20% overshoot of the fully kinematically reconstructed yW+ distribution over the truedistribution. Beyond |yW | > 2.0, it undershoots significantly by more than 30-40%.Figure 3.13 c) shows the ratio of the fully kinematically reconstruction yW distribu-tions and the true yW distributions, which accentuates the poor performance of thefull kinematic reconstruction. This poor performance is due to the inherent problemsat the LHC to decide between the two rapidity solutions. From the weight distributionfor the solution closest to the truth, see figure 3.11, one could have already predictedthat the weighting of the two solutions would yield worse results for yW+ comparedto yW−.

In the figure 3.14, the fully kinematically reconstructed yW are shown as full redtriangles. The true yW distribution from MC (without cuts) is shown as full blackcircles. The acceptance correction is calculated from these distributions as the ratioof the fully kinematically reconstructed yW distributions to true yW distributions,where no acceptance cuts are applied. The full acceptance corrections are around0.6 and drop to lower values beyond |yW | > 2. Comparing figures 3.13 and 3.14,shows that the bias of the fully reconstructed yW distributions due to the acceptancecuts is still larger than the bias due to the weighting applied in step 1+2. Yet thereare features in the acceptance corrections, that are generated by biases in the fullkinematic reconstruction procedure. The most prominent feature is visible aroundyW = 1.5 in the acceptance correction for W+ bosons as little bump.

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Figure 3.14: The kinematicallyfully reconstructed (red triangles)and true (without acceptance cuts,grey open circles) yW± distribu-tions are shown for LHC. Alsoshown are the ratios of the kine-matically fully reconstructed andthe true yW distributions withoutany cuts. Full kinematic recon-struction refers to the weightingof both solutions of equation 3.2(step 1 + 2).

Again it is instructive to evaluate the asymmetry distribution at the various stagesof the iterative weighting procedure. This is done in figure 3.15 a). Additionally, figure3.15 b) depicts the ratio of the fully kinematically reconstructed asymmetry distribu-tion to true asymmetry distribution without acceptance cuts in full triangles. In opencircles the ratio of the reconstructed asymmetry distribution to true asymmetry dis-tribution with acceptance cuts is shown. The figure shows that in the central region,the corrections for biases in the full kinematic reconstruction dominates, while in theforward region genuine acceptance corrections dominate. Comparing this figure to theequivalent plots for the TeVatron (figure 3.8 b) reveals that the acceptance correctionsare more important at the LHC than at the TeVatron. While at the TeVatron theratio of the reconstructed asymmetry and the true asymmetry with cuts is between0.8-1.1, the same ratio is 0.5-3.0 at the LHC. Equally the ratio of the reconstructedasymmetry and the true asymmetry without cuts is with 1.5-3.0 larger at the LHCthan at the the TeVatron (0.8-1.8).

Applying the Full Iterative Weighting Procedure to Pseudo-Data

In the previous section, specific features of the iterative weighting procedure weretested using the same data sample as MC input and ‘pseudo-data’. This howeverdoes not allow testing of the full iterative weighting procedure, since the acceptancecorrections obtained from the MC input are by construction perfect and restore theasymmetry of the pseudo-data exactly.

In the following the method of the direct W rapidity reconstruction is tested for

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Figure 3.15: This figure shows the asymmetry as evaluated at various stages of theiterative weighting procedure (a). In b) the ratios of reconstructed asymmetry andtrue asymmetries (with and without cuts) are depicted. In the central region, thecorrections for biases in the full kinematic reconstruction dominates, while in theforward region genuine acceptance corrections dominate.

a full iteration cycle in order to assess the performance of the procedure at the LHC.For this four different data sets were used:

• Pythia sample, CTEQ66 PDF set, 8×106 events,√s = 14 TeV

• Pythia sample, MSTW08 PDF set, 8×106 events,√s = 14 TeV

• Pythia sample, MSTW08 PDF set, 8×106 events,√s = 10 TeV

• Herwig++ sample, MSTW08 PDF set, 1×106 events,√s = 10 TeV

In order to test the procedure, the weighting scheme as summarised in figure 3.3is carried out for the following combinations of pseudo-data and MC input for theweighting tables:

1. The Pythia MSTW08 sample is used as a pseudo-’data’ sample and the Pythia

CTEQ66 sample is used as the MC input for the weighting tables. Both sam-ples were generated with

√s = 14 TeV. This tests the influence of different PDF

parametrisation on the weighting procedure and how well the asymmetry can berecovered, when the input PDF is vastly different from the PDF set measuredin the data.

2. Herwig++ MSTW08 sample was used as a pseudo-’data’ sample and the Pythia

MSTW08 sample was used as the MC input for the weighting tables. Both sam-ples were generated with

√s = 10 TeV. This investigates, how important the

inclusion of higher orders in the used MC input is. Using a LO MC input for aNLO pseudo-data set can be used to estimate the effects of using a fixed orderMC input for real data.

From the MC inputs, the weighting tables are obtained with 50 bins from 0 <|yW | < 3.0. The weighting tables for the q/q ratios have 25 bins from 0 < |yW | < 3.0

37

and 20 logarithmically distributed bins between 0 and 200 GeV in pWT . In this study,

look-up tables were used for the weighting, not smooth functions, thus introducingbinning in the weights for the solution. Smooth distributions might lead to a slightlybetter performance of the weighting, but then introduce other biases if the fit is notperfect. The use of a smooth function for the yW distribution weighting was tested andno significant improvements could be observed. There are no dramatic improvementsexpected by using a parametrisation of the q/q ratio tables either. Bodek et al. useda convolution of a Landau with an higher order exponential, but the functional formis different at the LHC. There is no immediate candidate for the functional formmotivated by physics arguments. Therefore in these studies, binned weighting tablesare used.

The results of the iterative weighting procedure is shown in figure 3.16. Whenusing the Pythia MSTW08 sample as ’data’, the asymmetry of the ‘data’, shownas red circles, is almost restored when comparing with the reconstructed asymmetryof the 1st iteration, shown as grey upwards triangles. The exception are the threehighest bins of |yW | > 2.0, where there is visual disagreement between the original‘data’ asymmetry and the asymmetry reconstruction in the iterative procedure. Theasymmetry of the input MC, shown as black circles, does not seem to influence the re-constructed W asymmetry very much. The respective iterations are shown as differentmarkers in grey shades.

For some bins, a drift of the asymmetry with each iteration can be clearly observed.This drift is an effect of statistical fluctuations in the data sets. These fluctuationsslightly bias the reconstructed rapidity distributions in a certain direction. That thisis indeed an effect of statistical fluctuations was checked by reducing the number ofevents by a factor of 10 only in the input, only in the ‘data’ and both the ‘data’ and theinput. In particular, when only the input MC and when both, ‘data’ and MC sample,are used with a reduced number of events, the random walks are very prominent andalso larger in size. This confirms that they stem from random fluctuations. The sameeffect, an increased size of the random walk, is observed when the numbers of events isreduced for the TeVatron setting. The size of the random walk as such and the increaseof the scatter is however still far smaller than at LHC conditions. This indicates onceagain, that the weighting procedure is inherently more stable at the TeVatron thanat the LHC. Bodek et al. investigated the random walks by conducting 600 pseudoexperiments on subsets of their initial MC input sample and used the spread of thereconstructed asymmetry in the 600 pseudo experiments to determine the statisticalerror of the asymmetry measurement (cf. [57], p. 121). This statistical error can bereduced by using a larger MC input sample, but it will not be feasible to generate aninfinite number of MC events, especially if the full detector simulation is to be used.

The statistical fluctuations cause the measured asymmetry to be shifted with re-gard to the MC input asymmetry in each iteration by exactly the same amount. Onlyin the first iteration, a different shift between measured asymmetry and MC inputasymmetry is observed. This indicates that the iterative procedure converges afterthe first step of the iterative procedure and restores the original MSTW08 asymmetryof the ‘data’ with the exception of the three highest bins of rapidity.

A similar picture emerges for the higher yW bins and random walks due to statisti-cal fluctuations, when using a NLO ‘data’ sample with LO Pythia input as weightingtables, both generated with the same PDF (see figure 3.16, right hand side). Here,

38

however, the deviations for the higher yW bins are smaller, while due to the size ofthe sample, the random walks are slightly larger. In the central region, the originalNLO asymmetry is restored in the 1st iteration, any further iterations do not changethe reconstructed asymmetry much, apart from small random walks. For |yW | > 2.0the asymmetry is recovered better compared to the weighting scheme, where differentPDFs were used.

The main reason for the systematic disagreement in the case, where MSTW08 andCTEQ66 were used with Pythia , is the fact that the weights are mostly 0.5. Theoutcome of the weighting procedure is not crucially dependent of the actual inputs andthe acceptance corrections become more important. That the acceptance correctionsgain in importance, introduces problems in the iterative weighting procedure. If thedata acceptance is larger than predicted by the MC input and if this difference inthe acceptance is larger for W− than for W+, this will reflect on the reconstructedasymmetry by lowering the asymmetry. No amount of feedback reweighting will beable to recover this. This is exactly what causes the deviation of the reconstructedand the input asymmetry when trying to reconstruct Pythia MSTW08 with Pythia

CTEQ66 input. Figure 3.17 a) demonstrates this by displaying the W acceptances of‘data’ divided by the acceptance of the MC inputs for the MSTW08 Pythia ‘data’reconstructed with Pythia CTEQ66 PDF input MC (red dotted line for W+ andblue dashed line for W−). Also the double ratio of the W+ acceptance ratio dividedby the W− acceptance ratio is shown as a black solid line. It should however be notedthat depending on whether the ratio of the ratios of acceptances is below or aboveunity decides whether the reconstructed asymmetry is under- or overestimated by thereconstruction. The amount of under- or overestimation is dependent on how differentthe acceptances are.

Fig. 3.17 b) shows these ratios for the Herwig++ NLO ‘data’ reconstructed withPythia LO input MC. Here, large differences are observed above |yW | > 2.0. Here,the ratio of the acceptances deviates much more from unity than in the case of thePythia , but the effects are much smaller. This can however be understood: Theacceptance for W− is lowered with regard to the W+ acceptance, therefore the recon-structed asymmetry tends to be lower. Since the Pythia asymmetry used as input isin fact larger than the Herwig++ asymmetry to be reconstructed, this lowering of thereconstructed asymmetry due to the biased acceptances actually aids in the correctreconstruction of the asymmetry.

It should be stressed, that these effects inherently cannot be removed by an iter-ative procedure. Hence, it seems unsafe to use an iterative measurement like the onepresented here in order to measure the W asymmetry.

3.2.3 Conclusion

The weighting procedure to extract the W rapidities is inherently less stable at theLHC and therefore also less reliable compared to the application at the TeVatron.The acceptance corrections play a much larger role at the LHC than at the TeVatron.They mainly depend on the order of the MC calculation and to a lesser extent onthe PDFs themselves, but a difference in the predicted MC acceptances used in theweighting and in the actual data can lead to significant deviations of the reweightedfrom the input MC. The described problems emphasise the need to use only reliable

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Figure 3.16: The results of the iterative weighting procedure and the subsequent ac-ceptance corrections are shown for the LHC. On the top plot, the weighting procedurefor 2 iterations is shown for the Pythia MSTW08 data using Pythia CTEQ66 MCinput along side the original true asymmetries from Pythia MSTW08 and Pythia

CTEQ66 samples. On the bottom plot, 5 iterations are depicted for the weightingprocedure as applied to a Herwig++ MSTW08 ‘data’ sample using Pythia MSTW08MC input. As shown, the asymmetry are recovered mostly after the 0th iteration.Also, the iterations do not change the asymmetry much.

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Figure 3.17: The ratios of acceptances for ‘data’ and MC input samples are shownfor MSTW08 Pythia ‘data’ and CTEQ66 Pythia MC input (a) as well as forMSTW08 Herwig++ ‘data’ and MSTW08 Pythia MC input (b).

MC inputs for the weighting procedure at the LHC, that is MC input after its validityhas been tested with measured LHC data.

In addition, the acceptance corrections also include corrections for the detectorresolution, when used in a measurement with real data. It cannot be expected thatthe detector simulation of the Atlas detector will be able to describe early data withsufficient accuracy. The extraction of the direct W asymmetry can therefore only bea task for later data analysis, if it is conducted at all. Possible improvements of theweighting procedure include the usage of smooth, fitted functions instead of weight-ing tables and to shift emphasis from the yW cross-section weighting to the cos θ∗e,Wweighting for W+ bosons, while for W− bosons the opposite approach could be takento improve the weighting as such. A possible alternative would be to drop the weight-ing of the two solutions (step 1+2) altogether and just use each solution weighted by0.5. This would remove uncertainties dues to the MC input for the weighting tables,bit it would also put even more emphasis on the acceptance corrections and the feed-back loop. The flaws of the corrections and the MC reweighting feedback look couldon the other hand possibly be improved by including further variables, such as pW

T ,in the calculation of the acceptance corrections and the reweighting of the MC (step5) as function of (yW , pW

T , ...). However, all in all, the iterative weighting procedureto extract the direct W asymmetry is not a promising method at the LHC, especiallyfor early data.

Chapter 4

Detector and Experimental Setup

4.1 The Large Hadron Collider

The LHC [58] is a circular accelerator currently being commissioned at CERN1. It issituated in an underground tunnel of ∼27 km circumference, around 50-175 m belowthe surface near Geneva airport, crossing the Swiss-French border and stretching upto the onset of the Jura mountains.

The LHC [60] will collide protons with Ebeam = 7 TeV at four collisions points,delivering a centre of mass energy of

√s = 14 TeV. These beam energies are achieved

through a complex system of accelerators that gradually increase the energies of theprotons up to the maximal energy, at which they are then fed into the next acceleratoror stored and collided in the LHC.

The LHC will accelerate the protons in 2808 bunches of 1.1×1011 protons clockwiseand anticlockwise around the ring. The nominal bunch spacing is 25 ns, which resultsin a collision frequency of 40 MHz at each collision point. The actual collision rate willbe 31.6 MHz due to ‘gaps’ or empty bunches, allowing beam injection and dumping.The instantaneous luminosity of the collider, which is fixed by beam parameters suchas the number of particles in the beam, Np, their collision frequency ν and the lateralcoordinate widths of the bunches in the interaction region, σ2

xσ2y , will amount to

nominal luminosity of L = 1034cm−2s−1. During the commissioning and early runningphase, a reduced luminosity of L = 1031cm−2s−1 is envisaged and possibly also areduced centre of mass energy,

√s = 7 TeV.

Since the cross section for inelastic pp collisions, so-called soft interactions, is muchlarger than for the hard scatterings discussed in section 2.2, each hard scattering ison average accompanied by 20-25 soft interactions at nominal luminosity. The highrate of events as well as these multiple interactions pose enormous challenges for therecording and storage of the collisions.

There are six detectors under commissioning that will take measurements at theLHC. Among them, the Atlas [61] and the CMS [62] detector are the largest. Theyare both designed as general-purpose experiments and will be concentrating on pre-cision measurements of QCD and the standard model as well as on the search for theHiggs boson, supersymmetry and other new physics. The other four detectors arespecialised experiments. The LHCb detector [63] is a dedicated instrument to mea-

1CERN is the European Organisation for Nuclear Research founded in 1954 in order to carry outfundamental nuclear and particle physics research [59].

41

42

sure CP violation in particular in c and b-meson decays. The ALICE detector [64] isbuild to measure characteristics of the quark-gluon plasma. The measurement of veryforward production cross sections and energy spectra of neutral pions and neutronsis the goal of the LHCf collaboration [65]. The aim is to test the understanding ofhadronic interaction models and improve the description of high energy cosmic rayproduction. TOTEM [66] is an experiment to measure the total pp cross section,elastic scattering and diffractive processes.

4.2 The Atlas Detector

The Atlas (A Toroidal LHC ApparatuS) detector is situated next to the mainCERN site. The Atlas coordinate system, that is also used in this thesis, has thenominal interaction point as its origin. The +z axis is defined by the clockwise beamdirection, while the x− y plane is transverse to the beam direction with +x pointingtowards the centre of the LHC ring and the +y axis pointing upwards. As indicated infigure 4.1, the azimuthal angle φ is measured in the x− y-plane from −π−+π, whilethe polar angle θ is measured from the beam axis. The pseudorapidity is defined as:

η = − ln

(

tanθ

2

)

(4.1)

It is commonly used instead of θ, since it is equivalent to the Lorentz-invariantrapidity y in the case of massless particles. Distances in the detector are measured in∆R, which is defined in the pseudorapidity-azimuthal angle space:

∆R =√

∆φ2 + ∆η2 (4.2)

A half view of the Atlas detector is given in figure 4.1 along side with a sketchof the Atlas coordinate system. Atlas is designed as a multipurpose detector withdedicated subdetector systems. Directly around the interaction point, the inner

detector is found: The Atlas pixel detector, the semiconductor tracking detector(SCT) and the transition radiation track (TRT) provide precise space point informa-tion to reconstruct the tracks of charged particles up to |η| < 2.5 as well as primaryand secondary vertices. These subdetectors are discussed in more detail in section4.2.2. They are contained in the solenoidal magnetic system with a diameter of2.5 m. This magnetic system provides the magnetic field to bend the charged par-ticles to measure their curvature and thus their transverse momentum in the innerdetector. The field strength amounts to 2 T at the centre of the inner detector andto 0.5 T at the outer end of the detector. This decrease in field strength is due to thefact, that the solenoid is about 80 cm shorter than the inner detector system whichhas a length of L= 5.3 m. The solenoid is a superconducting magnet, sharing thecryostat with the calorimeter system. The calorimeter system, discussed in moredetail in section 4.2.3, consists of electromagnetic and hadronic calorimeters. Aroundthe calorimeter system the toroidal magnetic system can be found, that providesthe 0.5 T magnetic field to the muon system, measuring track of muons |η| < 2.7independently of the inner detector.

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Figure 4.1: Overview of the Atlas detector and its coordinate system

4.2.1 Trigger System

As explained in section 4.1, the bunch crossing frequency at the LHC will be 40 MHz.If all events were recorded, this would exceed the bandwidth for a complete detectorreadout as well as the capacities for processing and data storage. Therefore, at Atlas

a three-level trigger system will select only those events that are of interest for theAtlas physics programme [67]. On each of the sequential trigger levels, L1, L2 andthe event filter, a refined decision is taken as to whether to process that particularevent further or whether not to record the event [61]. L1 will reduce the 40 MHz inputrate to an output rate of roughly 75 - 100 kHz, using information from calorimeterand muon systems with a reduced granularity. It defines so-called regions of interest(ROIs) in η−φ space, where significant energy deposits are found in the detector. Inthe case that certain thresholds and conditions are met, the ROIs are further processedby L2 with full granularity within the ROIs (making up ∼2% of the full detector).At L2, tracker information is also used and combined with the information from theother trigger subsystems in order to make a decision. L2 is designed to output ∼3.5kHz. The event filter will be able to access the full granularity of the detector andwill be able to use offline analysis procedures, e.g. fully reconstructing electrons andapplying offline identification cuts. The output of the event filter will be roughly 200Hz, corresponding to an output of about 300 MB/s. An overview of the trigger isgiven in figure 4.2.

Despite the selectivity of the Atlas trigger system, not all events of interest canbe recorded. For example, the expected rate of W production and dijet production ofjets with ET ∼ 250 GeV is for each of these processes about 1 kHz and thus exceedsthe event filter output rate already by a factor of five. Therefore, Atlas will alsoemploy prescales, where randomly a certain amount N of events will be discarded[67], thus leaving only 1/N events to be recorded permanently. For early runningwith L = 1031cm−2s−1, it is envisaged, to prescale for example the jet trigger J50which has a threshold of ET ∼ 50 GeV by a factor of 42000 on L1, J180 which has athreshold of ET ∼ 180 GeV is planned to be prescaled by a factor of 100. Electrons

44

LEVEL 2TRIGGER

LEVEL 1TRIGGER

CALO MUON TRACKING

Event builder

Pipelinememories

Derandomizers

Readout buffers(ROBs)

EVENT FILTER

Bunch crossingrate 40 MHz

< 75 (100) kHz

~ 3.5 kHz

~ 200 Hz

Interaction rate~1 GHz

Regions of Interest Readout drivers(RODs)

Full-event buffersand

processor sub-farms

Data recording

Figure 4.2: Overview over the Atlas trigger system (updated from [69]).

with significant pT > 10 GeV (or pT > 5 GeV if there are two in the event) are notto be prescaled [68]. For higher luminosities the prescales for the jet triggers will beincreased, while the thresholds for the unprescaled electron triggers will be increasedand tighter identification cuts will be introduced.

4.2.2 Tracking Detectors

The Atlas tracking system is designed for a track reconstruction efficiency of 90%within |η| < 2.5 with full φ-coverage. It can reconstruct the tracks of charged particlesabove a transverse momentum of PT > 500 MeV with an average of seven hits pertrack with R-φ and z coordinates for |η| < 2.5. Additionally about 36 hits per trackwith R-φ information only are reconstructed in |η| < 2.0. The former measurementsare provided by the pixel detector and the semiconductor tracking detector (SCT),while the later stem from the transition radiation tracker(TRT). Figure 4.3 gives adetailed overview of the geometrical layout of the Atlas inner detector system.

The pixel detector is constructed with cylindrical 3 layers surrounding the beamin the central region and 2 × 3 disks in the end-cap region. The intrinsic resolutionof each pixel is 10µm in R− φ and 115µm in z for the barrel and 10µm in R−φ and115µm in R for the disks. Each track with |η| < 2.5 will cross at least 3 pixel layers.

The SCT is a silicon strip detector with 4 cylindrical layers in the barrel and 2×9disks in the end-caps. Each layer consists of 2 strips, crossed with a stereo angleof 40 mrad to reduce the number of possible combinations in track finding and thus

45

Pixel SCT TRT

Number of hits per track ≈3 ≈4 ≈ 36Resolution in R− φ (µm) 10 17 140Resolution in z/R (µm) 115 580 -|η| coverage <2.5 <2.5 <2.0Number of layers 3 cylindrical layers 4 cylindrical layers 73 straw planes

2×3 disks 2×9 disks 160 straw planes

Table 4.1: Main parameters of the Atlas tracking systems.

the computing time. In the barrel the strips run parallel to the beam pipe, whilein the disk they are arranged radially. The SCT measurement of a hit position hasan intrinsic resolution of 17 µm in R − φ and 580 µm in z (barrel) and R (end-cap)respectively. Per track 4 hits are expected to be detected within |η| < 2.5 .

The TRT consists of 4 mm diameter straw tubes each filled with a Xe-CO2-O2

gas mixture. Charged particles will ionise the gas mixture, the drift electrons willbe detected by a gold-plated tungsten wire in the centre of the straw. Additionally,the gas mixture is used to detect transition radiation emitted by charged particlespassing through a polyethylene material embedding the straws. The transition radi-ation photons will ionise the gas mixture in the straw tubes as well and thus add tothe total collected charge. Their number depends on the relativistic factor γ = E

m.

Electrons with mass me = 0.511 MeV will cause more charge to be deposited on thestraw wire due to the additional transition radiation compared to pions with massmπ = 140 MeV. This enables the TRT to provide not only drift time information,but also to apply different charge collection thresholds, a low and a high threshold.While the hits passing the low thresholds are used for track reconstruction, the highthreshold hits can be used to distinguish electrons from pions, since the former aremore likely to emit more transition radiation photons and thus deposit more charge.The spatial R − φ resolution of the barrel TRT is 140 µm. It does not provide anyinformation about the z coordinate, however the large number of hits along a TRTtrack allow reconstruction of long tracks which helps to determine the momenta ofparticles with high pT and small track curvature. The main parameters of the Atlas

tracking subdetectors are also summarised in table 4.1.

Material in the inner detector

Any particle traversing the inner detector will lose energy – energy that will be lost fordetection in the calorimeters. Furthermore, the probability of photon conversions andhard bremsstrahlung of electrons is correlated to the amount of material traversed.Therefore, the amount of material before the calorimeters influences the accuracy ofthe energy measurement as well as the general reconstruction of electrons and photons.The material of the inner detectors is shown in figure 4.4 given in radiation length

46

Envelopes

Pixel

SCT barrel

SCT end-cap

TRT barrel

TRT end-cap

255<R<549mm|Z|<805mm

251<R<610mm810<|Z|<2797mm

554<R<1082mm|Z|<780mm

617<R<1106mm827<|Z|<2744mm

45.5<R<242mm|Z|<3092mm

Cryostat

PPF1

CryostatSolenoid coil

z(mm)

Beam-pipe

Pixelsupport tubeSCT (end-cap)

TRT(end-cap)

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8

Pixel

400.5495

580

650749

853.8934

1091.5

1299.9

1399.7

1771.4 2115.2 2505 2720.200

R50.5R88.5

R122.5

R299

R371

R443R514R563

R1066

R1150

R229

R560

R438.8R408

R337.6R275

R644

R1004

2710848712 PPB1

Radius(mm)

TRT(barrel)

SCT(barrel)Pixel PP1

3512ID end-plate

Pixel

400.5 495 580 6500

0

R50.5

R88.5

R122.5

R88.8

R149.6

R34.3

Figure 4.3: Geometrical layout of the Atlas tracking system [61].

X02 (left) and interaction length λ3 (right) as a function of absolute pseudorapidity

|η|. For |η| & 0.5, the material increases significantly and peaks for |η| ∼ 1.5. Thisis also the region, where the barrel calorimeters end and the end-cap calorimetersbegin, leaving a small gap for services, readout cables and cooling. Since this regionis also not well instrumented, precise measurements of particles in this so-called crackregion is not feasible. This region is commonly cut out in physics analysis. Similarly,the region around |η| ∼ 2.9− 3.1 contains a lot of inner detector material, which candiminish the quality of the measurements in this region.

4.2.3 Calorimetry

The Atlas detector is equipped with dedicated electromagnetic (EM) and hadroniccalorimeter systems. The EM calorimeters are built around the inner detector andmeasure energy deposits of electron, positrons, photons, pions and other hadrons,which all produce showers of secondary particles in the absorber material of thecalorimeter. Most of the electromagnetic showers are fully contained in the EMcalorimeters. Showers caused by hadrons also contain an electromagnetic component,which they deposit in the EM calorimeters. Hadronic showers however are generallybroader and deeper than purely electromagnetic showers and therefore leak into the

2The radiation length X0 is the mean distance in a specific material, over which a high energyelectron or positron looses all but 1/e of its energy by bremsstrahlung. It is 7/9 of the mean freepath length for a pair production by high energy photons. It is commonly normalised to the densityof the material and given in units of g

cm2 .3An interaction length is the mean free path of a hadron between two nuclear interactions in a

specific material, usually measured as λ [cm].

47

|η|0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

) 0R

adia

tion

leng

th (

X

0

0.5

1

1.5

2

2.5

|η|0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

) 0R

adia

tion

leng

th (

X

0

0.5

1

1.5

2

2.5

ServicesTRTSCTPixelBeam-pipe

|η|0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

)λIn

tera

ctio

n le

ngth

(

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

|η|0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

)λIn

tera

ctio

n le

ngth

(

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7ServicesTRTSCTPixelBeam-pipe

Figure 4.4: Material distribution of the Atlas inner detector given in radiation lengthX0 (left) and interaction length λ (right) as a function of absolute pseudorapidity |η|[67].

hadronic calorimeters, which are optimised for the measurement of hadrons.Atlas employs two main technologies for calorimetry: For the EM calorimeters

as well as for the more forward (|η| > 1.5) hadronic calorimeters radiation hard androbust LAr-sampling technology is used. Lead absorbers and LAr sampling gapsin an accordion geometry are used for the EM calorimeters, while for the hadronicendcap calorimeter (HEC) copper/LAr and for the forward calorimeter (FCAL)copper-tungsten/LAr are used. For the measurement of hadrons a tile calorimeter isused in the central region. It employs a sampling technique using steel as absorberand scintillating tiles as active material. Figure 4.5 depicts schematically the Atlas

calorimeter and its electromagnetic and hadronic calorimeter systems.The EM calorimeters are subdivided into a barrel part (|η| < 1.475) and an end-

cap part (1.375 < |η| < 3.2). The accordion geometry allows full φ-coverage withoutazimuthal cracks. The radiation lengths of the EM calorimeters are X0 >22 and 24in barrel and end-cap regions respectively. Figure 4.6 shows a LAr-EM calorimetermodule in close-up at η = 0. It consists of 3 distinct layers. The first layer consistsof finely segmented strip cells of the order of 1/4 compared to the LAr cells of thesecond layer. These can be used to identify secondary maxima in EM showers in orderto distinguish neutral pions from electrons (see section 5.1.3). The second and thethird layer are coarser, with the second layer having a much larger depth (X0 =16)than the third (X0 =2) and thus measuring the bulk of the EM shower. The end-capcalorimeter has a lateral segmentation, that varies as a function of η. There is a gapbetween the EM barrel and end-cap, that is used for services and due to poor energyreconstruction needs to be cut out in analysis as already mentioned above.

The Atlas hadronic calorimeter system consists of three calorimeters. The tilecalorimeter is made up of a barrel part (|η| < 1.0) and an extended barrel (0.8 <|η| < 1.7). The tile calorimeter has 3 layers each in barrel and extended barrel witha total of ∼ 7 interaction length. The hadronic calorimeters are λ = 9.7 (barrel) andλ = 10 interaction lengths deep.

The LAr-HEC is built from two independent end-cap wheels, each consisting of 2layers with a coarser granularity of the cells at higher |η|. It extends from 1.5 < |η| <3.2 and shares the cryostat with the EM end-cap calorimeter and overlaps with the

48

Figure 4.5: Geometrical layout of the Atlas calorimeter system taken from [70].

FCAL by |η| = 0.1 and with the tile calorimeter by |η| = 0.2 units of pseudorapidity.The FCAL covers 3.1 < |η| < 4.9 and is approximately 10 interaction lengths

deep. It is built as a high-density calorimeter with three modules. The first oneuses copper as sampling material and LAr as active material and is optimised forEM measurements, while the other two are meant to measure hadrons and employtungsten-LAr technology.

Hadronic response of the calorimeters

All three Atlas calorimeters are non-compensating calorimeters: The response interms of collected charge is very different for hadrons and electrons with the sameincident energy. The reason for this is that the underlying processes for depositionof energy in materials differ for electromagnetically and strongly interacting particles.These processes are:

• Nuclear interactions: Only hadrons that interact strongly can undergo nu-clear interactions. Usually in these processes the primary nucleus breaks up intotwo smaller nuclei under emission of several mesons, mostly pions. The breakup

49

∆ϕ = 0.0245

∆η = 0.02537.5mm/8 = 4.69 mm ∆η = 0.0031

∆ϕ=0.0245x4 36.8mmx4 =147.3mm

Trigger Tower

TriggerTower∆ϕ = 0.0982

∆η = 0.1

16X0

4.3X0

2X0

1500

mm

470

mm

η

ϕ

η = 0

Strip cells in Layer 1

Square cells in Layer 2

1.7X0

Cells in Layer 3 ∆ϕ×�∆η = 0.0245×�0.05

Figure 4.6: Layout of an Atlas LAr-EM calorimeter module [61].

of the nuclei uses up energy that is lost for detection, this is so-called invisi-ble energy. In some of these interactions neutrinos might be produced (e.g. indecays of produced hadrons or neutrons), that escape the detector undetected.This escaped energy again reduces the response of the calorimeter to hadronswith respect to electrons. Escaped and invisible energy make up to 25% of thetotal energy deposited by a hadron in a non-compensating calorimeter, thereforefor hadrons an energy is measured that is in most cases less than the true energyof the incident hadron.

• Energy loss due to ionisation (dE/dx): Charged particles can ionise atomsthey pass by, photons can as well ionise atoms via the photoelectric effect. Thefree charges can then be directly collected as deposited charge in the activematerial. For electrons this process is negligible, however hadrons lose about25% of their energy due to ioniziation.

• Electromagnetic processes (Bremsstrahlung, pair production): Highenergy electrons can radiate off photons, similarly these photons can produceelectron positron pairs, that – provided their energies are still large enough – canagain radiate off more photons that again can undergo pair production, stimu-lating an EM shower. For electrons these electromagnetic processes are by fardominant over a critical energy Ec ∼600 MeV/Z, where Z is the atomic numberof the material. For the Atlas barrel and end-cap LAr detectors ZPb=164 andtherefore Ec ∼3.7 MeV – which is much smaller than the typical energies ofelectrons measured at Atlas . Electrons and photons below Ec deposit theirenergies via ionisation in the active materials of the detector. Not only electrons

50

and photons but also hadrons can deposit energy electromagnetically via EMshowers. This is the case, if the nuclear interaction of a hadron produces a neu-tral pion that then decays into photons. For hadrons, EM processes contributeonly about 50% to their total energy deposits.

Electrons and photons deposit almost 100% of their energy in electromagnetic pro-cesses with a good linearity between collected charge and deposited energy and withrelatively little statistical fluctuations, enabling good calibration of the calorimeter.The contributions of the various processes to the total energy deposition of hadronsin calorimeters fluctuate heavily from event to event and also depend on the energyof the incident hadron. The different response of a calorimeter to hadrons and elec-tromagnetically interacting particles can be measured as e/π – the energy responseof electrons normalised to that of pions. The Atlas calorimeters have e/π > 1. Dueto the fact that the Atlas calorimeters have a different response to dominantly elec-tromagnetically interacting particles and hadrons, specific calibration schemes needto be devised for the energy measurement of hadrons. These calibrations are meantto calibrate from the basic electromagnetic scale4 to the hadronic scale, where alsoinvisible and escaped energy are corrected for. They shall be discussed in section5.2.3 of chapter 5, where the reconstruction of electrons and jets, collimated showersof hadrons, in the Atlas detector is described in more detail.

4The electromagnetic scale refers to the basic signal read out from the calorimeter with electron-ics and detector related corrections, but without any corrections typically applied in the precisionmeasurement of electrons or photons.

Chapter 5

Reconstruction

5.1 Electron Reconstruction

The measurement of electrons with the Atlas detector is described elsewhere in moredetail in [67], [61]. Here, only the most relevant points for triggering, reconstructionand identifying electrons are briefly reviewed.

5.1.1 EM Trigger

The L1 trigger at Atlas operates using sliding windows, where the energy sum of4 trigger towers (each spanning a 0.1 × 0.1 η × φ region and shown in figure 4.6)is used to find an electromagnetic (EM) trigger cluster, which is required to be alocal ET maximum. The sum of two adjacent towers must exceed the L1 thresholdin order to trigger at L1. In addition to the threshold, requirements can be put onthe electromagnetic isolation of the EM trigger cluster, its hadronic core Ehad

core and itshadronic isolation, which are also schematically shown in figure 5.1.

The level 2 trigger receives only the regions of interest (ROIs) defined by theEM trigger clusters of size 0.4 × 0.4 in η × φ identified on L1. It has access to thetotal granularity of the calorimeter within the ROIs and the L2 EM trigger clusteris created as a cluster around the cell containing the highest energy in a ROI. Thecluster size used is 0.075 × 0.175 in η × φ, where the larger size in φ is meant tocollect the energy due to photon conversion and electron bremsstrahlung. Due to thefact, that cell level information and information from other subdetectors such as thetracking system is available, several cuts related to energy, track and shower shapecan be employed on trigger level:

• Transverse energy of the L2 EM trigger cluster,

• Transverse energy in the first layer of the hadronic calorimeter to reject clusterswith significant hadronic leakage, since this is an indication of hadronic showers,

• Shower shape in the second sampling of the calorimeter, calculated as the ratioof the energy deposition in 3×7 cells to the energy in 7×7 cells in η×φ, Rcore =E3×7

E7×7 ,

• Cut on a second energy maximum in the first EM sampling of the calorimeter.The second energy maximum is searched in a window of η × φ = 0.125 × 0.2

51

52

Figure 5.1: Trigger towers for electron and photon triggers [61].

and the asymmetry between the two highest local energy maxima in the clusterare calculated as Rstrips = (E1st − E2nd)/(E1st + E2nd). This ratio is close to 0for π0s, while it is almost 1 for isolated electrons and photons,

• pT of the matched track,

• Minimum and maximum values of E/P of cluster and track,

• Maximum ∆η and ∆Φ distances between cluster and track.

The e20 loose trigger chain will be the main physics trigger for W and singleelectron analyses in early data. It is foreseen to be run without any prescale. Itemploys on L1 a simple energy cut of ET > 18 GeV. On L2 with its more preciseinformation another cut of ET > 19 GeV is used alongside cuts on the hadronicleakage, Rcore and Rstrips as well as tracks, their values are detailed in [71]. As eventfilter (EF) the full offline reconstruction is run – here the transverse energy cut ofET > 20 GeV is applied and also a set of so-called loose offline identification cuts,that will be specified in the following section 5.1.2.

5.1.2 Reconstruction of Electrons

In triggered events, electrons (and photons) are reconstructed from electromagnetic(EM) clusters in the calorimeters. These EM clusters are formed using a slidingwindow technique described in [72], where the window size is ∆η × ∆φ = 0.075 ×0.175 in the barrel and 0.125 × 0.125 in the endcaps, which is slightly different fromthe values applied in the trigger algorithm. After all EM clusters are found, duplicatesare removed by keeping only the cluster with the maximum energy in a given η × φregion. Then a matching track is looked for in a window of 0.05 × 0.10 in η × φ.The track is required to have a momentum p fulfilling a cut of E/p < 10. In casesuch a track is found, the EM cluster becomes an electron candidate. If there isno compatible track found, the EM cluster is considered to be a photon candidate.In order to identify whether these reconstructed electron and photon candidates areindeed caused by electrons and photons, identification cuts are applied to distinguishthem from hadrons.

53

5.1.3 Electron Identification

The electron identification cuts separate real electrons from fake electrons (hadrons,photon conversions, muons and others), that were wrongly reconstructed as EM clus-ters. In order to do so information from the calorimeters as well as tracking infor-mation is used. In Atlas, predefined sets of cuts are used to achieve different levelsof electron ID efficiency versus fake rejection, referred to as loose, medium and tightcuts. All these cuts are detailed in [67], but shall be shortly discussed here, becauseof their relevance for the studies presented in chapter 7. Table 5.1 lists all cuts with ashort description. The individual cut values of most of the identification cuts dependon the ET , and the η values of the EM cluster. They are each specified for the latestAtlas software release in [73] and are given in appendix B for the release used in thisthesis.

5.1.4 Photon Identification

EM clusters are only reconstructed as photons, if they cannot be matched to a trackwithin a window of ∆η × ∆φ = 0.05×0.10. Therefore, for photons only calorimeterbased ID cuts are defined and used (L1-M5, T8). The individual cut values of most ofthe photon ID cuts depend on the ET , and the η values of the EM cluster. They areeach specified for the latest Atlas software release in [73] and are given in appendixB for the release used in this thesis.

5.2 Jet Reconstruction

Quarks and gluons cannot be observed directly in the detectors due to the confinementproperties of strong interactions. Immediately after production they fragment intocolourless hadrons, that can be detected in the Atlas detector. The final stateparticles of a fragmentation chain can be in principle grouped back together and re-clustered into a so-called jet, whose properties are strongly correlated with ones ofthe initial parton. In this section, the reconstruction of jets in Atlas is described.

5.2.1 Inputs to jet reconstruction

The Atlas calorimeters described above have in total about 200,000 individual cells,that sample the showers of hadrons and leptons entering the calorimeters. In thereconstruction process, energy deposits in the cells are firstly combined into largerentities, before these are further processes as four vector input by the jet algorithm.At Atlas there are three approaches used in order to combine the cells into largerobjects:

• Calorimeter Towers: To form calorimeter towers, a fixed grid in η and φis applied to the calorimeters. The grid size is η × φ = 0.1 over the wholeacceptance. The energies of all cells falling into a certain calorimeter tower aresummed up without any calibration or corrections, that is on electromagneticenergy scale [67].

54

loose ID cutsmost basic set of cuts, also used in the EF offline trigger selectionBasic acceptance and hadronic leakage cuts

L1 |ηEMcluster| < 2.47

L2 Hadronic leakage,E1st sampling hadronicCalo

T, EM cluster

Eall deposited energyT, EM cluster

Lateral shower shape cuts, based on the second layer of the EM calorime-ter

L3 Lateral shower shape in η, R77 = 3×77×7

L4 Lateral shower shape in φ, R37 = 3×33×7

L5 Lateral width in η, calculated in a window of 3×5 cells, with Ec the energy deposited

in each cell c, wη2 =

√

P

c(Ec×η2c )

P

c Ec−[

P

c(Ec×η2c )

P

c Ec

]2

medium ID cutsforeseen and used as standard ID cuts in [67] (L1-L5 included)

Cuts on shower shapes in calo strips in the 1st layer of the EM calorime-teronly applied if 5% of energy is reconstructed in the calo strips

M1 Difference between second energy maximum in strips and energy minimum in stripbetween maximum and second maximum energy strip, E2nd−Emin(E2nd ,E1st) = ∆ES

M2 Second largest energy maximum in strips normalised to cluster energy,Rmax2 = E2nd

EEMcluster

M3 Total shower width, wstot, calculated using a window of about 40 strips,

wstot =√

P

Ei×(i−imax)2P

Ei

M4 Shower width ws3, calculated using only ±3 strips around the most energetic one

M5 Fraction of energy outside three central strips, but within 7 strips, Fside =P7

i=3 Eicell

EEM cluster

Track quality cutsM6 Cuts on the number of hits in the pixel detector, NPi

M7 Cuts on the number of hits in the pixel and the SCT detectors, NPi+Si

M8 Transverse impact parameter, D0tight ID cuts

(L1-L5 and M1-M8 included)Tracking and vertex cuts

T1 Number of hits in the first layer of the Pixel detector (so-called B-layer), NBL

T2 Cuts on ∆η between cluster and trackT3 Cuts on ∆φ between cluster and trackT4 Cut on E/p

TRT cutsT5 Number of hits in TRT, NTRT

T6 Fraction of high threshold hits of total hits, fTRT =NTRThigh

NTRT

T7 Fraction of high threshold hits of total hits, fTRT =NTRThigh

NTRT(tightend cut, ǫ=90%)

Isolation cuts (these can be dropped in favour of a set of tightened TRT cuts)T8 Ratio of ET in a cone of ∆R = 0.45 to EEM cluster

T , Econe45T

Table 5.1: Electron identification cuts.

55

• Topological Clusters: The reconstruction of topological cell clusters is analternative to the use of towers in jet reconstruction [72]. The topo clus-ters are formed around seed cells, exceeding a specified signal-to-noise ratio,|Ecell/σnoise

cell| = |Γ| > 4. All direct neighbour cells in all three dimensions of each

seed cell are collected into the cluster. In case any of these added cells exceeds|Γ| > 2, their respective neighbour cells are again checked for their signal-to-noise ratio and added if |Γ| > 2. This is repeated until all neighbouring cellswith |Γ| > 2 are added to the cluster. Finally, all neighbouring cells of the outercells of the clusters are added if they fulfil |Γ| > 0. After the clusters havenbeen formed, they split between local energy maxima.

• Topological Towers: A compromise of these two cell combination schemes arethe so-called topological tower, topo towers. In this scheme, firstly the abovedescribed topo clusters are formed, then only the cells retained in the clustersare filled into the towers.

On MC generator or truth level, all stable final state truth particles of agenerated event are used as inputs to the jet finding step to form truth level jets. Ontruth level, no magnetic bending is taking into account.

5.2.2 Jet Algorithms

Jet algorithms combine four-momenta into final state jets, where the specifics of the jetfinder depends on the event topology to be considered. For example, narrow jets areadvantageous when narrow resonances, like W → hadrons, are to be reconstructed orwhen busy final states are to be considered, e.g. tt production. Wide jets on the otherhand should be used in inclusive jet cross section measurements to make sure thatthe kinematics of the hard scattered partons are completely captured and no energyfrom small angle initial or final state radiation is lost. All Atlas jet finders use afull four-momentum recombination scheme whenever adding, removing or otherwisechanging the constituents of a jet.

There exist two classes of jet algorithms, cone algorithms as well as sequentialrecombination algorithms (or kT-style algorithms), both of which are presently usedfor studies at Atlas:

• Atlas cone algorithm: Atlas cone jets are built by an iterative seededfixed-cone jet finder. The cone parameters used in Atlas are Rcone = 0.4 andRcone = 0.7 for narrow and wide jets respectively, it follows the cone algorithmdescribed in [74]. Only inputs above pT seed >1 GeV are considered as seeds inthe jet finding process. After jet finding, overlapping stable jets are split if theirshared pT , is below a fraction f= 0.5 and merged into one jet otherwise.

• Atlas kT algorithm: The principle of successive combination jet algorithmsare described in [75, 76]. In its Atlas implementation the kT algorithm calcu-lates for all pairs ij of inputs the distance dij, defined by

dij = min(p2T,i, p

2T,j)

∆R2ij

R2= min(p2

T,i, p2T,j)

∆η2 + ∆φ2

R2(5.1)

56

The two objects with the minimum dij between them are combined into a newobject, which is added to the input list, whilst i and j are removed. If theminimum dij is in fact a dii, it is considered a jet and removed from the inputlist. This procedure is iterated until all objects are moved from the list. R is ameasure for the width of a jet and at Atlas R =0.4 and R =0.6 are used.

• Atlas anti-kT algorithm: The anti-kT algorithm is described in [77]. It is verysimilar to the kT algorithm in that it is a successive combination jet algorithm,but it is very conical, which is an advantage for experimental jet calibrationand underlying event subtraction. Also the jet formation and in particularthe boundaries between jets are not influenced by soft particles but only byhard radiation. For the anti-kT algorithm, for all pairs ij of inputs the relativedistance dij, defined by

dij = min(p−2T,i, p

−2T,j)

∆R2ij

R2= min(p−2

T,i, p−2T,j)

∆y2 + ∆φ2

R2(5.2)

is calculated. Then the successive recombination is performed just like for thekT algorithm. Atlas uses R =0.4 and R =0.6.

5.2.3 Jet Calibration

There are two principle calibration methods used in Atlas , the local hadronic aswell as global calibration method. They shall be shortly presented in the following.

Global Calibration

The global calibration approach is based on physics objects. It attempts to restore inone step the relation between the partons or physics objects from the generator leveland the reconstructed physical objects. Here, all physics objects are reconstructed onuncalibrated energy deposits, which might be up to 30% off due to non-compensation.The calibration constants are determined inclusively, correcting for calorimeter anddetector effects as well as for biases coming from the reconstruction algorithm of thephysics object. This means that the calibration constants dependent inseparably onmany factors and are inherently physics dependent.

The global calibration is based on the energy densities1 of the calorimeter cellsbelonging to a reconstructed jet. This calibration scheme uses the general featurethat the measured energy density in a calorimeter cell is typically much lower forhadronic showers compared to electronmagnetic showers of incident particles of thesame energy, since the energy deposits of hadronic showers are partly not detectable.Also, hadronic showers are generally more spread out than electronmagnetic showersand thus deposit their energy over a larger spatial volume.

The global calibration makes use of generated and fully simulated dijet samplesto derive the weighting, where reconstructed jets are matched to the truth particles

1Therefore it is also commonly called H1 calibration within the Atlas collaboration, since the H1experiment [78] first made prominent use of a software compensation scheme using energy densitiesfor a LAr calorimeter after it had been pioneered by CDF [79]. It should however be noted, that atH1 the calibration was performed at cell level and never with regard to any reconstructed jets.

57

level jets using a spatial matching criterion of ∆R< 0.3. Over the full statistics a fitis performed, that minimises the χ2 between the energies of all reconstructed jets andtheir corresponding truth jets,

χ2 =∑

jets

(

Erecocalib − Etruth

Etruth

)2

(5.3)

where the calibrated energy of the reconstructed jets is calculated as:

Erecocalib =

Ncells∑

i

EiH1 =

Ncells∑

i

10∑

k=1

16∑

j=1

wikje

ikj +

7∑

k=1

vike

ik . (5.4)

.Here, the wkj are weights for each cell within a calorimeter layer k with a certain

energy density that falls into a bin j. There are certain layers without energy densitysegmentation, Presampler cells, first layer of electro-magnetic calorimeter cells, cryo-stat and gap scintillators, which receive consequently a weight denoted by vk, thatonly depends on the layer. Using a 3rd or 4th polynomial function to parametrise theweights in a given layer and also using the parametrisation of the energy densities inbins, the minimisation fit to obtain the weights has 45 free parameters.

This weighting in terms of energy density takes care of fluctuations of the mea-sured energy due to fluctuations in the hadronic showers. However, there might bestill residual residual non-linearities in transverse momentum pT and non-uniformitiesin azimuthal angle η. These fluctuations of the measured energy are cause by inhomo-geneities of the calorimeters and are corrected by an additional calibration functionparametrised in both variables. The energy density weights were found to dependvery little on the jet algorithms and are thus only obtained for one of the standardjet algorithms, while the pT -η corrections for linearity are to be determined for eachof the jet algorithms individually [67].

Local Calibration

The local hadron calibration method tries to break down the calibration procedureinto individual correction steps [80] for detector effects, specifically hadronic non-compensation, dead-material and effects of calorimeter reconstruction, and effects ofjet reconstruction. The local hadron calibration weights are applied to the topo clusterbefore the jet finding step, only after the weighting jets are reconstructed from thepre-calibrated detector objects. There still have to be physics-dependent correctionsapplied but they are much smaller compared to the global correction factors. Theactual weighting is largely based on the energy density in the cells like for the globalcalibration, however instead of using an inclusive dijet sample as truth reference, asingle pion particle sample of π± and π0 is generated and simulated and used as truthreference.

• Classification: Topological clusters, the input for the local hadronic calibra-tion, are classified as electromagnetic, hadronic or unknown. This is done forthe different |η|-regions based on cluster energy, cluster depth in the calorimeterand average cell energy density and the expected number of neutral and charged

58

pions in logarithmic bins of these quantities. For pions above 100 GeV the clas-sifications are correct 90% of the time, dropping to about 50% at 10 GeV. Onlyhadronic clusters are further processed in the hadronic weighting procedure.

• Hadronic weighting: The hadronic weights are derived as w = Etrue/Ereco foreach cell using Monte Carlo detector simulation [81], where the true energy isthe sum of visible energy deposits as well as invisible energy deposits. This isdone depending on the cluster energy and cell energy density for the individualcalorimeter samplings in 0.2-wide |η|-bins.

• Out-of-cluster (OOC) corrections: Since the jet finding takes as input onlythe topo cluster, their energy needs to be correct for energy deposited in thecalorimeters but not clustered into topo clusters due to the noise cuts. TheOOC corrections are derived depending on |η|, cluster energy, the cluster depthand isolation of the cluster.

• Dead material (DM) corrections: DM corrections compensate for energydeposits in insensitive regions of the detector, e.g. the cryostat and the gapregions. The corrections are obtained using a combination of fits and geometricalmeans in regions, where there are cluster observables highly correlated to thedead material energy losses, or look-up table binned in cluster energy, |η|, andshower depth, where there are no clear correlations.

After the hadronic calibration, jets are built from calibrated topo clusters, whichshould reflect the momenta of the incoming particles much closer than EM scaleclusters. Locally calibrated jets should thus reproduce more accurately the truthparticles jets. However, there are some inherent jet corrections that should be appliedto account for magnetic bending of particles out of the jet and particles not reachingthe calorimeters but being absorbed in the inner detector. These jet corrections arestill under active development [82].

5.2.4 Performance of the Jet Reconstruction

For measurements of the W asymmetry in the presence of jets and as a function ofvarious jet parameters, as described in appendix A, the reconstruction of jets needsto be well understood. As a preparation for these types of W+jet asymmetry mea-surements, in the context of this thesis a software framework has been developed toinvestigate jet performances in terms of linearity and resolution but also efficiency andpurity at Atlas . This work resulted in various publications, that shall only shortlybe cited here as reference for future work.

Firstly, two variations of the local hadronic calibration scheme are compared ina public Atlas note [83] and found to perform very similar – both still needingadditional genuine jet corrections on top of the hadronic calibrations. The quality ofthe different stages of the local hadronic calibration procedure is reviewed in a paperdescribing the expected performance of the Atlas detector, a public Atlas note [67].A general evaluation of the jet reconstruction performance at Atlas is presented inthe Atlas detector paper [61]. The linearity and resolution for various calibrationschemes for the anti-kT jet algorithm meant to be used for first data is detailled inan internal Atlas note [84] The software framework developed by the author of this

59

thesis and used to derive these findings on jets is shortly described in internal Atlas

documentation [85].

5.3 6ET Reconstruction

Transverse missing energy, 6ET , at Atlas is reconstructed by vectorially summingthe energy deposits in the calorimeters and muon system. The unbalanced energyindicates the presence of either an undetected particle or flaws in the calorimetercalibration or the muon reconstruction.

The Atlas 6ET reconstruction algorithm uses all calorimeter cells contained intopological clusters, because these efficiently suppress noise. The cells are initiallycalibrated using global calibration weights. In a second step, all cells that can beassociated to high pT objects in the event, are recalibrated according to the calibra-tion of this high pT object. The order in which possible objects are considered is thefollowing: electrons, photons, hadronically decaying τ -leptons, b-jets, light jets andmuons. To this refined 6ET calculation, the muon energy is added. This energy is mea-sured purely with the muon spectrometer, so that there is no double counting of muonenergy deposited in the calorimeter and the muon spectrometer. Finally a correctionfor energy losses in the cryostat between the barrel LAr electromagnetic calorimeterand the tile calorimeter is applied. Then 6ET is calculated as the unbalanced energyof calorimeter deposits, muon contribution and cryostat term.

Chapter 6

W → eν Candidate Event Selection:Signal and Backgrounds

This chapter discusses the signal and background samples used in this investigationof a measurement of the lepton asymmetry at Atlas .

6.1 Investigated Backgrounds

This measurement is selecting W bosons decaying into a single isolated electron orpositron and a neutrino, W → eνe. This provides a clean experimental signaturewith a lepton and missing transverse energy in the detector. The following events canmimic this signature and need to be taken into account as backgrounds:

• Z → ee : Events where one of the electron candidates from a Z decay is misre-constructed or escapes the detector acceptance can mimic W → eν events.

• W → τν : This class of events contains two neutrinos and therefore true missingtransverse energy and as the τ can decay into an electron, W → τν is anirreducible background and thus needs to be investigated.

• tt final state: The decay of the t quark involves a real W, so this process isagain a serious background.

• QCD dijets, prompt photons: Jets (or photons) can be misidentified asisolated electrons. Dijet and prompt photon events can also contain fake 6ET ,unbalanced transverse energy, due to mismeasurements of energy in the detector.Therefore, these types of events can mimic the signature of a genuine W → eνevent. Since the production of dijets and prompt photons is expected to be themost abundant hard process at the LHC, this is one of the biggest backgrounds.

Description of simulated Datasets used

All datasets used in this analysis were generated with the Monte Carlo programmePythia [86] using CTEQ6LL PDF [27], with the exception of the tt sample, thatwas generated with MC@NLO [87]. All samples are fed through a simulation ofthe Atlas detector and the trigger system using Geant4[81], the reconstruction

60

61

is performed using the Atlas specific software Athena. The Athena softwareversion is indicated in the name of the dataset, v1300x. The dataset name alsocontains a reference to an Atlas specific data set number and an abbreviation ofthe generated process, e.g 005104.PythiaWenu. The tag misal1 specifies that in thesimulation additional material was added to the nominal material budget in positiveφ as detailed in appendix C, despite the name there is no inner detector misalignment.The following datasets are used:

• W → eν : trig1 misal1 mc12.005104.PythiaWenu.recon.ESD.v13003004withan integrated luminosity of 63.6 pb−1.

• Z → ee : trig1 misal1 csc11 V1.005144.PythiaZee.recon.ESD.v13003003,generated with a cross section of 1432 pb. The size of the dataset correspondsto 264.3 pb−1.

• W → τν : trig1 misal1 mc12.005108.PythiaWtauhadNoEF.recon.AOD.v13003002

with a cross section of 17312.5 pb, corresponding to 10.8 pb−1.

• tt : trig1 misal1 mc12.005200.T1 McAtNlo Jimmy.recon.ESD.v13003004 witha cross section of 461 pb and an integrated luminosity of 1822.5pb−1.

• QCD dijets, γ: trig1 misal1 mc12 V1.005802.JF17 Pythia jet filter.r-

econ.ESD.v13003002 with a cross section of 1.91 × 108 pb , corresponding toan integrated luminosity of 0.02pb−1.

6.2 Event Selection

The event selection on the W candidates follows the strategy in recent Atlas publica-tions [67]. W → eν events are selected online using an lepton trigger with a thresholdof 20 GeV, the leptons from the W decays are reconstructed and identified using aset of cuts with medium efficiency and rejection rates, described in [67]. These eventselection cuts and the further kinematic cuts employed are summarised in table 6.1.

The number of events selected after each cut employed in the analysis is given intable 6.2, the corresponding efficiency is calculated as

ǫ =#events passing the cut

#generated events of that dataset(6.1)

Table 6.3 gives the efficiencies of each cut for the individual samples. It showsthat the trigger and ID as well as the 6ET cuts are most crucial in reject backgrounds.Firstly, by rejecting non-electron background (e.g. QCD dijets and W → τν ) andsecondly, by rejecting backgrounds that do not contain neutrinos (e.g. Z → ee andQCD dijets).

The percentage of background contamination is of the level of 44 % after the 6ET

cut (16% after the optional isolation cut). The QCD dijet sample has a very lowstatistics (37 events remain after all cuts up to the 6ET cuts, these 37 events need tobe scaled by a factor of about 5312) and the theoretical uncertainty on the QCD pro-duction is rather large, so that the QCD background could be over- or underestimated

62

Triggerselection EF: e20ID cuts medium [67]

Electron pseudorapidity |ηl| <1.37,1.52<|ηl| < 2.4Electron momentum pl

T > 25 GeVMissing ET 6ET > 25 GeVoptional:

Fractional isolation energy ET,isofrac < 0.1

ET in cone of ∆R around leptonnormalised to its energy (see section 7.2)

Table 6.1: Selection Cuts employed in the lepton asymmetry analysis.

Cut W → eν (± stat. ± sys.) Z → ee (± stat. ± sys.) W → τν (± stat. ± sys.)No Cuts 1730159 ± 1315 ± 2618 166512 ± 408 ± 292 1731250 ± 1316 ± 4003Acceptance 916196 ± 957 ± 1512 126972 ± 356 ± 236 766188 ± 875 ± 2663Trigger & ID 595579 ± 772 ± 1219 97778 ± 313 ± 207 28343 ± 168 ± 512pl

T 520303 ± 721 ± 1139 46199 ± 215 ± 143 18207 ± 135 ± 411ηl 506206 ± 711 ± 1124 44314 ± 211 ± 140 17643 ± 133 ± 4046ET 414634 ± 644 ± 1017 868 ± 29 ± 20 10265 ± 101 ± 308

ET,isofrac < 0.1 409060 ± 640 ± 1010 837 ± 29 ± 19 9654 ± 98 ± 299

Cut tt(± stat. ± sys.) QCD dijets (± stat. ± sys.) SS+B

(± stat. ± sys.)

No Cuts 85370 ± 292 ± 127 2.4e+11 ± 4.9e+05 ± 1.3e+08 7.2e-06 ± 5.5e-09 ± 0.0004Acceptance 43108 ± 208 ± 66 1.4e+10 ± 1.2e+05 ± 8.7e+06 6.5e-05 ± 6.8e-08 ± 0.0018Trigger & ID 11663 ± 108 ± 34 1.5e+07 ± 3.9e+03 ± 282934 0.038 ± 4.8e-05 ± 79pl

T 9526 ± 98 ± 31 6.9e+06 ± 2.6e+03 ± 191452 0.069 ± 9.3e-05 ± 1.9e+02ηl 9438 ± 97 ± 31 6.6e+06 ± 2.6e+03 ± 187807 0.07 ± 9.5e-05 ± 1.9e+026ET 8205 ± 91 ± 29 196543 ± 443 ± 32311.5 0.66 ± 0.0006 ± 1.3e+04

ET,isofrac < 0.1 8035 ± 90 ± 29 58431.7 ± 242 ± 17617.8 0.84 ± 0.00052 ± 2.1e+04

Table 6.2: Number of events selected in the W analysis by dataset. All datasets werescaled to an integrated luminosity of 100 pb−1. The errors given are the statisticalerror, calculated using the scaled statistics of 100 pb−1 and systematical error causedby the limited statistics of the generated datasets and calculated on the actual numberof events in the generated datasets.

W → eν Z → ee W → τν tt QCD dijetsǫ ǫ ǫ ǫ ǫ

Acceptance 0.53 0.76 0.44 0.5 0.059Cut ǫ ǫ ǫ ǫ ǫTrigger & ID 0.34 0.59 0.016 0.14 6.3e-05pl

T 0.3 0.28 0.011 0.11 2.9e-05ηl 0.29 0.27 0.01 0.11 2.8e-056ET 0.24 0.0052 0.0059 0.096 8.2e-07

ET,isofrac < 0.1 0.24 0.005 0.0056 0.096 2.4e-07

Table 6.3: Efficiency of cumulative cuts for each dataset.

63

by a factor 3 as stated elsewhere [67]. To determine the QCD background contribu-tion to the W → eν candidate sample accurately is one of the biggest challenges in ameasurement of the lepton asymmetry at Atlas .

Chapter 7

Determination of QCDBackgrounds in the W CandidateEvent Sample

There is a large numbers of ways in which a jet of partonic origin (quark or gluon) canmimic the signature of an electron1. Although the probability that a jet is misidenti-fied as an electron is small (≈0.01%), the rate at which QCD jets events are producedat the LHC is so large (≈1 mb) that QCD jets constitute the dominant background tomost analyses involving electron selections. In the following, reconstructed electronsin the detector which are in fact of non-leptonic origin shall be called fake electrons.

Relying on Monte Carlo to model these fake electron backgrounds cannot reachthe level of precision needed in analyses, since the fake rate is highly dependent onthe finer details of jet substructure, that is details of how the partons hadronise andfragment into jets, which is not very well modeled by current Monte Carlo. In ad-dition, the theoretical uncertainty on multijet production as well as the underlyingevent and multiple interaction are very large. Thus, even if it was possible to knowthe probability of a jet to fake an electron with unlimited accuracy, there is no ac-curate theoretical estimation of the total number of jets that might fake electronsavailable. Therefore, the actual number of fake electrons would be still known onlyto a very limited precision. Last, but not least, even if there were a reasonably goodMC available and if it could predict the number of jets and the fraction of the onesmimicking electrons with great precision, this would not help much. The low fakerate combined with the large jet cross section and the long simulation time for fulldetector simulation requires a computing power that makes it near impossible to havesufficient statistics to evaluate the QCD backgrounds.

In this chapter, data-driven methods to estimate the residual background of fakeelectrons in the selected candidate signal events are discussed. These data-driven tech-niques suffer from smaller sources of systematic uncertainty than Monte Carlo-basedapproaches, while offering a reliable way to estimate those errors. In the following,the estimate of the fraction of fake electron background with its associated error isperformed in the context of QCD background to W analyses with early Atlas data.The optimisation of the cuts to identify electrons and select very pure candidate eventsamples is not discussed, since this is a very different issue. In this chapter, the QCD

1In this chapter the term electrons will be used for both electrons and positrons.

64

65

background fraction or background rate is defined as the fraction of the number ofQCD events, NQCD, to the total candidate sample, being the sum of the number of allsignal events (plus possible other backgrounds such as Z → ee and tt) and all QCDevents, NQCD + Nsignal,

RQCD =NQCD

NQCD + Nsignal

(7.1)

7.1 MC Data Samples

If not explicitly stated otherwise, the MC samples used here are generated and recon-structed in the Athena framework at a centre of mass energy of

√s = 10 TeV. The

QCD dijet sample used to develop and test the fake background estimate methods isgenerated using LO Pythia at a centre of mass energy of 10 TeV. A minimum cut ofET > 15 GeV is applied to the hard scatter. The following final states were includedproportional to their respective cross sections: qq, qq, gg, qg, QQ, qγ, gγ, Z0 andW±, with q=u,d,s,c,b and Q = t. In summary, the dataset contains all hard QCDprocesses, prompt photon production, tt production as well as electroweak processes2.Before detector simulation (done with Geant4[81]) an event filter is run in order toonly perform simulation on events where there is a higher change of the occurrenceof a jet faking an electron. The filter selects event for which the summed transverseenergy of all generated stable truth particles except muons and neutrinos in a regionof ∆φ×∆η = 0.12 × 0.12 is found to be bigger than 17 GeV (ET

0.12×0.12stable truth > 17 GeV).

Once corrected for the filter efficiency of 7.1 × 10−02, the final data sample is freeof significant bias and can be used for proofs of principle and method developments.The 8.2 millions of events of the simulated and reconstructed sample correspond toan integrated luminosity of 0.08 pb−1. Table 7.1 gives an overview over this and otherdata sets used with their integrated luminosity.

Sample Name of data set integratedluminosity

QCD dijet sample mc08.105802.JF17 pythia jet filter.recon.AOD.e347 s462 r563 0.08 pb−1

Z → ee sample mc08.106050.PythiaZee 1Lepton.recon.AOD.e347 s462 r541 1973 pb−1

W → eν sample mc08.106020.PythiaWenu 1Lepton.recon.AOD.e352 s462 r541 99.9 pb−1

tt sample mc08.105200.T1 McAtNlo Jimmy.recon.AOD.e357 s462 r541 2371.4 pb−1

Table 7.1: Datasets used for QCD background studies

7.1.1 Origin of the Reconstructed Electron

To avoid biases in the estimates that can be caused by the electroweak processes,Z0 and W±, included in the filtered dijet sample, all non-QCD events must be re-

2The intention was to have a data set that would contain the most common Standard Model hardscattering processes that could be observed at Atlas with the appropriate contributions. It shouldbe noted that only for QQ final states, the quark mass is properly accounted for. Specifically, thePythia processes switched on in the generation step are: 1, 2, 11, 12, 13, 14, 28, 29, 53, 68, 81 (fortt), 82 (for tt)

66

moved from the sample, especially the W → eν events, in order to obtain a pureQCD background sample. As a first step, the QCD background is selected by re-quiring both the outgoing partons of the hard scatter on truth level to be either aquark, a gluon or a photon. tt events are excluded. In order to make sure that thisclassification scheme works and none of the electron candidates in the QCD eventscomes from a W → eν produced in a Drell-Yan process, a special Athena tool, theegammaMCTruthClassifier [88] is used. This tool matches electron and photon can-didates to truth particles, including GEANT4 particles, and classifies them accordingto their origin, e.g. hadronic (baryons, mesons etc.), isolated (Z or W from Drell-Yanprocesses), non-isolated electrons (weak decays, charm and bottom hadrons, J/ψ).The tool can also specify the actual mother particle of the found electron (e.g. Wor Z or J/ψ or photon conversion)3. This tool is used in a second step, in whichthe origin of each electron candidate in the preselected events is checked. For QCDbackground events, all electrons coming from Drell-Yan Z and W s are omitted. Whenusing pure Z → ee and W → eν samples, the matching procedure is omitted and allselected electron candidates are taken to be W → eν and Z → ee signal electrons.

7.2 The ”6ET vs. Iso” Method

This method has been used in previous CDF analyses to determine the QCD back-ground to W → eν signal samples [89, 46]. It assumes that the isolation energy ofan electron object is sufficiently uncorrelated to the 6ET of the event involving thiselectron object to be able to produce three different control samples, rich in QCDevents and poor in W → eν events, which can be used to obtain an unbiased esti-mate of the QCD background in the W → eν signal region. The absolute isolationenergy is defined as the total transverse energy collected in a cone of a certain size∆R =

√

∆η2 + ∆φ2 around the reconstructed cluster of the electron with the electrontransverse energy being subtracted from that total:

ET,isoabs (∆R) = ET

cone(∆R) −ETelectron cluster (7.2)

In the following only cone sizes of ∆R = 0.2 are used. This isolation energy caneither be measured by summing up the transverse energy of calorimeter cells in thechosen cone (calo iso), or the transverse momentum of the tracks surrounding theelectron cluster (track iso). Additionally to absolute, also fractional isolation energycan be studied. Fractional isolation is the absolute isolation energy normalised to theelectron transverse energy:

ET,isofrac =

ET,isoabs

ETelectron cluster

(7.3)

The advantage of the normalised version of the isolation definition is that it sig-nificantly reduces the ET dependence of the selection, allowing for a more robust

3The egammaMCTruthClassifier uses a cut of ∆R=√

∆φ2 + ∆η2 < 0.2 in the matching pro-cedure. For a photon candidate, its reconstructed calorimeter position is used. For an electroncandidate, its track parameters are used in the matching procedure. If the track of an electroncandidate is reconstructed from less than 3 SCT hits, instead of the ∆R cut only a ∆φ < 0.2 cut isapplied.

67

[GeV] missTE

0 20 40 60 80 100

Fra

ctio

nal I

sola

tion

0

0.2

0.4

0.6

0.8

1

5

10

15

20

25

30

35

40

A

B

C

D

Figure 7.1: An example of the ” 6ET vs. Iso” histograms used in the ” 6ET vs. Iso” Wbackground analysis. The plot depicts the QCD jet data with the event populationof each bin being represented by its grey shading as indicated. The W → eν signaldata is depicted as triangular markers, after the application of the selection cuts onthe used QCD dijet data sample. Medium electron identification cuts were used inboth cases.

efficiency estimate. In general, fake electrons have a much larger isolation energy, dueto hadronic activity around the fake electron. The 6ET in QCD events comes froma mismeasurement in the energy of the jets, and therefore tends to be significantlylower than in W → eν events where the 6ET , mainly due to the neutrino νe, has a realphysics origin.

The ” 6ET vs. Iso” method for determining the QCD background in a W candidatedata sample events uses a two-dimensional plot of ” 6ET vs. Iso” for events passingthe electron selection cuts used in standard W candidate event selection (see section6.2), except for isolation and 6ET cuts. An example of such a ” 6ET vs. Iso” plotusing fractional calorimeter isolation with ∆R=0.2 is shown in figure 7.1, where thebackground events are shown using a grey shading, and the signal events are depictedusing black markers. The two-dimensional plot of ” 6ET vs. Iso” is divided into fourregions, named A, B, C and D as indicated, and are separated by boundaries referredto as the low/high isolation and low/high 6ET boundaries. Additionally a minimum6ET cut is indicated by a dashed line. These boundaries are used to remove partsof the control regions which are significantly contaminated by W → eν signal, andwhich therefore bias the QCD background prediction. Region D is the signal region– it contains events with isolated electrons (that is with small fractional isolationvalues and large 6ET ). The number of background events in region D is estimated bycomparing to control regions with either small 6ET or large isolation energy. With theassumptions that isolation and 6ET are uncorrelated, and that the control regions A,B and C are dominated by background events, the QCD background and fractional

68

QCD background in region D are determined by:

NQCD = NCNB

NA(7.4)

RQCD =Bkg

Signal + Bkg=

NC

ND

NB

NA(7.5)

where NX is the number of events in region X. The low 6ET boundary is set at 15 GeV,the high 6ET boundary at 25 GeV. For the fractional isolation the boundaries are setto 0.1 and 0.2 for a calo isolation of ∆R = 0.2, these numbers however have to beadjusted for different cone sizes as well as for the absolute values, whose boundariesare here taken to be 4.0 and 7.0 GeV. As can be seen from the plot, there is still somesignal contamination in the various regions, which are assumed to be signal free. Thiscould cause problems and there might be a need to subtract electroweak backgroundsfrom the ” 6ET vs. Iso” plot.

The assumption that isolation and 6ET are uncorrelated is checked by comparingthe isolation distribution in different 6ET regions. In order to quantify the probabilitythat the isolation distributions are consistent in each 6ET region, Kolmogorov-Smirnovtests4 have been performed. The similarity of the isolation distributions in different6ET regions is also checked graphically in figure 7.2. Here, fractional and absolutecalorimeter-based isolation are shown for different 6ET regions. The low 6ET region( 6ET < 15 GeV) is shown with red squares, while the mid region (15 < 6ET < 25GeV) is depicted as blue triangles and the high 6ET region (> 25 GeV) with blackedfilled circles. These distributions look consistent within statistical uncertainty. TheKolmogorov-Smirnov tests however reveal subtle differences: While the fractionalisolation distributions are very likely independent of the selected 6ET region, the resultsof the test indicate that selecting specific 6ET regions introduces a bias in the absoluteisolation distribution (see table 7.2).

4The Kolmogorov-Smirnov test is a statistical test to decide, whether two distributions are com-patible in shape. The distributions a and b must have exactly the same binning. The probability,whether distribution a and distribution b are the same is then calculated as:

P = 2∞∑

j=1

(−1)j−1 exp (−2j2z2) (7.6)

Here, z = Dmax × Ma∗Mb

Ma+Mb

, with Dmax being the maximum deviation of the cumulative distributionsof the two distributions a and b:

Dmax = max1≤k≤Nbins

{

abs

(

∑k

bin i=1 Nabin i

∑Nbins

bin i=1 Nabin i

−∑k

bin i=1 N bbin i

∑Nb

bins

bin i=1 Nbin i

)}

(7.7)

Ma,b are calculated for each distribution a, b as:

Ma,b =

(

∑Nbins

bin i=1 Na,bbin i

)2

∑Nbins

bin i=1

(

σa,bbin i

)2(7.8)

The Kolmogorov-Smirnov test is assumed to give better results than the χ2 test in case of his-tograms with low statistics. The closer the returned probability is to unity, the more likely is thatdistribution a and b are random samples of the same distribution [90, 91].

69

Fractional Isolation0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Nor

mal

ized

# e

ntrie

s

0

0.05

0.1

0.15

0.2

0.25 < 15 GeVTE0 GeV <

< 25 GeVTE15 GeV <

> 25 GeVTE

=0.2 [GeV]Cone

Isolation energy R0 5 10 15 20 25 30

Nor

mal

ized

# e

ntrie

s

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2 < 15 GeVTE0 GeV <

< 25 GeVTE15 GeV <

> 25 GeVTE

Figure 7.2: Isolation distribution for 6ET regions of: 6ET < 15 GeV, 15 < 6ET < 25GeV and 6ET > 25 GeV. For both fractional (left) and absolute (right) isolation thereis reasonable agreement between the distributions in all three kinematic regions of6ET .

The fact that the value of the test decreases when a lower 6ET range is selected,suggests the existence of a bias. In order to minimise this bias in the estimate ofthe QCD background using the ” 6ET vs. Iso” method, the low 6ET control regionmust be chosen to be as close as possible to the high 6ET signal region. A minimum6ET boundary or cut of 15 GeV is therefore introduced, with the intermediate 6ET

region shifted to 20< 6ET <25 GeV. With this new choice of cuts, the probability thatthe absolute isolation is independent of the new 6ET regions reaches 39%, indicatingthat the residual bias is small enough to be washed out by the statistical limitationof the sample. In table 7.2, the result of Kolmogorov-Smirnov tests on track-basedisolation distributions are also shown. These tests indicate that the bias introducedby an 6ET cut on track-based isolation distribution is too large to be viable in a QCDbackground estimate. These distributions will therefore not be investigated further5.

The QCD background fraction RQCD for medium electron cuts is estimated usingequation 7.5 and is presented in table 7.3 with the corresponding statistical errorsand systematic uncertainty. RQCD is estimated for absolute and fractional isolation,both using the standard 6ET regions as well as the minimum 6ET cut and the shiftedboundaries for the 6ET cuts. In order to evaluate the performance of the ” 6ET vs. Iso”method, comparisons of the estimate with the true value of RQCD in the sample isalso provided.

The present studies on the ” 6ET vs. Iso” method are performed on pure dijetbackgrounds and a pure signal sample. However, it can be expected that there will bean additional contribution to the systematic error coming from several backgrounds.These backgrounds come from events which contain real electrons such as Z → ee ,

5It is not yet fully understood, what the cause of the correlation is. One possible cause is thefollowing: A recent study found a bias in the Atlas 6ET reconstruction [92]. This bias is probablydue to soft particles that are absorbed in the inner detector and never reach the calorimeters, thuscontributing to the 6ET calculation by appearing to be missing transverse energy. They still contributeto the calculation of track isolation, because they are still detected in the inner detector. Becausethese soft particles contribute to the track isolation and contribute to (fake) 6ET , they introduce to acertain degree a correlation between these two variables. For the calorimeter isolation this correlationcan not be observed, because to the calculation of calorimeter isolation only those energy depositscontribute, that are also fully accounted for in the transverse energy balance.

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Kolmogorov-Smirnov probability for isolation distributionsin 6ET region A and B to be the same

6ET region A 6ET <15 GeV 15< 6ET <20 GeV 15< 6ET <25 GeV 20< 6ET <25 GeV6ET region B 25 GeV< 6ET 25 GeV< 6ET 25 GeV< 6ET 25 GeV< 6ET

Isolation distribution Probability valuesfractional calo iso 0.85 0.99 0.99 0.98absolute calo iso 0.006 0.39 0.15 0.50fractional track iso 1.5e-06 0.0007 0.003 0.02absolute track iso 1.5e-06 0.002 0.01 0.05

Table 7.2: Kolmogorov-Probabilities for isolation distributions in different 6ET regionsto be the same distribution. The lower the quoted probability values, the lower theprobabilities for the isolation distributions in the 6ET regions A and B to be the same.

W → τν and tt. The effect of the additional backgrounds is investigated by addingZ → ee, W → τν and tt samples scaled to the luminosity of the QCD dijet sampleinto the sample. The resulting numbers of the QCD background estimate are alsolisted in table 7.3. It should be noted that the deviation of the QCD backgroundestimates with EWK background included and the QCD background estimates usingonly pure QCD and W sample is an extreme case and an upper limit on how differentthe estimate could be. It would be possible to remove EWK backgrounds, since theyare in general well described by MC. The removal procedure is not carried out in thisstudy due to the lack of reliable statistics.

In order to estimate the systematic uncertainties, the boundaries defining thefour regions are varied and the estimated background RQCD calculated as a functionof the boundary location. The true value of RQCD in the signal region defined bythe low isolation and the high 6ET boundaries does not depend on where the otherboundaries (high isolation, low and minimum 6ET ) are chosen to be. Neither should theestimated value of RQCD depend on where the high isolation, low and minimum 6ET

boundaries are chosen to be. The fact that the estimated RQCD does vary dependingon the boundary location indicates a systematic effect due to the boundaries – evenif the dependence does not seem to be statistically significant. This is because theestimates for the different boundary locations are actually highly correlated, becausethey consist to a large extent of the same events. If the estimates still vary dependingon the location of the boundary, this indicates a systematic effect. The systematicerror for a specific boundary is calculated as the average of maximal and minimalestimation for RQCD over the entire region where that boundary is varied:

σboundary = (RmaxQCD − Rmin

QCD)/2 (7.9)

The total systematic error from the variation of all boundaries is the sum of theindividual errors in quadrature.

The variation of the background fraction estimate, RQCD, as function of the bound-ary positions is shown in figure 7.3 for the fractional isolation. Figure 7.3 a) showsthis variation as function of the low 6ET boundary position. As is clear from figure 7.1there is more signal contamination present in region B than in A. Therefore, as thelow 6ET boundary is raised, the signal contamination in region B slightly increases, andthus the estimated background increases and moves further away from the nominal

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Figure 7.3: Plots used in the systematic error

calculation: Here the dependence of the back-

ground estimate as function of (a) the low 6ET

(20 GeV), (b) high isolation (ET,isofrac < 0.2), (c)

the minimum 6ET (15 GeV), (d) the high 6ET (25

GeV) and (e) the low isolation (ET,isofrac < 0.1)

boundaries are shown. The estimated back-

ground is depicted in red, open circles and the

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ror bars show the statistical errors. It should

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value. Figure 7.3 a) exhibits this behaviour and is used to determine the systematicuncertainty.

Figure 7.3 b) contains the fractional background as a function of the high isolationboundary. In this case, the difference in the signal contamination of regions C and Aof figure 7.1 is not apparent. However, if there is any residual effect, it is accountedfor in the systematic uncertainty, again estimated as half the total variation of thebackground fraction when the high isolation boundary is varied from 0.1 to 0.3. Sim-ilarly, figure 7.3 c) shows the variation of the estimated fractional background as afunction of the minimum 6ET boundary, i.e. the minimum 6ET cut. The blue lines inall these plots mark the choice of boundaries used in the nominal background deter-mination. The systematic errors that are extracted from these plots are summarisedfor all investigated samples in table 7.4.

Figures 7.3 d) and e) contain the estimated and true fractional backgrounds asfunctions of the high 6ET and low isolation boundaries respectively. Here a variationof the background fraction with the chosen boundary is expected, because for bothfigures the boundary is varied that actually selects the W candidate event sample orthe signal region, for which RQCD is determined. When decreasing the 6ET selectioncut, the fraction of QCD background will increase, since QCD events contain less6ET compared to W → eν events (figure 7.3 d). When making harsher cuts on theisolation, less QCD background will be found in the selected signal events, since inQCD events the fractional isolation is in general considerably larger (figure 7.3 e).These features can be observed in both the estimated and the true QCD backgroundfraction, which agree very well within statistical uncertainty. No systematic errorshould be attributed to this effect, since it is consistent with the expected behaviourand there is no way to disentangle, how much of the variation can be contributed tosystematical effects as opposed to physical effects.

Estimated background ± stat. ± sys. (±tot.) True backgroundfractional 10.9% ±1.9% ±1.4% (±2.5%) 8.7%with 6ET min. cut 9.40 % ±1.8% ±2.0% (±2.8%) 8.7%fractional with bkg. 10.6% ±2.0% ±1.3% (±2.3%) 8.7%with 6ET min. cut 9.20% ±1.9% ±1.8% (±2.6%) 8.7%absolute 18.0% ±2.4% ±2.2% (±3.3%) 9.3%with 6ET min. cut 13.8 % ±2.1% ±1.7% (±2.8%) 9.3%absolute with bkg. 17.6 % ±2.3% ±2.3% (±3.3%) 9.3%with 6ET min. cut 13.6 % ±2.1% ±1.9% (±2.9%) 9.3%

Table 7.3: ” 6ET vs. Iso” estimations for QCD background fractions. The estimateobtained using a minimum 6ET cut yields the best result.

The ” 6ET vs. Iso” method yields a background fraction estimate of RQCD=10.9%±1.9% (stat.) ±1.4% (sys.) using the fractional definition of isolation. This estimateis consistent within errors with the true QCD background fraction of RQCD=8.7%.However the prediction of RQCD=18.0% ±2.4%(stat.) ±2.2%(sys.) obtained with theabsolute version of the isolation definition is in complete disagreement with the truevalues. If a minimum 6ET cut is applied to the low 6ET control regions, both estimatesmove closer to the true background fraction RQCD, becoming for the fractional iso-lation RQCD=9.4% ±1.8% ±2.0% and for the absolute isolation RQCD=13.8% ±2.1%±1.7%.

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high isolation line low 6ET line min. 6ET cut total syst. σfractional 1.0% 0.4% 1.0% 1.4%with 6ET min. cut 1.0% 1.4% 1.2% 2.0%with backgrounds 0.9% 0.2% 0.9% 1.3%with bkg. and 6ET min. cut 0.7% 1.3% 1.1% 1.8%absolute 1.0% 0.6% 1.9% 2.2%with 6ET min. cut 0.6% 1.1% 1.1% 1.7%with backgrounds 0.9% 0.7% 2.0% 2.3%with bkg. and 6ET min. cut 0.7% 1.4% 1.1% 1.9%

Table 7.4: Systematic errors for the ” 6ET vs. Iso” estimations for QCD backgroundfractions

The fact that a minimum 6ET cut improves the ” 6ET vs. Iso” method, confirms aslight correlation between isolation and 6ET . Indeed, in figure 7.1 for the very low 6ET

region, fewer events for high isolation values can be observed than for higher valuesof 6ET . The reason is possibly a cut on the hadronic leakage that is applied in theelectron trigger selection. The bias can however be kept at a sufficiently low levelfor a consistent background estimate by choosing the low 6ET control region close thehigh 6ET signal region.

The ” 6ET vs. Iso” method is also stable again other backgrounds: Adding inbackgrounds such as Z → ee , tt and W → τν does not effect the QCD backgroundestimations significantly even when no attempt to remove the background is made.

7.3 The Photon Extrapolation Fit Method

The Photon Extrapolation Fit method uses photon events in order to model the 6ET

distribution of fake electron + 6ET events and relies on the usage of a sample almostpurely consisting of background. It uses the fact, that in photon events there isno source of genuine 6ET . Thus, photon events with significant amounts of 6ET aredominated by fake photons, and are basically QCD dijet events. The 6ET distributionof these fake photon events can be used to model the 6ET distribution of fake electron+ 6ET events. The photon events are used as background control sample topredict the background contamination of the W → eν candidate event sample.The W → eν candidate sample is the data sample selected for W → eν analysis. Itcontains real W → eν event but also fake electron. These need to be removed in orderto get a pure W → eν signal control sample. The method was first described in[67], using MC data produced and reconstructed with an earlier version of the ATLASsoftware. Here the same analysis is repeated using 10 TeV centre of mass energy andwith systematic error analysis. The basic procedure is:

1. Photon sample selection: First the photon sample, in the following alsocalled the background control sample, is selected using a single photon trigger(ET > 20 GeV and some identification cuts as described in section 5.1.3). Onthis sample, the same kinematic cuts as on the electron in the W → eν signalselection are employed, namely: pl

T > 25 GeV, |ηl| < 1.37 or 1.52 < |ηl| < 2.4.The photon is required to be reconstructed and identified using medium ID cuts

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for photons6. No other medium ID photon above 15 GeV must be found. Onthis sample no 6ET cut is applied.

2. Selection of the W → eν candidate sample: The W → eν candidatesample is selected using the similar cuts as for the photon selection: An EMtrigger with ET>20 GeV is used with a basic set of electron ID cuts, e20 loose,then the kinematic cuts of pl

T > 25 GeV, |ηl| < 1.37 or 1.52 < |ηl| < 2.4 areapplied. Additionally only one electron candidate above pl

T > 15 GeV is allowedin a selected event.

3. Extrapolation and normalisation of the photon+jet sample: The 6ET

distribution can be fitted using the following phenomenological parametrisation,which was chosen because it describes the distribution reasonably well:

fbkg(x) = (1 + ax)2 × e−bx (7.10)

The fit is restricted to an 6ET range, where the contamination of the backgroundsample by signal, e.g. electrons from W → eν misidentified as photons, isexpected to be small. The extrapolation fit is used to predict the slope of the fakeelectrons 6ET distribution7. The normalisation of each extrapolated distributionis obtained by comparing it to the amount of events selected for the W → eνcandidate signal sample in a control region over a specific normalisation range.The normalisation range used here is 10 < 6ET < 17 GeV. Two fit ranges are used,10 < 6ET < 22 GeV (low fit range) and 20 < 6ET < 35 GeV (high fit range).It was checked on an independent, high statistics W → eν signal sample, thatthe amount of photons (or rather electrons misidentified as photons) from thesignal W → eν sample selected for the control sample was considerably low:less than 3% for the high fit range, less than 0.2% for the low fit range and lessthan 0.05% for the normalization range. The numbers are also summarized intable 7.5. The contribution of real W → eν electrons to the background samplecould be reduced by applying additional cuts on the photons, e.g. requiring theirisolation energy to be above a certain value, since this enhances the background.

4. Prediction of the background: The final selection cut of 6ET > 25 GeVis applied to the W → eν candidate sample after the extrapolation fit to thephoton+jet background sample has been normalised to the number of signalcandidate events in the control region. The number of signal events is thencalculated as:

Npure signal = Ncandidate sample( 6ET > 25GeV) −∫ ∞

6ET > 25GeVfextrapolation fit( 6ET )

The principle advantage of the method is that it does not rely on Monte Carloto describe the distribution of fake electrons. The extrapolation fit requires only a

6As described in section 5.1.3 and B7Possibly, the extrapolation fit can be dropped, provided there is little signal contribution over

the whole 6ET range and more statistics in the control sample compared to the actual data events.Due to the small statistics of the analysed data set, the extrapolation fit will be used in the presentanalysis.

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Figure 7.4: a) A comparison between the fake electron and the photon control sample,plotted as the ratio of Nfake electrons/Nphotons is shown on the left. b) The right plotdepicts the control sample of selected photon events with pT

γ > 25 GeV shown inblack markers. In red the extrapolation fit is shown, with its fit range indicated byvertical lines.

low fit range high fit range normalisation range total sampleW → eν contribution to 0.11% 2.9% 0.04% 0.36%QCD control sample [%]W → eν , tt, Z → ee to 0.13% 3.0% 0.05% 0.4 %QCD control sample [%]

Table 7.5: Contributions of W → eν events to the QCD control sample in %.

background sample to predict the number of fake electrons using the extrapolation.No modelling of the signal sample of real electrons is needed, because the extrapo-lation fit is directly subtracted from the selected W → eν candidate sample. Thesignal contribution to the background sample is very small and can be suppressedusing further cuts. Also, the statistics of this sample is very large with around 3400events selected in 0.08 pb−1. However, the disadvantages are that there is no chargeinformation on the fake electrons, since the control sample is taken from photons.This is a drawback, since it is not a priori known, whether the distributions of fakepositrons and fake electrons do look alike.

Figure 7.4a) is a figure of merit: It compares the background sample directly withthe fake electron sample by dividing the later by the former: Nfake electrons/Nphotons.While the normalisation is not the same, the ratio itself is quite flat with 6ET .

Figure 7.4 b) shows the first step of this procedure. In black the selected photonevents are shown, while the extrapolation fit is shown as red line. The fit looks goodin the restricted fit range indicated by the black vertical lines and the extrapolation tohigher values of 6ET seems reasonable. The fitting range should not to be extended tothe very low 6ET region since this region will suffer from noise and poor 6ET resolutionand reconstruction. In figure 7.4 b) a clear turn-on curve of the 6ET distribution isvisible. It is caused by the minimum cut of ET > 15 GeV on the hard scatter in thegeneration of the used QCD dijet sample.

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Figure 7.5: Comparison between the extrapolation from the fit (blue boxes) and thefake electrons that would end up in the signal sample (black markers). Above 30 GeVthere is a significant deviation of the fit extrapolation from the data visible due to achange in slope of the 6ET distribution.

The comparison between the fit and the actual fake electrons that would end upin the signal event selection is depicted in figure 7.5. The fake electrons are shown inblack markers and are compared to the fit extrapolation in blue. Here some problemsare visible: The 6ET distribution of fake electrons changes its shape above 30 GeVand flattens out. The sharp falloff of the extrapolated fit however continues, so thatan underestimation of the QCD background seems to be inevitable. The change ofthe slope of the background is why it was tested to fit also in a higher region of 6ET of20 < 6ET< 35 GeV, which gives a better handle on the slope and yields better resultsas will be discussed in detail below.

Figure 7.6 shows the whole procedure of extracting the number of backgroundevents. Shown is what would be selected as W → eν signal candidate events indata (black markers). The contribution to this total candidate event sample fromreal W → eν signal events is shown in green upwards pointing triangles, while thebackground from fake electrons is depicted as red downwards pointing triangles. Thefit extrapolation is shown as blue filled areas. The quality of the fit is χ/NDF=5.7/10for the low fit range, for the high fit range it is χ/NDF=16.2/13. Above the signalselection cut of 25 GeV there is still significant contamination of the signal withbackground events and as already expected from the last figure, the extrapolation fitunderestimates this contamination slightly above 30 GeV. The number of backgroundevents is estimated as Nbackground =

∫∞6ET > 25GeV fextrapolation fit( 6ET ). For figure 7.6,

where the extrapolation fit as performed in the low region, the number of backgroundevents is estimated as 60 ± 7.7. The amount of fake electrons as extracted from MCtruth however equals 102. The number of signal events is consequently overestimatedwith 293.6±17.1, which again is significantly different from the true number of signalevents, 252 ± 15.8. The fake rate is calculated as

Nbackground

Nbackground+Nsignaland is found to be

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Figure 7.6: The figure shows how the estimation works in this method: Shown iswhat would be selected as W → eν signal candidate events in data (black markers).The contribution to this total data from real W → eν signal events is shown in greenupwards pointing triangles, while the background from fake electrons is depicted asred downwards pointing triangles. The fit extrapolation is shown as blue filled areas.Above the signal selection cut of 25 GeV there is still significant contamination of thesignal with background events and as already expected from the last figure 7.5, theextrapolation fit underestimates this contamination slightly above 30 GeV.

RQCD=28.8% (true) and RQCD=17.1%±2.0% (estimate). All errors given here so farare purely statistical. For the true value no statistical error is given, since it has nomeaning, the true RQCD in the sample is as it is. These numbers are also given in theoverview table 7.6.

This table also gives an estimate for the systematic uncertainties, which are eval-uated as follows:

• Variation of the fit range by 10%: The fit range, over which the photon6ET spectrum is fitted, ranges from fitmin to fitmax. It is varied by varying eachof the defining borders, fitmin and fitmax, independently of each other by 10%up or by 10% down or not at all, resulting in eight different estimations for thebackground, where at least one of these borders fitmax,min is varied with regardto the nominal value. The systematic error is then taken to be the averagedeviation8 of all these eight estimations from the nominal one.

• Variation of the fit parametrisation: The systematic error due to the spe-cific choice of the parametrisation was investigated by testing four different

8Another possibility would be to take the maximal variation. However, in the Photon Extrapola-

tion Fit method the systematic dependence on statistical fluctuations is quite large, therefore usingthe average yields a result that is more robust compared to using the maximal variation.

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number of events ± stat. uncertainty ± sys. uncertaintylow fit high fit low fit high fit low fit high fit

W → eν signal (MC) 252 - -W → eν signal (estimate) 293.6 282.7 17.1 16.8 - -fake electrons (MC) 102 - -fake electrons (estimate) 60.4 71.3 7.7 8.4 - -fake rate (MC) [%] 28.8 - -fake rate (estimate) [%] 17.1 20.1 2.0 2.1 5.3 14.1

Table 7.6: True (as obtained from MC information) and estimated (with the PhotonExtrapolation Fit method) numbers for real and fake electrons in the selected signalevents as well as the fake rate, calculated as background

signal+background, with their statistical

uncertainties and the systematical uncertainty for the estimates, obtained by varyingvarious parameters of the fit, the normalisation and the fit range. The low fit refersto a fit range of 10 < 6ET< 22 GeV, the high fit to 20 < 6ET< 35 GeV . For the true MCvalues, used as reference points, no statistical or systematic errors are given. For theestimates, only the systematic errors on RQCD are given, since this is the parameterthat is actually of interest.

alternative parametrisation:

fbkg(x) = (a + bx)x× e(cx+d)

fbkg(x) = ax× e(cx+d)

fbkg(x) = ax2 × e(cx+d)

fbkg(x) = (a + bx) × ecx2

(7.11)

These parametrisations were chosen because they describe the distribution equallywell. The systematic error is then taken to be the average deviation of the back-ground estimations obtained with the alternative fits with regard to the nominalone.

• Variation of the normalisation range by 10%: The normalization rangeis varied in the same way as the fit range. It should be noted that the obtainedsystematic uncertainties are partly due to statistical issues in the distributionsused and thus do not represent the systematic error that one would obtain witha statistics of 100 pb−1 of data.

• Variation of the bin width: The estimations are obtained with the bin widthand doubled in order to investigate systematic effects coming from the binning.The average of the deviations is taken to be the systematic error due to thebinning.

The total systematic uncertainty is then calculated as their sum in quadrature,the individual contribution are summarised in table 7.7.

The fake rate is thus estimated as RQCD=17.6%±%2.1 (stat.)%± 5.3 (sys.)% ifthe fit is performed outside the signal region in the low 6ET regime of 10 < 6ET< 22GeV. This estimation does not agree with the actual value as obtained by using MCtruth information. If the fit is performed in the high 6ET regime, 20 < 6ET< 35 GeV,

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source of uncertainty σ fake ratelow fit high fit

fit range (average) 2.0 12.8parametrisation of fit 4.9 4.7normalisation (average) 0.4 0.4bin width 0.5 3.5σ total 5.3 14.1

Table 7.7: Source for systematic uncertainties in the Photon Extrapolation Fit methodand their respective values. σ fake rate is given as the absolute error in percentage. Itshould be noted, that most of these systematic errors will probably shrink with morestatistics.

the estimation yields RQCD=20.6%±%2.3 (stat.)%± 14.1 (sys.)%, which agrees betterwith the MC truth within the errors, but has a larger error. So neither fit range seemsto be optimal: While the first give quite small errors and is quite stable, the actualtrue value lies outside the error range of what the estimation predicts. The high fitagrees within errors although the uncertainty is quite large and the estimation is notas stable as when fitting the low 6ET range. An optimisation of the fit range couldimprove the Photon Extrapolation Fit method, but is omitted here.

It should be mentioned that the slight change of slope of the 6ET distribution wasinvestigated (see figure 7.5). It was not possible to find out the reason for the changeof the slope of the 6ET distribution for fake lepton events when going from low-mid- 6ET

to the mid-high- 6ET region. One potential cause that was investigated was bb or ccevents. The c or b quarks hadronise into charmed or bottom hadrons that could decayvia weak currents into real, non-isolated electrons. These events would indeed containreal 6ET due to the escaping neutrino produced in the weak decay. The real 6ET inthese events could shift the 6ET distribution of these events towards higher values. Thiswould cause a change in the slope of the 6ET distribution of all fake electron events,if the contribution of these bb or cc events to the total sample would change as afunction of 6ET .

Fig. 7.7 shows the results of these investigations: On the left hand plot thenormalised 6ET distributions from fake electrons, identified as hadrons, non-isolatedand background electrons (mainly from photon conversions), are shown. The 6ET

distribution of the non-isolated electrons (shown as a red solid line) is indeed slightlyshifted towards higher values of 6ET with regard to the other distributions. However,the 6ET distribution of all fake electrons does not significantly deviate from the 6ET

distribution of hadrons faking electrons (shown as a black and a black dashed line).This indicates that the contribution of bb or cc events to the total sample is too smallto introduce a significant change to the slope of the 6ET distribution.

Fig. 7.7 shows on the right hand side of the plot, how big the relative contributionsto the total samples are. The relative contribution of the non-isolated electrons (redsolid line) to the total sum of all fakes rises significantly just above 18 GeV, whilethe contribution of hadronic fakes (dashed black line) decreases. The contributionof the non-isolated electrons is however still below 20% and not very significant. Ifonly hadronic fakes are included in this study, the problems faced in the Photon

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Extrapolation Fit method stay the same: The slope of the 6ET distribution for fakeelectrons is slightly different in the low 6ET region (< 20 GeV) as compared to the high6ET region (> 20 GeV). An extrapolation fit to the low 6ET region will extrapolatethe slope of the low 6ET region and underestimate the number of events in the high6ET region. An extrapolation fit carried out in the high 6ET region will represent theslope of the high 6ET region better. So, if the extrapolation fit is carried out in thehigh 6ET range the estimations of fake rate and number of fake electrons are in betteragreement with the MC truth but with larger uncertainty.

7.4 Template Fit Methods

Instead of using an extrapolation fit to predict the shape of the QCD background inthe signal, an alternative is to use a template fit method. The template fit methodrelies on the use of a pure background control sample and a pure signal controlsample to extract the amount of background and signal in the selected W → eνcandidate event sample. For each of these samples, the distribution of the sametemplate variable is plotted. The distribution of the template variable shouldbe very different for background and signal samples. This allows to determine thefractional contribution of background and signal to the data by determining theirrespective normalisations. The pure background and pure signal samples are alsoreferred to as control samples, because they are used to get control over the fractionsof background and signal in the W → eν candidate data sample.

In the following, firstly, the template method and its general implementation arediscussed in detail. Then, specific implementations of the template fit method arestudied. They vary in the strategy used to select the pure control samples and in thechoice of the template variable.

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The general procedure of the template fit method is:

• Selection of the pure control samples: A template fit requires two purecontrol samples: One pure background control sample and one pure signal con-trol sample. It is arbitrary how these samples are selected, as long as threeconditions are met. Firstly, the samples need to reproduce as closely as pos-sible, how the distributions of the template variable look for the fake and thereal signal electrons in the W → eν candidate event sample. Secondly, to en-sure this, the control samples need to be as pure as possible. Thirdly, theyneed to contain enough statistics. Below two different different selections forthe pure background sample are tested. These are the photon selection as usedin the Photon Extrapolation Fit method as described in section 7.3 and anotherselection using electron candidates failing certain electron ID cuts.

• Choosing a template variable: After having selected pure background andsignal control samples, it is essential to choose a variable that is used in thetemplate fits. The template variable should allow good discrimination betweensignal and background. The distributions of fake and real signal electrons shouldshow quite different dependence on the template variable. Candidate variablesto build the templates are therefore any of those used in the identificationscuts as well as for example isolation energy or possibly likelihood variables con-structed to distinguish between fake and signal electrons by combining severalvariables into one likelihood variable. The template for fake electrons is con-structed by plotting the template variable for events in the background controlsample. The template variable distribution of the electrons from the signal con-trol sample is used as the signal template. In the following, 6ET and ET,iso

frac willbe used as template variable. Other template variables such as hadronic leakage,track isolation (ptrack,cone40

T ) and isolation likelihood9 can also be used.

• Prediction of the background: In order to predict the background, both thesignal and the background templates are fitted simultaneously to the templatevariable distribution of the data. These fits are performed using the ROOTTFractionFitter class 10. The fitter class uses input histograms, that arebinned templates for signal and background as well as a binned data sample.It adjusts the respective contributions of signal and background in the datasample using a likelihood fit. Then the fitter returns the respective fractions ofthe signal and background templates in the data and thus allows extraction ofthe numbers of signal and fake electrons in the selected data sample. A fit rangeneeds to be chosen, over which the fit is performed. It should cover the region,

9The isolation loglikelihood method [93] combines four variables into a loglikelihood of the elec-tron, indicating the probability for this electron to be a real electron. It was predominantly de-veloped to distinguish between isolated and non-isolated electrons. However, here the interestis to estimate the background and since the isolation loglikelihood distribution is very differentfor isolated electrons and fake electrons from light quarks, we can use it as a test distribution.The isolation loglikelihood is constructed using the following input variables: ET,iso

abs (∆R=0.2),

ET,isoabs (∆R = 0.2) − ET,iso

abs (∆R=0.4), pT sum of all additional track in a cone of ∆R = 0.4 aroundthe electron cluster and the transverse impact parameter significance.

10The TFractionFitter is part of the software package ROOT [90]. It implements a standardlikelihood fit using Poisson statistics, based on a method suggested by Barlow and Beeston [94].

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where pure background and pure signal deviate most. Also, the fit range shouldbe evenly distributed between background and signal dominated regions. Thetemplate fit will return the normalisations of pure background and pure signalsample to the candidate data sample. Integrating over the normalised templatedistributions in the signal region will yield the number of background and signalevents in the data and will allow the calculation of RQCD.

In the template fit method, the systematic error is evaluated by regarding how theestimation of the background fraction RQCD varies when the following parameters arevaried:

• Statistical error on the fit templates: This is investigated by smearingthe number of entries in each bin using a Gaussian with a mean of µ = Nand a width of σ=

√N with N being the number of entries in that bin. Then

the template fit is carried out again with the smeared templates and another,alternative estimate of the background fraction obtained. 1000 of these pseudoexperiments are carried out, the resulting background estimations are filled intoa histogram, yielding a Gaussian distribution. To get an estimate of statisticalerror of the templates, the Gaussian width is taken to be the statistical error ofthe templates.

• Systematic error on the fit template: For the systematic error, the differ-ence between the mean background estimation of the 1000 pseudo experimentsand the background estimation from the template fit are taken as systematicerror on the fit templates.

• Variation of the bin width: The estimations are obtained with the bin widthhalved and doubled in order to investigate systematic effects coming from thebinning. The average of the deviations is taken to be the systematic error dueto the binning.

• Variation of the fit range by 10%: The fit range, over which the templatefit is carried out is varied by varying each of the defining borders, fitmin andfitmax, independently of each other by 10% up or by 10% down or not at all.This results in eight different estimations for the background, where at leaston of these borders fitmax,min is varied with regard to the nominal value. Thesystematic error is then taken to be the average deviation of all these eightestimations from the nominal one.

• Systematic error on the background control sample: The determinationof the systematic error on the background control sample depends on how it isselected. Therefore this will be discussed in the respective sections.

In the following the template fit method will be tested with the settings sum-marised in table 7.8.

7.4.1 Template Fit with Photon Selection and 6ET

It should be interesting to employ the same Photon Selection as used in the PhotonExtrapolation Fit method in a template fit. This should help to overcome the problems

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section Background Control Signal Control Templatesample Sample variable

7.4.1 same photon selection as in Photon Ex-

trapolation Fit methodMC W → eν sample 6ET

7.4.3 Failed ID Cut Selection selectionmethod, failed calo ID cuts (see sec.7.4.2)

MC W → eν sample 6ET

7.4.4 Failed ID Cut Selection selectionmethod, failed calo ID cuts (see sec.7.4.2)

Z → ee sample ET,isofrac

7.4.5 Failed ID Cut Selection selectionmethod, failed track ID cuts (see sec.7.4.2)

Z → ee sample ET,isofrac

Table 7.8: Settings tested for the template fitting

due to the changing slope of the 6ET distribution. The disadvantage of using PhotonSelection and 6ET in the template fit is that this requires a template for the signalelectrons. It could be feasible to use a W → µν signal control sample to extractthe signal template 6ET distribution, since the backgrounds in the W → µν channelare much smaller than in the electron channel. Another possibility is to use Z → eeevents and to model the signal template 6ET distribution by ‘neutrinofying’ one of theelectrons, that is removing all of its tracker hits and calorimeter cells from the eventsand reconstruct it again without the removed hits and energy deposits.

In this section, we intend to test how the template fit method works when using aPhoton Selection. Therefore, we decided to use a MC generator to model the W → eνsignal with subsequent detector simulation. The dataset used is the W → eν datasetdescribed in section 7. It should be stressed at this point that all used samples,W → eν signal control sample and the photon background control sample and thecandidate event sample, the data (selected from the QCD dijet sample, section 7), arestatistically independent of each other. This is because they are either independentMC samples (W → eν signal sample and QCD dijet sample) or an orthogonal selectionis applied to select these samples (Photon Selection and electron selection cuts).

Figure 7.8 demonstrates how the template fit method works. The upper plotshows the selected candidate sample as full markers. The simulated data was fittedusing a template fit to determine the contributions of background and signal. Theseare shown as dashed (signal) and dotted (background) lines. The region, in whichthe template fit is performed, fitmin = 15 < 6ET < fitmax = 40 GeV, is indicated byblack lines. The lower plots compares these fitted contributions (lines) to the truecontributions as determined using MC information (full markers). Above 40 GeV,the template distribution for the background slightly lacks statistics compared to theactual background distribution.

The QCD background fraction RQCD is evaluated for the same kinematic cuts onthe electron as in the W → eν signal selection, see section 6.2. The results of the fitare shown in figure 7.8. Additionally, the QCD background fraction RQCD is evaluated

also for an optional isolation cut of ET,isofrac < 0.1 on top of the basic selection cuts.

When no isolation cut is applied, the fake rate is estimated to be RQCD=23.3% ±2.3% (stat.) ± 4.2% (sys.), which agrees well within errors with the true value of the

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b) Predictions for background and signal contributions compared to true contributions

Figure 7.8: Template fit results using a Photon Selection and 6ET as template variable:This figure demonstrates how the template fit method works. The upper plot showsthe selected candidate sample as full markers. The simulated data was fitted using atemplate fit to determine the contributions of background and signal. These are shownas dashed (signal) and dotted (background) lines. The lower plot compares these fittedcontributions (lines) to the true contributions as determined using MC information(full markers). Above 40 GeV, the template distribution for the background slightlylacks statistics compared to the actual background distribution.

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number of events ± stat. uncertainty ± sys. uncertainty

No cut ET,isofrac < 0.1 No cut ET,iso

frac < 0.1 No cut ET,isofrac < 0.1

W → eν signal (MC) 252 242 15.9 15.6 - -W → eν signal (estimate) 248.2 239.1 15.8 15.5fake electrons (MC) 102 23 10.1 4.8 - -fake electrons (estimate) 75.3 8.1 8.7 2.9fake rate (MC) [%] 28.8 8.7 2.4 1.7 - -fake rate (estimate) [%] 23.3 3.4 2.3 1.1 4.2 1.3

Table 7.9: True (as obtained from MC information) and estimated (with the templatefit with Photon Selection) numbers for real and fake electrons in the selected signalevents as well as the fake rate, calculated as background

singal+background, with their statistical

uncertainties and the systematical uncertainty for the estimates. The estimates wereobtained using a template fit with a Photon Selection for the background controlsample and 6ET as template variable. Because of the very small statistics, fluctuationsin the tails of the distributions can severely affect the fit result, e.g. here for thetemplate fit where the ET,iso

frac < cut is applied.

source of uncertainty σ fake rate (%)

no cut ET,isofrac < 0.1

fit range (average) 1.0 0.1bin width 1.5 0.3statistical error of template 2.3 0.8systematical error of template 3.0 1.0σ total 4.2 1.3

Table 7.10: Source for systematic uncertainties in the template fit method using aPhoton Selection. σ fake rate is given as absolute error. It should be noted, that mostof these systematic errors will probably shrink with more statistics. The estimateswere obtained using a template fit with a Photon Selection for the background controlsample and 6ET as template variable.

fake rate of RQCD=28.8%±2.4% as determined using MC information. The method is

also investigated for a sample where a fractional isolation cut, ET,isofrac <0.1, is applied,

in order to be able to compare with the ” 6ET vs. Iso” method. The template fit methodusing a Photon Selection underestimates the background rate for the sample with theET,iso

frac <0.1 cut, yielding an estimate RQCD=3.4% ± 1.1% (stat.) ± 1.3% (sys.). Thisestimate does not agree with the MC value of RQCD=8.7±1.7 within errors. It should

however be noted, that using the ET,isofrac (∆R = 0.2) cut indeed severely shrinks the

statistics and thus makes the estimation less accurate. The results of the template fitare summarised in table 7.9, the single source of systematic uncertainties are listedin table 7.10. When comparing the results for the estimation of RQCD where noadditional isolation cut is applied, the estimation obtained with the template fit usinga Photon Selection is closer to the MC truth than the estimation obtained with thePhoton Extrapolation Fit method, which also employs a photon selection.

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7.4.2 Failed ID Cut Selection to select Background Control

Samples

This section introduces an alternative method to select the background control sample.It uses the electron ID cuts described in section 5.1.3. These ID cuts have a very highefficiency for real electrons while fake electrons are rejected with a high rejection rate.Thus a sample consisting of electron candidates that fail those identification cuts willconsist almost purely of fake electrons and can be used as the background controlsample.

There is a slight caveat: One cannot be sure that this control sample will exhibitthe same features in all possible template variables as the fake electron that wouldend up in our signal candidate sample. After all, they were rejected by the ID cutsfor one reason or another. The aim is to find a control sample that is as close to thereal fake electrons as possible while minimising the amount of signal electrons in thissample. The strategy for this is simple: Require at least two and at most three IDcuts to fail in order to minimise the real electron contamination, whilst requiring allother ID cuts to be fulfilled by the electron candidate in question.

In the following, two sets of background control samples are selected: The firstrequires calorimeter-based ID cuts to be failed, the second requires track-based IDcuts to be failed by the electron candidate. For the first set, the calo ID cuts requiredto be failed are all connected to the width of the shower in the strips, namely ∆ES,Rmax2, ws3, wstot and Fside, which are are described in table 5.1, page 54 in section5.1.3. The second set requires track ID cuts to be failed. These cuts are based uponthe number of pixel hits, the transverse impact parameter of the electron candidate,the ∆η of EM calorimeter cluster and matched track, ∆φ of EM calorimeter clusterand matched track and the E/P values for energy of the calo cluster and momentumof the track (cf. table 5.1, page 54 in section 5.1.3).

Using the Failed ID Cut Selection method has the advantage that the charge ofthe fake electrons in the background control sample can be determined. However ithas also disadvantages: The statistics are much lower than using the Photon Selectionmethod, roughly by a factor of 10. This should not pose a big problem, since withreal data there should still be sufficiently large background control samples availablefor both methods. However, with the available statistics of only 0.08 pb−1, a largerstatistical and systematic error is to be expected on the estimations of the Failed IDCut Selection method. It should be noted, that with higher statistics these errors areexpected to shrink.

Another problem is that the contamination of the background control sample withreal electrons is larger for the Failed ID Cut Selection method than for the PhotonSelection method and can amount up to 25% over the range used in the template fit.Therefore, in real data, one should make an effort to cut harder on the selected controlsample and also to subtract real electrons using a W → eν MC sample. This is notdone here, since only pure samples are used in order to demonstrate the working ofthe method11.

11Subtracting a 25% real electron contribution to the background control sample, would yield atmost an additional 3,75% systematic error to be added in quadrature. This is just a crude estimate,meant to give some feeling of how much this contribution could increase the systematic error on theQCD background estimation. The additional 3,75% systematic error are based on the assumptionthat the error on the W → eν MC sample used to subtract the real electron contribution from

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7.4.3 Template Fit with calo-based Failed ID Cut Selection

and 6ETas template variable

This section discusses the performance of the template fit method using a Failed IDCut Selection based on calo ID cuts and 6ET as template variable. The signal controlsample is selected from a statistically independent W → eν MC dataset.

The QCD background fraction RQCD is evaluated for the same kinematic cuts onthe electron as in the W → eν analysis signal selection, see section 6.2. The results ofthe fit are shown in figure 7.9. Additionally, the QCD background fraction RQCD is

evaluated also for an optional isolation cut of ET,isofrac < 0.1 on top of the basic selection

cuts.Figure 7.9 shows the results of the template fits for the basic set of cuts (left)

and the additional isolation cut (right). Here, the template fits are shown as dottedline for the fake electrons (red) and as dashed line the true signal electrons (blue),each compared to the actual amount of fake electrons (red downwards triangles) andthe true signal electrons (blue upwards triangles) as well as to the total data (blackfull circles). The region, in which the template fit is performed, fitmin = 15 < 6ET <fitmax = 40 GeV, is indicated by black lines.

Table 7.11 lists the true and estimated numbers for real and fake electrons inthe selected signal events as well as the fake rate together with statistical and totalsystematic errors. The sources of systematic uncertainties and their individual valuesare detailed in table 7.12. The estimated background fraction without any isolationcut is RQCD=41.5±2.6 (stat.) ±10.0 (sys.), which just about agrees with the true valueof RQCD=28.8% as determined using MC information. For an event selection, where a

fractional isolation of ET,isofrac <0.1 was required, the estimation yields RQCD=21.3±2.9

(stat.) ±8.6 (sys.), which does not agree with the MC truth of RQCD=8.7% withinerrors. The disagreement of estimated and true values is much larger compared to theestimates obtained using the Photon Extrapolation Fit method. Also, the statisticaland systematic errors are much bigger. The reason for this behaviour can be explainedby the smaller statistics of the background control sample for the Failed ID CutSelection method.

Figure 7.9 illustrates this. For basic cuts (left) there are almost no events above40 GeV, however this is compensated to a degree by the fact, the few events above 40GeV are scaled up in the fit by quite a lot to achieve a good normalisation at lower 6ET .The lack of statistics is even more prominent for the sample with the isolation cut:Above 25 GeV the statistical error become rather large and above 31 GeV there are noentries in the control sample template. In each of the bins at 6ET =29 and 30 GeV thereis only one entry in the control sample, both are scaled up to 11 entries in the templatefit. There are 5 fake electrons that would end up in the candidate events for 6ET>31GeV, indicating that the control background sample has a slightly smaller statisticalreach compared to the actual background. This could be adjusted by enlarging theset of ID cuts that belong to those that can be failed. Another possibility, used here,is to use a different test distribution, where there are more statistics in the fit region

the background control sample is 15%. This is a rather conservative estimation, since usually thetheoretical error on W production is taken to be 5% [67], but then also an uncertainty on the detectorsimulation should be taken into account. The statistical errors are assumed to be negligible comparedto the systematic errors.

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Figure 7.9: Showing the template Fit Method with calo-based Failed ID Cut Selectionand 6ET for basic cuts (left) and an additional isolation cut of ET,iso

frac < 0.1 (right)using the 6ET distribution as a test distribution. The signal electrons are shown asblue upwards triangles, the template fit to their contribution to the data (shown asblack markers) is indicated as a dashed blue line. The fake electrons are shown as reddownwards triangles, their template is depicted as red dotted line. The backgroundcontrol sample reaches its statistical limit: For basic cuts (left) there are almostno events above 40 GeV, however this is compensated to a degree by the fact, thefew events above 40 GeV are scaled up in the fit by quite a lot to achieve a goodnormalisation at lower 6ET . In case that the isolation cut is applied, above 31 GeVthere are no events left in the template, while there are still some fake electron, thatcannot be predicted by the template.

number of events ± stat. uncertainty ± sys. uncertainty [%]

No cut ET,isofrac <0.1 No cut ET,iso

frac <0.1 No cut ET,isofrac <0.1


Table 7.11: True and estimated numbers for real and fake electrons in the selectedsignal candidate events as well as the fake rate. The estimates were obtained usingthe templat fit method using a calo-based Failed ID Cut Selection for the backgroundcontrol sample with 6ET as a template variable. Again, due to the small statistics,fluctuations in the tails affect the fit.

as well as in the signal region. This is done in the next section, where the fractionalisolation energy in the calorimeter is used as test distribution.

7.4.4 Template Fit with calo-based Failed ID Cut Selection

and ET,isofrac

As an alternative to event variables such as 6ET object-specific variables such as thefractional isolation ET,iso

frac of the electron candidate can be used. This has the ad-

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source of uncertainty σ fake rate (%)no cut isofractional

calo < 0.1fit range (average) 5.3 1.8bin width 1.7 3.6statistical error of template 5.0 3.5systematic error of template 6.5 0.6systematic error of control sample 1.5 6.7σ total 10.0 8.6

Table 7.12: Source for systematic uncertainties in the Failed ID Cut Selection methodusing 6ET as a test distribution. σ fake rate is given as absolute error. It should benoted, that most of these systematic errors will probably shrink with more statistics.The estimates were obtained using the templat fit method using a calo-based FailedID Cut Selection for the background control sample with 6ET as a template variable.

vantage that it is possible to extract the signal control sample from data, using aZ → ee sample with tight cuts on mass and identification of the other electron, thusreducing the QCD contribution to the signal template to a negligible amount. Here,the fractional isolation ET,iso

frac is used, already introduced and defined in the previoussections. The fit is shown in figure 7.10, where the fit to the signal candidate sample isshown as black line, while the signal candidate sample is shown as full black markers.The actual content of the signal candidate sample as tagged using MC information isshown in blue upward triangles for the signal electrons from W → eν, while the fakeelectrons from the QCD dijets sample are shown as red downwards triangles. Thefitted contributions of the signal and background control samples to the full templatefit are shown as blue and red dashed lines. The black vertical lines indicate the fitrange, fitmin = −0.05 < ET,iso

frac < fitmax = 0.2.The estimated background fraction without any isolation cut is RQCD=45.0±1.9

(stat.) ±7.2 (sys.), which does not agree within errors with the true value of RQCD=28.8%as determined using MC information. The reason is that the shape of the backgroundcontrol sample template does not exactly reproduce the shape of the actual back-ground in the signal candidate sample. The background template is slightly shiftedtowards larger values of ET,iso

frac compared to the actual background as can be also seenin in figure 7.10. Therefore, when fitting between −0.05 < ET,iso

frac < 0.2, when thenormalisation of the background template is adjusted in that fit region, it will slightlyovershoot the data for higher values of the isolation. The bias could be reduced,if the fit range were extended towards higher values of the isolation, however thiswould put a higher emphasis on the fake electron template compared to the signalelectron template, which is not necessarily desirable. The bias should be investigatedin more detail with more statistics. Here, we restrict ourselves towards applying themethod and presenting an estimation of the QCD background from data without us-ing Monte Carlo information. When applying an isolation cut, the estimation yieldsRQCD=8.3±1.6 (stat.) ±4.0 (sys.), which agrees much better with the MC truth ofRQCD=8.7% compared to the agreement seen for the estimation without the isolationcut or for the Photon Extrapolation Fit method. This is partly due to the fact, thatthe fit is performed mostly over the signal region and extends only slightly beyond

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Figure 7.10: The template fit method using a calo-based Failed ID Cut Selectionmethod using ET,iso

frac as template variable. The slight shift of the maxima of thebackground control template distribution (red dashed line) and the distribution ofthe fake electrons in the sample (red downwards triangles) is visible. In the fit range,indicated by black vertical lines, the template can however be scaled reasonably wellto the fake electron distribution. The signal electrons are shown in blue upwardstriangles, the signal template as a blue dashed line. The black markers are the sumof signal and fake electrons and represent the selected candidate events as they wouldbe seen in real data.

the cut value of ET,isofrac < 0.1. The higher tails of the distribution are not taken into

account in the template fit and do not enter the background estimation either. Thetemplate fit adjusts the normalisation for the low ET,iso

frac range, so that on averagethe background control sample fits the data in the signal region and will also predictthe background considerably well. Discrepancies with the data in the tails of highisolation energy values carry no weight since these events are not taken into accountdue to the cut.

7.4.5 Template Fit with track-based Failed ID Cut Selection

and ET,isofrac

So far, two different, orthogonal background control samples were used: candidateevents with photons instead of electrons as well as candidate events with electroncandidates failing some calorimeter based ID cuts. An alternative possibility to cre-ate the background control sample is to require the electron candidates to pass allcalorimeter cuts and to fail instead a selection of track cuts as described above insection 7.4.2. The resulting control sample distribution can alternatively be used in

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Table 7.13: True and estimated numbers for real and fake electrons in the selectedsignal candidate events as well as the fake rate. The estimates were obtained using thetemplate fit method using a calo-based Failed ID Cut Selection for the backgroundcontrol sample using ET,iso

frac as test distribution.



fit range (average) 0.1 0.2bin width 3.8 1.2statistical error of template 5.0 3.5systematic error of template 3.2 0.04systematic error of control sample 1.3 1.4σ total 7.2 4.0

Table 7.14: Source for systematic uncertainties in the template fit method using acalo-based Failed ID Cut Selection with ET,iso

frac distribution as a test distribution. σfake rate is given as absolute error in percentage points. It should be noted, that mostof these systematic errors will probably shrink with more statistics. The estimateswere obtained using the template fit method using a calo-based Failed ID Cut Selectionfor the background control sample using ET,iso


order to determine the QCD background to W → eν events using template fits.The resulting isolation distribution for the background control sample is closer to

the actual isolation distribution of the faking electrons. This is also shown in figure7.11. The estimate for the fake rate without an isolation cut is with RQCD=30.6±2.0(stat.) ±4.5 (sys.) close to the true value of RQCD=28.8%. If a fractional isolation cut,

ET,isofrac < 0.1, is applied, the estimated values are RQCD=7.5±1.5 (stat.) ±3.2 (sys.),

which is to be compared to the true value of RQCD=8.7%. Both of the estimationsagree with the true values within errors. Table 7.15 and table 7.16 summarize thesenumbers.

7.4.6 Effect of Statistics on the Systematic Error Estimation

As already pointed out, due to the small luminosity of the QCD sample used here,there are large statistical fluctuations. These can affect the estimation of the sys-tematic errors. This effect is investigated here, using the template fit method withcalo-based Failed ID Cut Selection and ET,iso

frac .

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Figure 7.11: The template with method applied using a track-based Failed ID CutSelection and ET,iso

frac as a test distribution. The background control template distri-bution (red dashed line) is compared to the distribution of the fake electrons in thesample (red downwards triangles) as well as signal control template (blue dashed line)is compared to the true distributions of the signal electrons (blue upwards triangles).The black markers are the sum of signal and fake electrons and represent the selectedcandidate events as they would be seen in real data. The fit range is indicated byblack lines.





Table 7.15: True and estimated numbers for real and fake electrons in the selectedsignal candidate events as well as the fake rate. The estimates were obtained using thetemplate fit method using a track-based Failed ID Cut Selection for the backgroundcontrol sample with ET,iso


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fit range (average) 1.1 0.08bin width 0.04 0.2statistical error of template 2.8 2.5systematic error of template 1.1 1.3systematic error of control sample 3.1 1.6σ total 4.5 3.2

Table 7.16: Source for systematic uncertainties in the Failed ID Cut Selection methodusing the ET,iso

frac distribution as a test distribution and using a background controlsample consisting of electron candidates having failed certain track ID cuts. σ fakerate is given as absolute error. It should be noted, that most of these systematic errorswill probably shrink with more statistics. The estimates were obtained using thetemplate fit method using a track-based Failed ID Cut Selection for the backgroundcontrol sample using ET,iso


In order to estimate the influence of the statistics on the determination of thesystematic error, the used sample was split up into two samples of an integrated lu-minosity of 0.04 pb−1 each, containing only odd and even events respectively. Thesystematic errors were determined on these smaller samples, then the average wastaken and compared to the systematic error for the whole sample. In the case no iso-lation cut was applied the average systematic error for the smaller samples is ±15.1%,which is larger than the ±7.2% estimated for the full sample. Also, the average for thesmaller samples with the isolation cut is with ±5.8% larger than the ±4.8% systematicerror on the estimation for the full sample. There are not enough statistics to fullyappreciate by how much the systematic error might decrease with increased luminos-ity. As another way to check the assumption of shrinking errors with more statistics,the method was applied to a sample with an 6ET cut of 11 GeV only. This allowedfor enough statistics to apply the method with an isolation cut to the full sample, toevery second and every tenth event only and to determine the systematic errors fordifferent event sample sizes with the result being ±8.3% (full sample), ±12.7% (onlyodd events) and ±13.9% (only every tenth event). Here, a trend to smaller systematicerrors with larger statistics is again visible.

7.5 Conclusion

In this chapter several methods to estimate backgrounds to a W → eν candidateevent sample have been presented: the ” 6ET vs. Iso”, Photon Extrapolation Fit andthe Template fit method using different settings. They were tested using a QCDsample of 0.08pb−1 at 10 TeV centre-of-mass energy with a simulation of the ATLASdetector.

The advantage of the ” 6ET vs. Iso” method is that it is relatively stable, becauseit only counts events instead of using distributions. Also, the method allows access tocharge information. However, it assumes an independence of 6ET and isolation energy

94

Method fake rate [%] ± stat. uncert. ± sys. uncert.

No cut ET,isofrac < 0.1

MC truth 28.8 8.7 2.4 1.7 - -” 6ET vs. Iso” 9.4 1.8 2.0Template fit methodPhoton Selection 23.3 3.4 2.3 1.1 4.2 1.3calo-based with Failed ID Cut Selection 45.0 8.3 1.9 1.6 7.2 4.0track-based with Failed ID Cut Selection 30.6 7.5 2.0 1.5 4.5 3.2

Table 7.17: Overview of the fake rate estimations for the different methods.

distributions, which is not necessarily fullfilled and can introduce a bias.The Photon Extrapolation Fit method has the advantage of having a high statisti-

cal reach and a low contamination of signal events in the background control sample.However, it does not help to determine the charge of the fake electrons. It is recom-mended to use the Photon Selection with an template fit instead of an extrapolationfit, since the used 6ET distribution seems to change its shape in the signal region andthus using an extrapolation fit introduces a bias. However, on the other hand, a tem-plate fit introduces the need to create a template from MC or data, which will leadto additional uncertainties due to the fact, that the determination of 6ET will have alarge uncertainty at the ATLAS start-up.

Using the template fit method with a Failed ID Cut Selection method gives ac-cess to charge information. When using an object-variable as template variable, bothcontrol and signal control samples can be extracted from data. But it will suffer froma larger real electron contamination in the background control sample, has smallerstatistics and might also be subject to biases connected with the agreement of back-ground control sample and faking electrons in the test distribution. A sample withlarger statistics will be useful in determining the best ID cuts to be reversed in themethod. For the reversal of track cuts, a better agreement between the fake templateobtained with the background control sample and the ET,iso

frac distribution of the fakeelectrons is found.

Table 7.17 summarises the estimates for the fake rate for the three methods andallows for a comparison with the true MC values. Since all three methods are inde-pendent in that they use different background control samples and a different testdistribution (or in the case of the ” 6ET vs. Iso” method a completely different ap-proach), their estimates for the fake rate RQCD can be combined using the assumptionthat the errors are uncorrelated12. For uncorrelated errors, a standard weighted least-squares procedure can be used. This averaging works in favour of the estimation withthe smallest error. Therefore if the errors are very different, the uncertainty on theaverage is adjusted using the same procedure as also applied by the Particle DataGroup13. Table 7.18 gives an overview of the combined estimates of RQCD, where thescaled errors are given in brackets. In the combined estimates either the Failed ID

12This is not necessarily strictly true, since there is some overlap in the methods used, e.g. thefact that the same template fitter was used. A better way of combining the estimations is describedby Lyons et al. in [95], however this requires a determination of the full error matrix for the methodsused and their correlation, which is not possible with the MC statistics available at the moment.

13cf. [1], chapter Introduction p.10

95

Combined methods fake rate [%] ± tot. uncertainty

MC (without iso cut) 28.8Photon Selection - Failed ID Cut Selection (calo) 29.7 4.0 (10.8)Photon Selection - Failed ID Cut Selection (track) 26.9 3.4 (3.7)MC (with iso cut) 8.7” 6ET vs. Iso” combined withPhoton Selection - Failed ID Cut Selection (calo) 5.4 1.7 (2.2)Photon Selection - Failed ID Cut Selection (track) 5.4 1.3 (1.7)

Table 7.18: Combined fake rate RQCD. The increased error is given in parathesis.

Cut Selection method using reversed calorimeter ID cuts or reversed track ID cutsusing fractional isolation is included, because the estimates are too correlated to beused together in a combination of estimates.

The combined estimations of RQCD=29.7%±4.0% (Failed ID Cut Selection, calo IDreversal) and RQCD=26.9%±3.4% (Failed ID Cut Selection, track ID reversal) agreewell with the true value of 28.8%. When the isolation cut is applied however, thebackground fraction RQCD is slightly underestimated with RQCD=5.4%±1.7% (FailedID Cut Selection, calo ID reversal) and RQCD=5.4%±1.3% compared to the true valueof RQCD=8.7%. This is partly due to the small statistics of the template samples afterthe isolation cut has been applied, which affects in particular the Photon ExtrapolationFit method, that dominates the combination due to its small error. The investigationof better methods of combining the estimations should be further investigated.

Chapter 8

Experimental Prospects for theLepton Asymmetry Measurementwith Atlas

8.1 Systematic Uncertainties on the Measurement

This section discusses various systematic uncertainties connected with the leptonasymmetry measurement, including the uncertainty due to backgrounds, scale andresolution uncertainties, trigger biases and charge misidentification. An overview overall uncertainties and their combination are given in section 8.2.

8.1.1 Systematic Effect of Backgrounds on the AsymmetryMeasurement

Since there is a sizable amount of background, the distortion through backgroundsshall be examined here. The sample size of the dijet and prompt photon eventsafter all cuts (37 events) is too small to evaluate the fake electron and positron ηl

distributions and their effect on the lepton asymmetry separately. However, to geta first rough feeling of the size and the shape of the QCD background and how itdistorts the lepton asymmetry, an extrapolation method is used. For this, all cutsapart from the 6ET cut are applied to the QCD sample. Then the efficiency of the 6ET

cut is calculated as

ǫcut =#events after all cuts

#events after all cuts except 6ET > 25 GeV(8.1)

As can be seen in figure 8.1 a), the efficiency is flat as function of ηl withinstatistical uncertainty. Thus to estimate the shape of the ηl distribution of the QCDbackground, the ηl distribution is evaluated before the 6ET cut. The statistics beforethe 6ET cut is 1250 events, much higher than after the cut (37 events) and yields asmooth distribution. To investigate the QCD background as a function of ηl a scalingmethod is employed. First, the ηl averaged efficiency of the 6ET cut is measured for fakepositrons and electrons separately. Then, the distribution of selected fake electronsand positrons before the 6ET cut are scaled with the respective 6ET cut efficiencies.As a result one gets a smooth distribution that contains the right number of events.

96

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a) Efficiency of the 6ET cut in the QCD sample

η pseudorapidity -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

num

ber

of e

vent

s

0

2

4

6

8

10

12 QCD sample with all cuts

cut,corrected for cut efficiencyTE

TEQCD sample without

b) Comparison of QCD sample, scaled andunscaled

Figure 8.1: a) shows that the efficiency of the 6ET cut for positrons (red) and electrons(blue) is flat in ηl and thus indicated that it is justified to use an ηl averaged scalingfactor to get a smooth ηl distribution of fake leptons using the QCD sample where allcuts apart from the 6ET cut are applied. This is also demonstrated in b) where thescaled sample without the 6ET cut (filled area) is compared to the unscaled distribution(black markers). The distributions agree within statistical uncertainty. In b) positronsand electrons are used.

Figure 8.1b) demonstrates, that the scaling works for the charge inclusive sample.There are slight, non-significant disagreements for the outer ηl regions, where for+ηl the scaling underestimates the number of fake leptons and for -ηl the scalingoverestimates it. This is a very slight effect and is most probably due to statisticalfluctuations. Since in general there are no huge deviations, it should yield a reasonableestimate of the effect the QCD background has on the measured lepton asymmetry.

The effect of backgrounds on the lepton asymmetry for an integrated luminosity of100 pb−1 is shown figure 8.2. Here the lepton asymmetry from a pure W → eν set isshown in red markers. Its values after the adding of the Z → ee , tt and W → τν datasets are depicted in black open triangles. These backgrounds have little effect on theobserved asymmetry. Black solid triangles depict the asymmetry after the inclusionof the QCD dijets. It is obvious that this background induces the largest distortionof the lepton asymmetry, reducing the asymmetry by about 50% in the central regionand by about 20% in the forward region. The QCD background is therefore not onlythe largest background as discussed in section 6.2, but also distorts the asymmetrymost severely.

Figure 8.3 examines the asymmetries of the individual backgrounds, with a hori-zontal line drawn at zero. They show the expected behaviour and are mostly flat asa function of ηl. One exception is the W → τν sample, which has also an asymmetrystemming from momentum differences of u and d quarks. The asymmetry in W → τνevents is however washed out due to the fact that the W decays to a τ , which decaysfurther to leptons of the first generation. There seems to be also a slight asymmetryin the QCD sample, which is probably due to the lack of statistics. This should beclosely monitored with more statistics and real data, since it might be possible thatmore fake positrons are be reconstructed, due to the fact that in a pp machine onaverage more positive than negative charged particles are produced1.

1However, for the√

s = 10 TeV QCD dijets data sample used in chapter 7, specified in table 7.1,

98

η lepton pseudorapidity -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

lept

on a

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met

ry

0

0.05

0.1

0.15

0.2

0.25 Pure W Asymmetry

)τ → + Wt ee + t→W Asymmetry (+ Z

W Asymmetry (with all backgrounds)

Figure 8.2: The influence of the inclusion of the background on the measured leptonasymmetry is shown here. While the red markers show the pure lepton asymmetry,the black open triangles show the asymmetry of the combined W → eν , Z → ee , ttand W → τν data sets, where the positron and electron data samples were scaled andadded before calculating the asymmetry of the combined data set. The black solidtriangles depict the asymmetry after the inclusion of the QCD dijets. The fits are justto guide the eyes. It is obvious that this background induces the largest distortion ofthe lepton asymmetry.

Effects of the Electroweak Backgrounds on the Asymmetry Measurement

The contribution of Z → ee , tt and W → τν backgrounds, to the total candidateevent sample after all selection cuts is quite small, see section 6.2. These electroweakbackgrounds can be subtracted using Monte Carlo simulation. The resulting relativeuncertainty of the lepton asymmetry due to each background in bins of ηl is shownin table 8.1 as percentage error.

In order to derive these values, the number of residual background events afterall selection cuts was determined for an integrated luminosity of 100 pb−1. Thereis a statistical uncertainty associated with the number of events of each of thesebackgrounds, but also a systematic uncertainty due to the theoretical uncertaintyon the MC predictions for the production rates of these processes, as stated in [67].The combined statistical and systematic uncertainty on the number of backgroundpositrons or electrons in the candidate event sample is calculated as:

σ2Bkg = (

√

NBkg)2 + (σsys(%) × NBkg)

2, (8.2)

where σBkg is the uncertainty on the number of leptons due to a specific back-ground. NBkg is the number of background events after all selection cuts have been

with a slightly larger luminosity of 0.08 pb−1 no asymmetry could be observed.

99


ee

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eve

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etry

in d

ijet e

vent

s-0.2

-0.1

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0.2

0.3

0.4

0.5ATLAS

Figure 8.3: The lepton asymmetry of the Z → ee , tt, W → τν and QCD backgroundsamples.

applied (see table 6.2). σsys(%) is the systematic uncertainty (expressed as a percent-age) assigned to the theoretical prediction of this specific background. The relativesystematic error on the number of leptons is 15% in the case of tt and 5% in the caseof Z → ee and W → τν as stated in previous Atlas publications [67]. These num-bers are reflections of the uncertainty of the modelling of these processes. The numberof background leptons due to a specific background is approximately fully correlatedover the ηl bins. Therefore, in order to calculate the resulting uncertainty of thebackground on the lepton asymmetry, the expected numbers of background leptonsare added to or subtracted off the signal leptons for each bin of ηl and the asymmetryis recalculated and compared to the signal asymmetry without backgrounds.

The relative uncertainty of the lepton asymmetry due to each electroweak back-ground in bins of ηl is shown in table 8.12. It is clear from these numbers that thebackgrounds from Z → e+e−, tt and W → τν are not the dominant source of un-certainty on the lepton asymmetry measurement, the statistical imprecision of thesample size is bigger.

Effects of the QCD Background on the Asymmetry Measurement

The QCD background has an asymmetry that is on average zero within statisticaluncertainty as shown in figure 8.3. This means the number of fake positrons is equalto the number of fake electrons. With this assumption, it is possible to correct forthe QCD background using a scaling factor:

2The contribution of single top events was investigated with a different version of the detectorsimulation and at

√s=10 TeV. It is estimated to be of the same order as the Z → ee background

error, that is below 0.5% [96]. It will be neglected here.

100

percentage error on lepton asymmetry [%]pseudorapidity η Z → ee [%] tt [%] W → τν [%] W → eν [%]

(stat. + 5% sys.) (stat. + 15% sys.) (stat. + 5% sys.) stat. error-2.40 ≤ η < -1.92 0.12 0.78 2.07 2.31-1.92 ≤ η < -1.44 0.42 1.47 0.23 3.41-1.44 ≤ η < -0.96 0.03 2.07 1.18 4.09-0.96 ≤ η < -0.48 0.27 2.36 0.55 4.53-0.48 ≤ η < 0.00 0.15 2.75 0.68 4.790.00 ≤ η < 0.48 0.05 2.47 0.46 4.810.48 ≤ η < 0.96 0.09 1.68 1.47 4.820.96 ≤ η < 1.44 0.45 2.18 2.83 3.971.44 ≤ η < 1.92 0.15 1.37 0.34 3.681.92 ≤ η < 2.40 0.27 0.91 1.59 2.26

Table 8.1: Relative error on the lepton asymmetry due to contributions from Z → ee ,tt and W → τν backgrounds.Also quoted is the statistical uncertainty of the W → eνsample for comparison.

.

Ameasured =(N+ + Nfake

2) − (N− + Nfake

2)

(N+ + Nfake

2) + (N− + Nfake

2)

=N+ −N−

(N+ +N−) +Nfake

{

(N+ +N−)

(N+ +N−)

}

=N+ −N−

(N+ +N−)

{

(N+ +N−)

(N+ +N− +Nfake)

}

=N+ −N−

(N+ +N−)

{

(N+ +N− +Nfake)

(N+ +N− +Nfake)+

−Nfake

(N+ +N− +Nfake)

}

=N+ −N−

(N+ +N−)

{

1 − Nfake

(N+ +N− +Nfake)

}

= Atrue × (1 − RQCD) (8.3)

Here, RQCD denotes the inclusive fake rate, the fraction of QCD events in the se-lected candidate events in a given ηl bin. Only W signal events apart from the QCDbackground are considered in the candidate sample, assuming the electroweak back-ground has been subtracted already. The true lepton asymmetry can thus be recoveredfrom the measured asymmetry, Ameasured, which contains the QCD background, usingthe following relation:

Atrue = Ameasured/(1 − RQCD) (8.4)

Since correction for the QCD background is applied as a multiplicative factorto the lepton asymmetry, the estimation of the error in the measurement due tothe uncertainty on the QCD background is quite straightforward. Because there isnot enough simulated data available to perform a bin-by-bin estimation of the QCDbackground in ηl, for the following it will be assumed, that the QCD backgroundfraction, RQCD, is perfectly flat in ηl. This is not necessarily the case as can be seen infigure 8.1, where in the crack regions, around |ηl| ∼1.4, the number of fake leptons is

101

lepton

η Pseudorapidity 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Asy

mm

etry

0.05

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0.15

0.2

0.25

0.3 = 32 %

QCDCorrected Asymmetry with R

16 % uncertainty (50 %)± 8 % uncertainty (25 %)±

3.2 % uncertainty (10 %)±

PDF uncertainty (5 %)

lepton

η Pseudorapidity 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Asy

mm

etry

0.05

0.1

0.15

0.2

0.25

0.3 = 12 %

QCDCorrected Asymmetry with R

12 % uncertainty (100 %)± 6 % uncertainty (50 %)± 3 % uncertainty (25 %)±

PDF uncertainty (5 %)

Figure 8.4: A comparison between the PDF uncertainties on the asymmetry and theuncertainty on the measured asymmetry caused by the QCD background. For theQCD background, the estimated values of RQCD=32 % (left plot) and RQCD=12 %(right plot) are used. If the used values of RQCD agreed perfectly with the QCDbackground actually present, the true asymmetry would be recovered, shown as blackmarkers. But there would be uncertainties on the reconstructed, corrected asymmetrydue to the relative uncertainty on RQCD. Red lines in the plots indicate the uncertaintyon the corrected asymmetry due to relative uncertainties on RQCD of 50%, 25% and10%. For the PDF uncertainties a global factor of 5% was assumed and is shown asyellow error band.

significantly increased, despite the cut of 1.37< |ηl| <1.52. This is an indication, thatthe flatness of the QCD background rate as a function of ηl will have to be tested indata and that the correction factor (1 − RQCD) may have to be derived and appliedin bins of ηl.

Another assumption made here is that RQCD is independent of the fake leptoncharge, which again is only approximately true as can be seen in figure 8.3, where theasymmetry of the QCD background is shown.

For the time being, for each bin in ηl the same percentage rate of QCD backgroundis assumed. The consequences for the measured and corrected lepton asymmetry andits uncertainty are shown in figure 8.4, where two QCD background scenarios, RQCD =32% and RQCD = 12%, are explored. For both these scenarios the reconstructed leptonasymmetry is shown together with red lines indicating the uncertainty resulting froma 50%, 25% and 10% uncertainty on RQCD. These QCD errors are compared to anotional 5% PDF uncertainty.

The QCD error scenarios correspond to different cut scenarios. Here, RQCD = 32%corresponds to the QCD background level that results from the basic set of cutsexplored in section 6.1. It would be beneficial to reduce the background fraction aswell as the error on its estimation. Indeed the second scenario explored in figure 8.4shows the effect of a QCD background rate of RQCD = 12%, which is what is to beexpected if an isolation cut is applied on the lepton. Here, a fractional isolation cutof ET,iso

frac is applied. When this additional cut is applied, the QCD background ratedrops to RQCD = 12% and the relative accuracy with which it needs to be determinedis about 25% for the error on the asymmetry to be below 5%. As shown in chapter 7,the expected relative uncertainty of the QCD background determination comes closeto 25% for RQCD = 12% and to 10 % for RQCD = 32%.

102

[%]QCD

QCD background fraction R10 20 30 40 50

[%]

Asy

σ R

elat

ive

Err

or o

n A

sym

met

ry,

0

5101520253035

404550

0.050.10.150.20.250.30.350.40.450.5 [%]QCDrelative error on R

Figure 8.5: The correlations for the QCD background fraction, RQCD, its relativeuncertainty and σAsy are shown. Here, the relative uncertainty on the asymmetry,σAsy, is depicted for various relative uncertainties on RQCD (indicated by colouredlines) as function of RQCD.

The actual resulting uncertainty on the measured and QCD corrected lepton asym-metry is determined by adding the number of fake leptons equivalent to RQCD = 12%or RQCD = 32% to the selected W events. If the lepton asymmetry derived fromthis sample is corrected using the correct factor of (1-RQCD), then the corrected lep-ton asymmetry agrees perfectly well with the original asymmetry. If instead (1-RQCD ± σRQCD

) is used, the corrected asymmetry will deviate from the original asym-metry. This deviation of the corrected asymmetry from the original asymmetry isthen the error on the asymmetry due to the uncertainty on the QCD background,±σAl

RQCD.

The relative error on the asymmetry can be calculated as function of RQCD andits relative uncertainty using the procedure described in the last paragraph. Theresults are shown in figure 8.5, where the relative error on the asymmetry is shownas a function of RQCD for various colour-coded curves, representing different levels ofrelative uncertainty on RQCD. Here, the needed precision of the QCD backgrounddetermination can be read off easily as a function of RQCD for a specific value of σAsy,e.g. to achieve a level of σAsy ≤5% with a relative uncertainty on the backgroundof 10%, 25% and 50% the background fraction RQCD must not be larger than 33%,16.6% and 9% respectively.

On the basis of what is discussed in chapter 7, RQCD = 12 ± 3%, determinedwith 25% relative uncertainty, and RQCD = 32 ± 4.8%, determined with 15% relativeuncertainty, will be used as QCD background fractions and relative uncertainties inthe measurement of the lepton asymmetry. These numbers yield a relative error onthe lepton asymmetry of 3.4% (RQCD = 12%) and of 7.1% (RQCD = 32%) in each bin

103

of ηl .

8.1.2 Influence of Scales and Resolutions

The uncertainty on the determination of the actual energy of the lepton, its pseu-dorapidity and the amount of missing transverse energy affects the measurement ofthe lepton asymmetry in the individual ηl bins. This effect and the related errors arestudied in this section.

For the Atlas detector, the uncertainty on the scale and resolution is expectedto be 1% (ηl ), 5% (pl

T ) and 10% (6ET ) for the linearity and 1% (ηl ), 5% (plT ) and

50% (6ET ) for the resolution with early data as stated in [67]. In order to estimate theerror on the lepton asymmetry due to uncertainties on the determination of resolu-tion of pl

T , the following approach is taken: The reconstructed leptons that pass thetrigger selection and the medium ID cuts are smeared using a Gaussian with a meanof 1.0 and a width of expected uncertainty on the resolution of pl

T . Then the nominalcuts are applied to the smeared leptons. The resulting asymmetry of the smearedleptons is compared to the nominal asymmetry distribution of the reconstructed lep-tons. To investigate the uncertainty on the linearity of pl

T , the plT of reconstructed

leptons passing the trigger selection and the medium ID cuts are scaled by a factor(1 ± σscale). σscale is the relative uncertainty of the pl

T scale. The same procedure isused to determine the systematic effects for the ηl and the 6ET scale and resolutionuncertainties.

The errors from the scale variations of plT are less than 1% in general without

any ηl dependence. The sign of the deviation from the nominal lepton asymmetrydistribution does not depend on whether the scale is varied up- or downwards. Forthe scale variations of 6ET on the other hand, there is a clear trend for the downwardvariations to also result in a downward variation in the lepton asymmetry. This is dueto the fact that for lower 6ET values, lower values of Q2 and x are sampled, where thedifferences between u and d quarks are less pronounced. Also, cuts on the neutrinoor the lepton pT change the correlation between the lepton and the W rapidity andhence the asymmetry as a function of ηl itself [17, 46]. This trend is not visible forthe pl

T variations, since the plT scale is only varied by 1%, a much smaller value than

the 6ET scale variation of 10%. The absolute values of the downward variations, for6ET , are also slightly larger in general compared to the deviations from the upwardvariations. This is due to the 6ET distribution itself which is approximately a Jacobianpeak. For ηl no clear picture emerges, the variations are of the order of 1-1.5%. Thevariations due to uncertainties on the resolution do not show any pattern of sign andsize as a function of ηl.

A straight line fit is shown for all of the distortions in the last row of table 8.2 togive an average value of the error due to the variation of the specific variable. Theaverage mean values of the distortions are also given with their respective errors. Theerrors on the means are smaller than the errors on the fit, since the latter dependon the errors of the individual data points while the former do only depend on thedeviations of the data points from the mean.The analysis should be repeated with alarger sample to get a clearer picture. As a conservative estimation and because of thelarger fluctuations, for the scale uncertainties the larger uncertainty is taken to be theuncertainty on the lepton asymmetry and used as systematic error in the following.

104

pseudorapidity η plT scale 6ET scale ηl scale pl

T 6ET ηl

- + - + - + resol. resol. resol.

-2.40 ≤ η < -1.92 0.18 0.13 -3.7 1.2 2.4 -1.5 0.56 -2.5 -0.62-1.92 ≤ η < -1.44 0.72 -0.042 -3.5 2.4 0.2 -0.97 0.44 0.43 1.5-1.44 ≤ η < -0.96 0.15 0.13 -4.2 2.8 0.85 -0.52 0.91 -1.8 -0.074-0.96 ≤ η < -0.48 0.97 0.036 -8.1 3.9 1.4 -0.56 0.37 0.56 -0.27-0.48 ≤ η < 0.00 -0.0071 0.1 -3.6 1.8 -0.75 0.041 0.38 0.24 -0.130.00 ≤ η < 0.48 0.41 -0.0098 -3.2 -0.68 0.41 0.27 0.35 -5.3 -0.0480.48 ≤ η < 0.96 -0.65 0.094 -2 3.9 1.8 -1.8 0.23 6.3 -0.760.96 ≤ η < 1.44 -1.3 0.019 -5.5 2.6 -1.1 1 -1.7 -0.64 1.51.44 ≤ η < 1.92 1.1 -0.89 -5.9 5.9 3.8 -2.8 0.41 6.1 -0.731.92 ≤ η < 2.40 -0.84 0.067 -4.4 3.1 -0.32 -1.5 0.4 -4.6 -1.1straight line fit -0.018 -0.0094 -4.3 2.7 1.0 -1.1 -0.23 -0.68 0.32σ (fit) ± 2.5 ± 2.5 ± 2.7 ± 2.4 ± 2.4 ± 2.5 ±2.3 ±2.5 ±2.3mean 0.071 -0.037 -4.4 2.7 0.87 -0.83 -0.067 -0.12 0.23σ (mean) ± 0.74 ± 0.29 ± 1.6 ± 1.7 ± 1.4 ± 1.1 ± 0.85 ± 3.7 ± 0.68

Table 8.2: Distortions of the lepton asymmetry due to resolution and scale uncer-tainties. The quoted values are the relative change in percent in the measured leptonasymmetry when the parameters are varied upwards (+) and downwards (-) accordingto the uncertainty of the scale (1% (ηl ), 5% (pl

T ) and 10% (6ET )). Also the relativechange in percent is shown, for when the respective variable was varied using a Gaus-sian with a mean of 1 and a width of the expected uncertainty on the resolution – 1%(ηl ), 5% (pl

T ) and 50% (6ET ). The result of a straight line fit as well as the mean ofthe variations are shown for all of the distortions in the last row of the table togetherwith their respective errors. The larger size of the errors on the constant fit can beexplained with the large errors on the data points. The errors of the means do notdepend on the errors on the data points and are therefore smaller.

Alternatively, the results of the averaging or the mean could be used as systematicerrors.

8.1.3 Trigger and Lepton Identification Biases

Another factor that can have an impact on the measurement is a potential chargebias introduced by the trigger selection and the lepton identification.

Trigger Bias

In this thesis, the bias introduced by the trigger is investigated using two differentmethods:

• The Tag & Probe method is using two EM clusters coming from Z → eedecays. Events are selected requiring two EM clusters in the electromagneticcalorimeter, whose invariant mass lies within a window of 30 GeV around thenominal Z mass, MZ = 91.2 GeV. Further requirements on the events are thatthey be triggered using the e25i signature (at least one isolated lepton above 25GeV) or the e20 trigger (at least one lepton above 20 GeV), 6ET < 20 GeV, thatthe EM clusters have opposite charge and be back-to-back (∆φ > π/2). For real

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data, these cuts suppress background without biasing the measured efficienciesmuch, since a real lepton is reconstructed as an EM cluster in 99.92% of allcases, as was shown in MC studies [67]. In each event, a tag lepton is selected,which needs to fulfill all relevant ID and trigger cuts, namely all tight leptonID cuts, the EM object needs to have triggered on all trigger levels and it mustlie within the acceptance in |ηl| (|ηl| < 1.37 and 1.52 < |ηl| < 2.4). The otherlepton is the probe lepton, which needs to fulfil only the cuts under investigation.This probes the efficiency of the various ID and trigger cuts. This method candetermine trigger as well as ID cut efficiencies. The efficiency is calculated as

ǫtrigger =#probe leptonsfullfilling cuts under investigation

#all valid tag leptons(8.5)

• Selection & Monitor triggers can be used to determined trigger biases di-rectly on a W → eν dataset. One uses a monitor trigger that selects eventsindependently from the selection trigger used in the analysis. The monitor andthe selection trigger need to be uncorrelated. The monitor trigger defines thebasic population of events. On both samples the full event selection is appliedand the efficiency is calculated as:

ǫtrigger =selectiontrigger

raw∩ monitortrigger

actual∩ eventselection

monitortriggeractual

∩ eventselection(8.6)

The expressions raw and actual here refer to the fact, that triggers can beprescaled. That means, that only every xth event will actually trigger the record-ing of the event. All other events are discarded, unless randomly recorded byanother trigger, then these randomly triggered events are referred to as raw. Itneeds to be ensured, that only events, that were actually recorded by the moni-tor trigger would be taken into the data sample in order to define a well-definedbasic population. It should be stressed, that this method only reliably helps todetermine pure trigger efficiencies, its applicability to the determination of IDcuts is very limited and will be discussed in section 8.1.3 specifically.

Both of these methods have certain advantages and disadvantages: The tag &probe method will probably be the one used to determine lepton efficiencies in mostlepton analyses in Atlas and it is well documented and tested for inclusive W pro-duction [67, 92]. However, there is one disadvantage. Since this method employs aZ → ee sample rather than a W → eν sample, the efficiencies measured need to becarefully determined as functions of ηl and pl

T and possibly other variables, becausethese distributions are inherently different for Z → ee and W → eν events. In ad-dition systematic differences may be introduced by the tag & probe method itself,because it requires a certain type of event and imposes mass and possibly charge cutson the lepton pair as has been shown in [97]. Also, if the trigger efficiencies for elec-trons and positrons are different, efficiency corrections need to be applied. It mightbe more complicated to extract the correction factors from a Z → ee rather than froma W → eν sample, because of the kinematic differences between the samples. Also,since the cross section of Z → ee is an order of magnitude smaller than W → eν itmight be advisable to determine the trigger bias with a (potentially) larger data set.

In the case that one tries to use selection & monitor triggers the advantage is thatone uses more or less the same data set as for the analysis, so that derived correction

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factors for trigger biases can be applied in a very straightforward way. Anotherpossible advantage is the larger sample of W → eν events compared to Z → eeevents. However, a big disadvantage is that selection and monitor trigger need to betotally independent of each other but still trigger the same type of events. This is verydifficult in Atlas where there are only triggers for two detector subsystems: Muon-and calorimeter triggers. Muon triggers should not trigger for pure W → eν eventsdue to the lack of genuine muons in these events. So there is a problem in finding asuitable monitor trigger. However, it can be argued that in this particular analysis itis sufficient for the selection and the monitor trigger to have an independent responseto the charge of the lepton. Or to put it differently: selection and monitor trigger maybe correlated as long as this correlation is independent of the charge of the lepton.It is plausible to assume that charge biases in the lepton trigger would not affect the6ET triggers, since it would be most likely be caused by a faulty track reconstructionin the inner detector or track association in the trigger. The 6ET trigger does not useinner detector and track information. Therefore, we can assume our selection and ourmonitor trigger to be uncorrelated for the variable we are interested in – the differenceof the absolute efficiencies for the two lepton charges.

In the following results from the tag & probe method as well as from the selection& monitor trigger method are presented as obtained from the Z → ee and the W →eν dataset, both scaled to 100 pb−1. Since for the Z → ee sample, only triggerinformation in the e25i trigger was available, tag & probe as well as selection &monitor trigger methods are first evaluated using the 25i trigger. For the selection &monitor trigger method the 6ET trigger x20 was chosen and scaled with a factor of1/10 to imitate a prescale that might be applied to this trigger at the Atlas start-up.

Since we are using MC simulated data, we can compare the efficiencies estimatedwith the two methods to MC efficiencies as evaluated using MC truth information.Figure 8.6 and figure 8.7 show the trigger efficiencies for different charges in bins ofηl as obtained for the tag & probe (figure 8.6) and the selection & monitor triggermethod (figure 8.7) respectively. In both plots red (positrons) and blue (electrons)markers show the absolute efficiencies for simulated data, the corresponding bandsshow the efficiencies as obtained using truth information.

For the Z → ee sample the truth information is obtained by matching the truthleptons to the reconstructed leptons by requiring their distance ∆R < 0.2. Then it ischecked for the reconstructed lepton, whether it triggers or not. Each reconstructedevent from the W → eν sample is checked to see whether it would have triggered.For all these plots the full set of selection cuts is applied (see table 6.1), includinganti-crack cuts which reject all leptons with 1.37 < |ηl| < 1.52. The plots significantfor this analysis are the lower plots in each figure. They show the difference betweenpositron and electron efficiencies:

∆ǫ = ǫe+ − ǫe− (8.7)

Here, ǫ is the efficiency of triggering an event, given by ǫ = #eventstriggered/#all eventsfor the MC efficiency and by the respective efficiencies for tag & probe and selection& monitor trigger method, as defined in eq. 8.5 and eq. 8.6.

As can be seen from table 8.3 and from figure 8.6 and 8.7, the true MC and themeasured efficiencies agree well with each other for Z → ee as well as for W → eνsamples. The efficiencies obtained for the W → eν with the efficiencies for the Z → ee

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sample also agree well. However, the overall efficiency for the W → eν sample is veryslightly smaller (1% for both, reconstructed and truth level). Even though this isstill within statistical errors, part of this is the difference in the pl

T spectrum of thetwo samples. The triggered W → eν sample contains a higher fraction of low pl

T

leptons, with the plT distribution peaking around 25-30 GeV. In Z → ee events the pl

T

distribution peak around 40 GeV, it contains on average more high plT leptons than

there are to be found in W → eν events. The e25i trigger has a plT turn-on curve, the

efficiency reaches only a plateau around 30-35 GeV. Therefore leptons from Z → eedecays are on average more likely to be triggered than leptons from W → eν decays,if only an inclusive efficiency is considered. This emphasizes the need to parametrizethe trigger efficiencies obtained with a Z → ee sample in bins of various variablesbefore applying them to a W → eν sample.

Table 8.3 gives an overview over the integrated absolute trigger efficiencies forpositrons and electrons, the integrated difference between them and the result of astraight line fit through the differences for various triggers and estimation methods.This is done for the e25i trigger efficiencies obtained with the tag & probe (using aZ → ee sample) and the selection & monitor trigger method (W → eν sample). Alsothe e20 trigger efficiency obtained using the selection & monitor trigger method witha W → eν sample is shown, which is the trigger actually used in the analysis. Theintegrated differences are calculated as means and the errors given are the errors onthe mean, calculated using 10 bins in ηl. The error on the fit is the error of the fitparameter as given by the fit programme. To check, whether the efficiencies obtainedwith MC truth information agree with the efficiencies as estimated using a data-drivenapproach, bin-by-bin χ2-tests between the data and MC distributions are carried out.The results are also given in the table, showing that they are largely compatible. Oneexception is the data/MC comparison for the combined efficiency of the e25i triggerand the medium identification cuts as measured with the Z → ee tag & probe method.The other exception is for the e25i trigger efficiency for positrons as measured withthe Z → ee tag & probe method. The bad χ2/NDF-values are due mainly to thepredictions not agreeing in one or two particular bins, all of them close to the crackregion, 1.37 < |ηl| < 1.52. This is because the lepton reconstruction suffers slightlyin this transition region in the calorimeter. However, overall there is good agreementbetween truth and reconstruction for the various tested samples.

In principle, there will be background in either of the two methods consideredhere. However, it has been checked, that the fake leptons from the QCD backgroundsample, passing the medium identification cuts, will be triggered with exactly thesame probability (pseudodata: 0.99 ± 0.006 and MC: 0.98 ± 0.008, for each of thecharges) as real leptons in case they are identified with medium identification cuts. Sothere will be no distortion of the measured trigger efficiency in case they are identifiedwith medium ID cuts.

Lepton ID Bias

The lepton identification cuts could also introduce a bias that should be investigatedand accounted for in the determination of the systematic error of the lepton asym-metry. For this, it is straightforward to use the Z → ee tag & probe method, whichcan determine efficiencies of any combination of identification and trigger selectionsrelative to the probe EM cluster found opposite the tag lepton.

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Figure 8.6: The upper plot shows the absolute trigger efficiencies for the e25i trigger forpositrons (red markers) and electrons (blue markers) as obtained from simulated datawith the Z → ee tag & probe method. The corresponding Monte Carlo efficiencies areshown as red and blue bands indicating statistical errors. The lower plots depicts thedifference in efficiencies between electrons and positrons with the absolute efficienciesfor data shown as black makers and for MC shown as yellow band.

Figure 8.7: The upper plot shows the absolute trigger efficiencies for the e25i triggerfor positrons (red markers) and electrons (blue markers) for a W → eν sample asobtained from simulated data using selection & monitor trigger method, with thetrigger x20 and the selection trigger e25i. The corresponding Monte Carlo efficienciesare shown as red and blue bands. The lower plots depicts the difference between theabsolute efficiencies for data (black markers) and MC (yellow band).

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The use of the selection & monitor trigger method is more problematic, because:

• Determining the inclusive efficiency of combined trigger and identifi-cations cuts will not be feasible using a general selection & monitor samplemethod, which the selection & monitor trigger method is just a specific imple-mentation of. If leptons triggered with the xe20 trigger but without any leptonID cuts are used as a monitor sample, this monitor sample will be swamped withQCD background events. The selection sample on the other hand, where thee20 trigger and the medium ID cuts are applied, will have a much smaller QCDbackground contribution due to the large rejection rate of QCD backgroundevents. The combined efficiency will be a vast underestimation of the combinedefficiency for real leptons. In fact, using this method for a sample containingsignal and QCD background events, the combined efficiency of e20 trigger andmedium lepton ID cuts is estimated to be 0.038 ± 0.014 (electrons) and 0.047± 0.019 (positrons), which has to be compared with the true efficiencies for realleptons as obtained from a pure W signal sample of 0.85 ± 0.052 (electrons) and0.86 ± 0.049 (positrons). In this case, the combined efficiency for real leptonsin a pure sample is more than an order of magnitude larger than for the averageefficiency for real and fake electrons in a sample with backgrounds.

• Another possibility would be to investigate the efficiencies of only the iden-tification cuts with regard to sample already triggered by e20. Here,the selection sample where the full event selection is applied would be comparedto a monitor sample with all cuts including the trigger e20 but not the leptonID cuts. No monitor trigger is needed, the monitor would be a triggered EMcluster, possibly with loose ID cuts applied. The electron trigger already imple-ments some cuts to prevent hadronic jets triggering the lepton trigger, thereforea sample selected using an electron trigger will be purer in the sense that therewill be less fake electrons in the triggered sample. However, there is still someQCD background in the monitor sample, which will lower the identificationcut efficiency to 0.75 ± 0.15 (electrons) and 0.75 ± 0.12 (positrons), which isabout 10 percentage points smaller than those obtained from a pure W sample.Therefore, this method will not allow to measure absolute efficiencies either.

As demonstrated, the absolute ID efficiencies determined using the selection &monitor method will not reflect the absolute medium ID efficiencies of true leptons.However, they could still be useful to investigate a possible charge bias in the ID cuts.One could for instance check the different stages of lepton ID or even just single leptonID cuts, e.g. check, whether any charge bias occurs in the probability of a looselyidentified lepton to also pass stricter identification cuts or this one lepton ID cut.In principle the difference between positron efficiencies and electron ID efficienciesshould be zero, regardless of whether they are fake leptons or real leptons. If for anysingle ID cut, a charge bias is found, it might hint to problems in the reconstructionthat are prevailing for both fake and real leptons. The assumption that the differenceof the efficiencies for fake electrons and fake positrons is the same as for the differenceof the efficiencies for real electrons and real positrons could not be validated due tolack of statistics in the QCD sample.

Using the selection & monitor method provides a sample that will be significantlyhigher in statistics than the sample that can be used in the Z → ee tag & probe

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method. Since here it is not necessary to use an additional xe20 monitor triggerwith a high prescale, it will be possible to exploit the full size of the candidate signalsample. This means a factor of 5-10 increase in statistics, because of the higher crosssection of W → eν compared to Z → ee .

So, the selection & monitor sample method can, in principle, help to investigatecharge biases of different levels of lepton ID cuts. One interesting feature has alreadybeen uncovered using this method. It is demonstrated in figure 8.8. Here the mediumID efficiencies as obtained with a Z → ee tag & probe method (shaded bands) arecompared to the ones determined using a W sample (red and blue markers). Themedium ID efficiencies for the W sample are determined using the selection & monitorsample method with regard to an e20 triggered monitor sample, where all kinematicselection cuts are applied on the lepton, apart from the ID cuts. The lower part of theplot shows the difference between positron and electron efficiencies, where the yellowerror band indicate the difference for the Z → ee sample. The black rectangles showthe difference for all selected W → eν events, while the red triangles show the resultsfor only those W → eν events, where the leptons are reconstructed with the correctcharge. A charge misidentified lepton is a reconstructed lepton with a wrong chargeassignment (a wrong charge assignment occurs when a wrong track is associated tothe reconstructed EM cluster). Using all reconstructed leptons, that is leptons withwrong and correct charge assignment, in the efficiency determination significantlychanges the estimated efficiencies. Only using the leptons from the W → eν samplereconstructed with the right charge agrees much better with the efficiency differenceobtained with the Z → ee sample. The origin of this charge bias is not yet fullyunderstood, but seems to be connected to an ID cut on the impact parameter A0. Itwill be subject of future investigations with the objective to reduce the systematicerror due to the charge bias of the lepton ID cuts.

Since there are still unresolved problems with the identification cuts and the chargebias for misidentified leptons and since the QCD background sample is with 0.02 pb−1

just big enough to give an estimate of its influence on the efficiency, the W → eνsample is not used to determine the charge bias on the ID efficiencies. It is howeverused to determine the trigger efficiencies.

The bias on the trigger efficiencies was estimated to be 8.8e-05 ± 0.0007 (fromthe W → eν sample), the charge bias of the ID efficiencies 0.00076 ± 0.002 (usingthe Z → ee sample), using the mean and the error on the mean along the y-axes ofthe plots display the difference in efficiencies, e.g the lower part of figure 8.7 for theW → eν sample. Here, both of these biases are compatible with zero. To estimatethe final uncertainty on the lepton asymmetry, the errors on the charge bias are takenand used to scale either the electron or the positron distribution down with this value,before evaluating the asymmetry. Then the percentage deviation of this distortedasymmetry is taken to be the error on the asymmetry. The results are summarised intable 8.4.

8.1.4 Charge misidentification

Another systematic is the charge misidentification rate, which is most prominent forhigher |ηl| values. In order to get an estimate of the misidentification rate, f, thefollowing procedure was employed. Z → ee events are selected by requiring two

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method and cuts integrated efficiency difference between minus and pluselectrons positrons integrated fit

Zee tag & probe data 0.96 ± 0.01 0.96 ± 0.01 0.0014 ± 0.0009 0.0019 ± 0.0012ǫ (e25i) MC 0.95 ± 0.01 0.96 ± 0.01 0.0004 ± 0.001 0.00009 ± 0.0009

χ2

NDF[data/MC] 16.7/10 63.5/10 10.2/10 -

Zee tag & probe data 0.89 ± 0.05 0.89 ± 0.05 0.00076 ± 0.002 0.00029 ± 0.0024ǫ (IsEM medium) MC 0.89 ± 0.05 0.89 ± 0.05 0.003 ± 0.002 0.002 ± 0.001

χ2

NDF[data/MC] 3.0/10 7.0/10 3.7/10 -

Zee tag & probe data 0.82 ± 0.05 0.82 ± 0.05 0.0019 ± 0.0023 0.002 ± 0.0021ǫ (e25i MC 0.83 ± 0.05 0.83 ± 0.05 0.003 ± 0.002 0.001 ± 0.001

+IsEM medium) χ2

NDF[data/MC] 29.0/10 26.4/10 7.5/10 -

W sel. & mon. data 0.95 ± 0.02 0.95 ± 0.02 -0.0019 ± 0.0013 -0.0021 ± 0.002x20 e25i MC 0.95 ± 0.02 0.94 ± 0.02 -0.0028 ± 0.003 -0.0028 ± 0.001

χ2

NDF[data/MC] 7.4/10 10.2/10 0.7/10 -

W sel. & mon. data 0.99 ± 0.006 0.99 ± 0.006 8.8e-05 ± 0.0007 -0.00046 ± 0.003x20 e20 MC 0.98 ± 0.007 0.98 ± 0.008 6.5e-05 ± 0.0004 0.00011 ± 0.00051

χ2

NDF[data/MC] 1.0/10 1.2/10 0.6/10 -

Table 8.3: Absolute trigger efficiencies for electrons and positrons and the differencesbetween them for different datasets and triggers. The integrated efficiencies are cal-culated as the mean, while the quoted error is the error on the mean. The error onthe straight line fit is the error from the fit. For the straight line fits no compatibilitychecks are carried out.

ID cut bias Trigger bias-2.40 ≤ η < -1.92 0.45 -0.45 0.16 -0.16-1.92 ≤ η < -1.44 0.57 -0.57 0.2 -0.2-1.44 ≤ η < -0.96 0.81 -0.81 0.28 -0.28-0.96 ≤ η < -0.48 1 -1 0.35 -0.35-0.48 ≤ η < 0.00 1.1 -1.1 0.38 -0.380.00 ≤ η < 0.48 1.1 -1.1 0.38 -0.380.48 ≤ η < 0.96 1.1 -1.1 0.37 -0.370.96 ≤ η < 1.44 0.77 -0.77 0.27 -0.271.44 ≤ η < 1.92 0.62 -0.62 0.22 -0.221.92 ≤ η < 2.40 0.44 -0.44 0.15 -0.15

Table 8.4: Relative uncertainties on the lepton asymmetry given in percent due tothe uncertainty on the bias of the trigger event and identification selection for thedifferent regions of pseudorapidity η, where the uncertainty on the difference betweenǫpositrons − ǫelectrons is assumed to be 0.0007 and 0.002 respectively.

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Figure 8.8: The upper plot shows the absolute efficiencies of the medium ID cutsfor positrons (red markers) and electrons (blue markers) as determined using a Wsample and the selection & monitor trigger method. In this method, for the selectionsample all selection cuts including the ID cuts were applied and for the monitorsample no ID cuts were applied, only the other selection cuts including the triggercuts. These efficiencies are compared to the ones obtained from a Z → ee samplewith the tag & probe method (shaded areas). The lower plot shows the differencebetween the efficiencies for positron and electron samples. While the rectangularmarkers show the difference of the efficiencies for a full W → eν samples, the redtriangles show the difference in the case only leptons reconstructed with the correctcharge where regarded. The shaded band shows the difference between the positronID efficiencies and the electron ID efficiencies for the Z → ee sample. The W → eνsample without the charge misidentified leptons reproduces the difference betweenpositron and electron efficiencies much better than the sample with all W → eνleptons.

leptons above 25 GeV each, outside the crack regions and within |ηl| < 2.4, sinceall leptons fulfilling this condition will pass all layers of the pixel and strip trackingdetectors. Both leptons are required to pass all medium identification cuts. Theircombined four-momenta are required to lie within a 30 GeV window around thenominal Z mass of 91.2 GeV. Then a tag lepton is searched for and required to bedetected within |ηl| < 1.0. The raw charge misidentification rate is then calculatedas a function of the pseudorapidity |ηl| of the probe lepton:

fraw =#events equal charges

#all events(8.8)

If both leptons in an event could be used as tag leptons, each of the leptons isused once as tag and once as probe. The ηl of the probe electron is then filled with aweight of 0.5 in order not to change the total number of events used.

In order to derive the actual misidentification rate, f tagactual, the raw misidentifica-

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tion rate, f tagraw, needs to be corrected for the possibility that the tag lepton may be

misidentified, because we simply do not know and cannot know in data, which of thetwo leptons is misidentified.

fraw = (1 − f tagactual)f

probeactual + (1 − fprobe

actual)ftagactual (8.9)

The two contributions can be disentangled by assuming that for ηl bins in thecentral region of |ηl| < 1.0, the misidentification rates for the probe and the tag leptonare equal, f tag = fprobe = f central

actual . Therefore, the actual misidentification rate in eachbin of the central region, f central bin i

actual , can be extracted from the following relation

f central bin iraw = (1 − f tag)fprobe + (1 − fprobe)f tag = 2(1 − f tag)f central bin i

actual (8.10)

Since the tag electron is restricted to the central region of |ηl| < 1.0, its misiden-tification rate is equivalent to the actual central misidentification rate. As this actualcentral misidentification rate the average of the actual misidentification rates in thesingle central rapidity bins, ∅f central bin

actual , is used, since it does not make sense to ran-domly pick a specific f central bin i

actual to represent the misidentification rate of the taglepton in the whole of the central region. So, for the forward region (|ηl| > 1.0),the misidentification rate of the tag lepton is assumed to be the average of the actualmisidentification rate in the central region, ∅f central bin

actual and the actual misidentificationrate for a forward probe can then be extracted binwise as

f forwardbinraw = (1 − ∅f central bin)fprobe + (1 − fprobe)∅f central bin

= (1 − ∅f central bin)f forwardbin i + (1 − f forwardbin i)∅f central bin (8.11)

Equations 8.10 and 8.11 therefore allow us to extract the actual misidentificationrates in the single ηl bins can for central and forward regions.

The different stages of the calculation of the misidentification rate f are depictedin figure 8.9. Here fraw (black full circles) and the actual misidentification rate f asreconstructed using eq. 8.10 and 8.11 (open black circles) are shown as measuredfrom simulated Z → ee data. These two misidentification rates are compared to thetrue misidentification rate f as obtained from MC information for the Z → ee datasample as well as for a W → eν sample. To extract the true misidentification ratefrom the MC for the Z → ee sample, the leptons are matched to the true leptonwhen closer than ∆R < 0.2. Misidentified leptons are those, where the charge ofthe reconstructed matched lepton is different from the charge of the truth lepton.To extract the true misidentification rate from a W → eν sample, the W selectioncuts are used (see section 6.2). Misidentified leptons are identified by comparing thecharge of the selected reconstructed lepton with the charge of the generated W bosonin that event. Here, no matching is required, because there is only one true lepton ineach event, which determines the charge that should be measured. The errors shownin figure 8.9 are purely statistical from the actual size of the sample to be able to see,how the results compare3.

3Since the used MC Z → ee data set is larger than 100 pb−1, the actual errors that are to beexpected in early data are larger – for the estimation of the uncertainty on the lepton asymmetrydue to the misidentification rate these larger errors are used.

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The misidentification rates as obtained with the tag and probe method agrees verywell with the rate obtained using the MC truth information of the Z → ee sample.Moreover, the results of the data-driven tag & probe method agree very well with themisidentification rate obtained using MC truth information from a W → eν sample.

In order to correct the lepton asymmetry for distortions due to misidentified lep-tons, this formula is used, its derivation is discussed in appendix D

AMisID corrected =(Ameasured + ∆f)

(1 −∑ f)(8.12)

∆f is the difference and∑

f is the sum of the misidentification rates for electronsand positrons calculated as

∆f = f+corrected − f−

corrected∑

f = f+corrected + f−

corrected (8.13)

∆f and∑

f are shown in figure 8.10. Their size in each ηl bin including the upperand lower errors are summarised in table 8.5, the errors are of the same size and listedonly once. Figure and table show that ∆f is quite small in each ηl bin, with slightlyhigher corrections for higher values of ηl . Judging from figure 8.10, the true valuesof ∆f and

∑

f (W → eν ) and the values of ∆f and∑

f determined using the tag& probe method (Z → ee ) agree quite well.

When correcting the measured asymmetry using ∆f and∑

f , the propagation oferrors is as follows. Since their errors are 100% correlated, both, ∆f and

∑

f , areapplied as ∆f + σ+

∆f and∑

f + σ+P

f to calculate σ+Asymmetry and as ∆f − σ−

∆f and∑

f − σ−P

f to calculate σ−Asymmetry. σ

±Asymmetry is calculated as the difference between

the nominal corrected asymmetry (obtained using ∆f and∑

f) and the correctedasymmetry calculated using ∆f ± σ±

∆f and∑

f ± σ±P

f . The resulting relative erroron the corrected asymmetry is given in table 8.6 in percent. It is found to be lessthan 2.5% for all ηl bins.

8.1.5 Effects of Electroweak Corrections

The theoretical uncertainties on W production due to QCD effects have become in-creasingly small. The residual scale dependencies for resonant W production at thethe LHC are below 1% when QCD next-to-next-to-leading order (NNLO) correctionsare included, that takes into account matrix elements of the order of α3 when calculat-ing the Drell-Yan hard process. The rapidity distribution is completely stable againsthigher-order QCD corrections [98]. This means in turn, that other theoretical effectsgain relative importance. The differential cross sections and the shapes of differentialdistributions relevant for W measurements could be changed above the 1% level byhigher order electroweak (EW) effects. Analytical studies of electroweak corrections[99] have already shown, that higher EW corrections have an impact on the W massdetermination. The aim of this subsection is to determine the impact of electroweakcorrections for W Bosons measured at Atlas , with a specific focus on the leptoncharge asymmetry from W decays.

115

ηpseudorapidity -2 -1 0 1 2

char

ge m

isid

entif

icat

ion

rate

0

0.005

0.01

0.015

0.02

0.025Raw Data MisID Rate (Zee)True MisID Rate (Wenu)actual MisID Rate (Zee)True MisID Rate (Zee)

a) misidentification rate for electrons


char

ge m

isid

entif

icat

ion

rate

0

0.005

0.01

0.015

0.02

0.025Raw Data MisID Rate (Zee)True MisID Rate (Wenu)actual MisID rate (Zee)True MisID Rate (Zee)

b) misidentification rate for positrons

Figure 8.9: The reconstructed raw (black dots) and actual (open circles) misidentifi-cation rates obtained from a Z → ee data sample for electrons (a) and positrons (b)is compared to the true misidentification rate obtained from Z → ee (blue dots) andW → eν (red triangles) samples.


f∆D

iffer

ence

of M

isID

Rat

es

-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0

0.001

0.002

a) Difference of misid. rates, ∆f


fΣS

um o

f Mis

ID R

ates

0.005

0.01

0.015

0.02

0.025

0.03

0.035

b) Sum of misidentification rates,∑

f

Figure 8.10: Figure a) shows the comparison of the difference in the actual misiden-tification rates between positrons and electrons (black open circles) and the truedifference (red triangles). Figure b) shows the sum of the misidentification rates.

There are two classes of EW corrections, virtual corrections and real corrections,both of which contribute to the normalisation, i.e. the total cross section. The real cor-rections have additionally bremsstrahlung photons, so-called prompt photons, in theevent. Among the programs used to take into account these EW corrections is PHO-TOS [100], which implements the virtual and the real corrections in a QED partonshower approach in leading-log approximation. The programme modifies the kinemat-ics appropriately, assuming energy-momentum conservation, in a parton shower stepthat follows the Born-level matrix element calculation. In this analysis PHOTOS willbe used to study the effect of EW corrections on selected W boson measurements.

The results are obtained using the datasets described in table 8.7, where the EWcorrections as implemented in PHOTOS are either switched on or off, such that twootherwise identical samples with identical random seeds could be compared. Forthis purpose, PHOTOS is interfaced to the MC generator HERWIG. The studies arecarried out on generator truth level. On generator level a lepton filter cut is applied;only events with final state leptons with pl

T > 10 GeV and |ηl| < 2.7 are processed

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pseudorapidity η correction factor ∆f correction factor∑

f -σ∆f +σ∆f

-2.4 ≤ η < -1.92 -0.002184 0.02496 0.0038 0.0048-1.92 ≤ η < -1.44 0.0004204 0.008044 0.0018 0.0026-1.44 ≤ η < -0.96 0.0003387 0.005787 0.0011 0.0015-0.96 ≤ η < -0.48 1.341e-05 0.001384 0.00076 0.0013-0.48 ≤ η < 0 -0.0006262 0.0006262 0.00047 0.000960 ≤ η < 0.48 -0.0006238 0.0006238 0.00046 0.000960.48 ≤ η < 0.96 0 0 0.00013 0.000810.96 ≤ η < 1.44 -0.0008551 0.004776 0.001 0.00141.44 ≤ η < 1.92 -0.0016 0.01018 0.0021 0.00291.92 ≤ η < 2.4 -0.004301 0.021 0.0034 0.0044

Table 8.5: Misidentification correction factors ∆f and∑

f in the different regions ofpseudorapidity ηl , the errors given reflect the uncertainty in 100 pb−1, they are thesame for ∆f and

∑

f .

pseudorapidity η error (-, %) error (+, %)-2.4 ≤ η < -1.92 2.19 2.8-1.92 ≤ η < -1.44 1.26 1.81-1.44 ≤ η < -0.96 1.05 1.42-0.96 ≤ η < -0.48 0.845 1.43-0.48 ≤ η < 0 0.566 1.160 ≤ η < 0.48 0.553 1.160.48 ≤ η < 0.96 0.152 0.9450.96 ≤ η < 1.44 0.915 1.281.44 ≤ η < 1.92 1.53 2.131.92 ≤ η < 2.4 1.94 2.49

Table 8.6: Relative error on lepton asymmetry due to charge misidentification in thedifferent regions of pseudorapidity η.

further.The main difference between the samples with and without EW corrections is a

shift of the lepton to lower transverse momenta. This is shown in figure 8.11, whichdepicts the ratio (NPHOTOS

l /NBornl ) as a function of pl

T . A dotted line indicates the cutvalue of pl

T < 25 GeV. The error bars in figure 8.11 are showing the pure statisticaluncertainties. Since the samples are highly correlated and the events, apart frommodifications due to the EW parton showers, are identical an additional approachwas used in order to determine the uncertainty on NPHOTOS

l /NBornl . For each of the

datasets two subsamples were created, which comprised events with either even orodd event numbers. For each of these subsamples the ratio NPHOTOS

l /NBornl was

determined and then used in order to create the coloured error band in figure 8.114.

4The error band is create by using the ratio calculated on the full sample as the central value.Then the differences of this central value and the central values of the ratios calculated with the oddand even sample respectively are added in quadrature and used as errors to create the band:

117

It is clearly visible that PHOTOS induces a shift to lower plT values – for lower values

of lepton transverse momentum the observed event rate for PHOTOS can be as muchas 15% higher compared to the sample generated without EW corrections. For highertransverse momenta the observed rate when taking into account EW corrections isabout 10% lower compared to the Born level rate.

Due to the shifted plT values, EW corrections affect the number of events that

pass the lepton filter cuts (plT > 10 GeV and |ηl| < 2.7) and the event selection

cuts (plT > 25 GeV and |ηl| < 2.5). This can also be seen in table 8.7, where the

efficiencies of these selections are given. For example, after the event kinematics havebeen modified by the PHOTOS parton shower, the low pl

T leptons no longer fulfil thelepton filter cuts and a 1.3% lower acceptance cut efficiency is reported for the samplewith EW corrections.

This plT difference has profound consequences for other distributions as shown in

figure 8.12. The figure shows the absolute rapidity distributions of the leptons, com-paring the sample with electroweak corrections (black squares) to the sample withoutEW corrections (red circles) for electrons a) and positrons b) respectively. Also shownin figure 8.12 c) and d) are the ratios of these distributions, NPHOTOS

l /NBornl . For these

distributions basic event selections cuts of plT > 25 GeV and |ηl| < 2.5 are applied

on generator level on the samples. Depending on the samples, the cuts have differentselection efficiencies due to the pl

T shift, also leading to observable differences in theηl distributions.

Figure 8.12 shows that while the relative difference between the samples is initself flat in shape, it is still far from being zero. The relative differences in the ηl

distributions between the samples with and without EW corrections, calculated as1.− (NPHOTOS

l /NBornl ), amount to 4.5±0.1% for positrons and 4.3±0.1% for electrons.

These are mean values, obtained by averaging over the values of each bin and usingthe standard deviation σ as error. Fitting a constant gives a relative difference of4.5±0.2% (positrons) and 4.3±0.3% (electrons). The differences between the sampleswith and without EW corrections are also evaluated for the lepton filter cuts ongenerator level of pl

T > 10 GeV and |ηl| < 2.7. The differences for these cuts amountto 1.2 ± 0.1% (1.2 ± 0.2% from the fit) for the e− distribution and 1.4 ± 0.1% (1.4 ±0.2%, fit) for the e+ distribution. For these softer cuts, the differences are again causedby a the global shift of pl

T . No distortion of the shape of the rapidity distributions isvisible and the distributions are therefore not shown here.

µnominal ± σerror band = µnominal ±√

(µnominal − µeven)2 + (µnominal − µodd)2 (8.14)

Herwig+Jimmy+Tauola ATHENA 12.0.6.1 Lepton Filter efficiency LuminosityMC truth sample pl

T > 10 GeV plT > 25 GeV

# events |ηl| < 2.7 |ηl| < 2.5

with PHOTOS ∼ 825661 0.6402 0.4590 N.A.

Born level ∼ 836572 0.6486 0.4801 48.1 pb−1

Table 8.7: Datasets used for the study of EW effects on the W asymmetry measure-ment. The luminosity for the PHOTOS dataset is not given, as there is no crosssection estimate for the EW processes in the PHOTOS parton shower approach.

118

[GeV]T

p10 20 30 40 50 60 70 80

Bor

nNP

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total sampleodd/even subsample

ATLAS

a) Ratio for the pT of the decay lepton

Figure 8.11: The ratio NPHOTOS/NBorn for transverse momentum of the lepton comingfrom the W boson decay, pl

T , is depicted. The error bars show statistical uncertainties,the yellow error band indicates variations between data subsample to get an errorestimate from statistical fluctuations in these highly correlated samples. A dashedline indicates a cut of pl

T > 25 GeV.

The lepton asymmetry distribution for the two high statistics sample with andwithout EW corrections is depicted in figure 8.13a) as a function of lepton rapidityagain for cuts of pl

T > 25 GeV and |ηl| < 2.5. There are no significant differencesbetween the Born level and the higher order calculations visible. This is also seen in8.13 b), where the ratio of the two asymmetry distributions APHOTOS

l /ABornl is shown.

A coloured error band indicates statistical fluctuations as calculated using the odd andthe even subsamples. The relative difference in the lepton asymmetry between thesamples with and without electroweak corrections, calculated as 1.−APHOTOS

l /ABornl ,

is 0.4±0.4%. Fitting a constant yields 0.7±1.1%. If we evaluate the differences forthe basic lepton filter cuts on generator level of pl

T > 10 GeV and |ηl| < 2.7, we findthat the averaged difference is 0.3 ± 0.3%, while fitting a constant gives a relativedifference of 0.5 ± 0.7%. Again, the distributions are not shown for the softer cuts.

These differences for the samples with and without EW corrections are summarisedfor the rapidity and for the asymmetry distributions in table 8.8. For the rapiditydistributions the differences are of the order of several percent. This means thatfor measurements which utilise the rapidity distribution of the leptons in order toconstrain the PDFs, EW corrections cannot be neglected, because they are of thesame order as the PDF uncertainties. However for the lepton asymmetry distributionthe differences between the samples are compatible with zero.

It should be noted, that here no e/γ merging procedure was implemented, whichmerges photons and leptons if they are so close together that they cannot be ex-perimentally measured as two single particles. This implies that the effects of theelectroweak correction on the acceptances are possibly overestimated and should be

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d) ratio NPHOTOS/NBorn for the rapiditydistribution of e+.

Figure 8.12: Comparison of the lepton rapidities for the samples generated with PHO-TOS and without PHOTOS, once as a direct comparison (a and b) and also presentedas the ratio NPHOTOS/NBorn is shown for electrons (c) and positrons (d). Here, theerror bars show the pure statistical uncertainties and the coloured error bands showvariations between events with even and odd event numbers respectively. Basic eventselection cuts are applied of pl

T > 25 GeV and |ηl| < 2.5.

η rapidity -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

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pton

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b) ratio APHOTOSl /ABorn

l

Figure 8.13: Comparison of the lepton asymmetry for the samples generated withPHOTOS and without PHOTOS, once as a direct comparison (a) and also pre-sented as the ratio APHOTOS

l /ABornl (b). Here, the error bars show the pure statis-

tical uncertainties and the coloured error bands show variations between events witheven and odd event numbers respectively. Basic event selections cuts are applied ofpl

T > 25 GeV and |ηl| < 2.5.

120

relative difference (constant fit) relative difference (mean)pl

T > 10 GeV plT > 25 GeV pl

T > 10 GeV peT > 25 GeV

APHOTOSl /ABorn

l -0.5 ± 0.7% -0.7±1.1% -0.3 ± 0.3% -0.4±0.4%NPHOTOS/NBorn

|η| (positive leptons) -1.4 ± 0.2% -4.5±0.2% -1.4 ± 0.1% -4.5±0.1%NPHOTOS/NBorn

|ηl| (negative leptons) -1.2 ± 0.2% -4.3±0.3% -1.2 ± 0.1% -4.3±0.1%

Table 8.8: Difference due to the electroweak corrections as obtained from a constantfit and from the mean of the distributions.

re-evaluated with a merging procedure when preparing a measurement of the differ-ential cross section dσW/dy.

Since the difference between the samples with and without EW corrections iscompatible with zero for the lepton asymmetry distribution, we do not attribute asystematic uncertainty on the lepton asymmetry due to EW corrections.

8.2 Expected Uncertainties and Implications for

PDFs at the LHC

8.2.1 Expected Uncertainties on Lepton Asymmetry

In the previous sections, various aspects of a W asymmetry measurement at theLHC are explored for a data sample generated using

√s = 14 TeV with an integrated

luminosity of 100 pb−1. Independent of the actual centre of mass energy used for earlyrunning, which is more likely to be around

√s = 7 TeV, an integrated luminosity of

100 pb−1 is a reasonable expectation for the first year of data taking. It is expected,that the size of the uncertainties on the lepton asymmetry depends strongly on thesize of the collected data sample and only very little on the centre of mass energy.Hence, the uncertainties estimated in this thesis can serve as predictions also for othercentre of mass energies. In the following the size of the individual uncertainties shallbe compared and the expected total systematical as well as statistical error on ameasurement of the lepton asymmetry with first data at Atlas are given. The totalsystematical and statistical errors are determined in bins of absolute pseudorapidity,|ηl| , with and without an additional isolation cut of ET,iso

frac < 0.1.Figure 8.14 depicts the size of the individual systematic errors as well as the statis-

tical uncertainty on a measurement of the lepton asymmetry at Atlas as estimated inthe previous sections. Table 8.9 summarises the errors, listing the individual sourcesof uncertainty, their relative size in percent on the lepton asymmetry and the be-haviour of these relative errors as a function of ηl . The errors as absolute values andtheir variation with ηl are given in table 8.10. For the standard set of cuts, implyingRQCD = 32± 4.8%, the error due to the QCD background is at 7% the largest for thelepton asymmetry measured at Atlas . It is followed by the statistical error, whosesize changes from 3.5% in the end cap regions to 7% in the central barrel for ηl=1.It should be noted that the lepton asymmetry value itself varies from 0.08 at ηl=0 toaround 0.22 at ηl=2.4, so that a decrease of the percentage errors on the asymmetrywith ηl does not necessarily reflect a decrease in the absolute values of the errors as

121

source of uncertainty behaviour as function of ηl relativeuncertainty [%]

QCD background flat, possible slightly larger in the crack region ∼7% (RQCD = 32 ± 4.8%)and the endcaps ∼3.5% (RQCD = 12 ± 3%)

6ET scale uncertainty relatively flat as function of ηl 4-5%larger around ηl =1, most likely fluctuation

Statistical error percentage errors smallest in the endcaps, 2.5 - 5%about twice as large for central ηl

EWK Backgrounds largest for ηl =0, smallest in endcaps 1.5-3.5%ηl scale uncertainty relatively flat as function of ηl , fluctuations 1-2%

ID cut charge bias largest for ηl =0, smallest in endcaps 0.5-1.5 %

charge mis-ID larger for ηl >2.0 0.5-2.5%6ET resolution uncertainty large statistical fluctuations, 0.5-2%

relatively flat as function of ηl

plT scale uncertainty large fluctuations 0.2-1%

trigger charge bias largest for ηl =0, smallest in endcaps 0.2-0.5 %

ηl resolution uncertainty relatively flat as function of ηl 0.3%

plT resolution uncertainty relatively flat as function of ηl , fluctuations 0.2-0.4%

Table 8.9: The sources for errors on a measurement of the lepton charge asymmetry atAtlas are summarised as determined in the previous sections. Listed are the sourceof the individual errors, their relative size and how the percentage errors change as afunction of ηl .

well.The largest uncertainty after the QCD background and the statistical errors is the

uncertainty on the 6ET scale, whose size is 4-5%. It does not change systematicallywith ηl, but fluctuates heavily due to the statistical size of the MC sample usedto determine this uncertainty. The same is true also for the ηl and pl

T scale andresolution uncertainties. The electroweak background contributes with 1.5-3.5% to theuncertainty of the measurement, where here tt, W → τν and Z → ee backgroundsare considered. The percentage error due to the electroweak backgrounds dependsstrongly on ηl, again with the largest percentage error in the central region aroundηl=0 and the smallest in the end caps, ηl=2.4. The percentage error due to the IDcut charge bias is with 1-3% the next largest and varies again as a function of ηl. Theerrors due to the misidentification are around 0.5-2.5%, which will be reduced withmore statistics. ηl scale uncertainty (1-2%) and 6ET resolution uncertainty (0.5-2%)follow as the last ones above a percentage error of 1%. Both fluctuate wildly due tolimited statistics of the available MC sample with full detector simulation. All otherpercentage errors lie below 1%.

Adding these errors in quadrature gives the total relative error on the lepton asym-metry as measured at Atlas . It varies from 8.5 to 11% for RQCD = 32±4.8%, wherethe relative error is in general larger at smaller |ηl|. The asymmetry as it would bemeasured is also depicted in figure 8.15. It is corrected for the misidentification rateas measured with a data-driven method (see section 8.1.4). The three major contri-butions to the total uncertainty are shown separately as cumulative errors bars for 1.)the statistical error only, 2.) the combined statistical and systematic errors excludingQCD background as well as 3.) the total error on the measurement. The yellowerror band shows a global 5% uncertainty, the blue error band a 10% uncertainty,

122

source of uncertainty behaviour as function of ηl Absoluteuncertainty

QCD background rising with |ηl| ∼0.006-0.016 (RQCD = 32 ± 4.8%)∼0.003-0.008 (RQCD = 12 ± 3%)

6ET scale uncertainty rising as function of |ηl| 0.003-0.01

Statistical error relatively flat as function of ηl 0.003-0.006bigger in crack region (small ǫ)

EWK Backgrounds relatively flat as function of ηl 0.002-0.004

ηl scale uncertainty rising with |ηl|, fluctuations 0.0003-0.005ID cut charge bias flat as function of ηl 0.001

charge mis-ID flat, larger for |ηl| >2.0 0.0005-0.0056ET resolution uncertainty large statistical fluctuations, 0.0001-0.002

relatively flat as function of ηl

plT scale uncertainty large fluctuations 0.0001-0.002

trigger charge bias flat as function of |ηl| 0.0005ηl resolution uncertainty large fluctuations 0.00005-0.001

plT resolution uncertainty relatively flat, fluctuations 0.0001-0.0006

Table 8.10: The sources for errors on a measurement of the lepton charge asymmetryat Atlas are summarised as determined in the previous sections. Listed are thesource of the individual errors, their absolute size and how the absolute errors changeas a function of ηl .

η region Asymmetry σstat. σsys. σtot σstat. σsys. σtot

[%] [%] [%] abs. abs. abs.-2.4 < η < -1.92 0.22 2.3 7.9 8.2 0.0049 0.017 0.018-1.92 < η < -1.44 0.17 3.4 7.7 8.4 0.0058 0.013 0.014-1.44 < η < -0.96 0.12 4.1 7.8 8.7 0.005 0.0095 0.011-0.96 < η < -0.48 0.099 4.5 8.4 9.5 0.0045 0.0083 0.0094

-0.48 < η < 0 0.091 4.8 7.9 9.2 0.0044 0.0071 0.00830 < η < 0.48 0.091 4.8 7.4 8.8 0.0044 0.0067 0.008

0.48 < η < 0.96 0.094 4.8 8.5 9.8 0.0045 0.008 0.00920.96 < η < 1.44 0.13 4 8 8.9 0.0051 0.01 0.0111.44 < η < 1.92 0.16 3.7 10 11 0.0058 0.016 0.0171.92 < η < 2.4 0.22 2.3 8.1 8.4 0.0049 0.018 0.018

Table 8.11: Statistic, systematic and total relative and absolute errors on leptonasymmetry with RQCD=32±4.8% as a function of ηl.

the magenta error band a 20% uncertainty. How well this reconstructed asymme-try recovers the true asymmetry of the sample investigated is discussed in section 8.3,where also different methods to extract the true lepton asymmetry from the measuredreconstructed lepton asymmetry are discussed. The numerical values of the expectedstatistical, systematic and total relative uncertainties are quoted for each ηl bin intable 8.11.

Using the standard cuts, causing RQCD=32±4.8%, and conducting the measure-ment as a function of ηl leads to a total error of around 8.5 to 11%. There are nonoticeable differences in the size of the errors on the measured asymmetry between

123

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Statistical errors

scale uncertaintyTEBkg uncert. (EWK, ttbar)

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scale uncertaintyηMisID uncertainty

resolution uncertaintyTETrigger uncertainty

scale uncertaintyTP

resolution uncertaintyη resolution uncertaintyTP

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ativ

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Figure 8.14: The percentage errors on lepton asymmetry for the various uncertaintiesare explored here, shown in linear and logarithmic scale. This plots makes it evident,that the most prominent uncertainties apart from the uncertainty due to QCD back-grounds and the statistical uncertainty are coming from the 6ET scale and electronidentification cuts.

the positive η and negative η regimes. This can also be seen in figure 8.14, where allrelative errors are plotted as a function of ηl. Therefore, due to the symmetry of thedetector it is possible to measure the asymmetry as a function of |ηl|, thus mainlydecreasing the statistical error. The analysis presented in the previous sections istherefore repeated as function of |ηl| for the standard set of cuts, described in table6.1.

Additionally the uncertainties are re-evaluated for an additional isolation cut ontop of the standard cuts, ET,iso

frac < 0.1. The cut suppresses significantly the QCDbackground contribution to a value of RQCD = 12 ± 3%.

In the following, the uncertainties on the asymmetry measurements shall be inves-tigated for standard as well as for optional isolation cuts as a function of absolutepseudorapidity, |ηl|. The results for the individual systematic errors are not discussedand presented as detailed as in the previous sections, but only graphically comparedregarding their size (figure 8.16 and 8.17 with linear and logarithmic scale) and sum-

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0.24 QCD error± sys. ± stat. ±Asymmetry sys.± stat. ±Asymmetry

stat.±Asymmetry 5% error band10% error band20% error band

Figure 8.15: Lepton asymmetry at Atlas with statistical, statistical and systemat-ical errors excluding QCD background as well as the total error to be expected forthe measurement at Atlas are shown as different errors bars on full black markers.Coloured error bands indicated relative uncertainties of 5, 10 and 20 %.

marised as a list of statistical, systematic and total uncertainty on each ηl bin (table8.12).

The top plot in figure 8.16 shows the relative uncertainties for the individualsystematic uncertainties as a function of |ηl| for the standard cuts, RQCD = 32 ±4.8%. Comparing the percentage errors for |ηl| and ηl , the statistical errors shrinkas expected due to the fact, that now there are roughly twice as many events in eachbin as before. The contribution to the uncertainty due to backgrounds other thanQCD has shrunk slightly as well (shown in black open crosses). Apart from that, nodifference to the relative uncertainties for the standard cuts as a function of ηl arevisible.

The bottom plot in figure 8.16 shows the relative uncertainties for the additionalisolation cut and RQCD = 12 ± 3%. They are very similar to the ones obtainedwith the standard cuts. The most prominent difference is of course the level of QCDbackground and the resulting systematic uncertainty (red triangles), which is a factorof two smaller for the sample with the isolation cut. Other than that, there are nosignificant differences between the relative uncertainties visible.

Table 8.12 summarises these findings by listing the statistical, systematic andtotal relative uncertainties for both cut scenarios for each |ηl| bin. For both, the totalrelative error tends to be larger in the central region, decreasing slightly when goingto higher values of |ηl| .

Figure 8.18 shows the reconstructed asymmetries, which are corrected for themisidentification, as a function of |ηl| for the standard cuts (left plot) and the addi-

125

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additional Isolation cut

Figure 8.16: The relative errors in percent for the various uncertainties are exploredhere as a function of absolute pseudorapidity, |ηl| for two different cut scenarios,resulting most prominently in different QCD background levels of RQCD=32% (top)and RQCD=12% (bottom).

tional isolation cut (right plot) with their errors. The asymmetries are reconstructedfrom a pure signal sample, the backgrounds are assumed to have been subtracted per-fectly. The uncertainty due to the subtracted backgrounds is still taken into accountin the error calculation. Error bands indicate relative errors of 5%, 10% and 20%.The total relative errors for the standard cuts are between 8-11%, just within the10% band. The total relative errors of the asymmetry obtained using isolation cutsfit more comfortably within 5-7.5% total relative error.

8.2.2 Comparison of Experimental with PDF Uncertainties

The expected uncertainty on the lepton asymmetry measurement is 8-9% (standardcuts) and 5-6.5% (additional isolation cut). In this section the resulting impact ofmeasurements with the quoted uncertainties is evaluated. For this purpose the eventgenerator Pythia 8 [44] is used. 100 million events are generated for each of the 41

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Figure 8.17: The relative errors in percent for the various uncertainties are exploredhere as a function of absolute pseudorapidity, |ηl| for two different cut scenarios,resulting most prominently in different QCD background levels of RQCD=32% (top)and RQCD=12% (bottom).

MSTW2008nlo90cl PDF error sets [17] and the 44 CTEQ66 PDF error set [18]. Equa-tion 2.9 was used in order to calculate the PDF errors on the lepton asymmetry aspredicted by Pythia 8 using CTEQ66 PDFs or alternatively MSTW08 PDFs. Addi-tionally 1 million events are generated for each of the 1000 error sets of the NNPDFcollaboration. For NNPDFs the central prediction in each bin of ηl is the mean valueof all the 1000 error set predictions. The error on the mean in each bin is the RMSof the 1000 NNPDF error set predictions. Basic acceptance cuts of pl

T > 25 GeV,pν

T > 25 GeV and |ηl| < 2.4 are applied to all events, reducing the statistics fromabout 100 mio. events to about 40 mio. events for each of the PDF sets. The twolepton asymmetries with their uncertainties are compared in figure 8.19, left. TheCTEQ66 prediction is shown as a black markers and its PDF uncertainty indicatedby a black error band. It agrees quite well with the NNPDF prediction, shown asyellow error band. But the CTEQ66 lepton asymmetry is significantly larger than theMSTW2008 prediction, shown in red. The differences between these most recent PDF

127

η region Asymmetry σstat. σsys. σtot σstat. σsys. σtot

[%] [%] [%] abs. abs. abs.RQCD = 32 ± 4.8%

0.00 ≤ η < 0.48 0.091 3.4 7.3 8.1 0.0031 0.0066 0.00730.48 ≤ η < 0.96 0.096 3.3 8.4 9.0 0.0032 0.0081 0.00870.96 ≤ η < 1.44 0.13 2.8 7.7 8.2 0.0036 0.0096 0.011.44 ≤ η < 1.92 0.17 2.5 8.6 9.0 0.0041 0.014 0.0151.92 ≤ η < 2.4 0.22 1.6 7.7 7.8 0.0035 0.017 0.017

RQCD = 12 ± 3%0.00 ≤ η < 0.48 0.091 3.4 3.9 5.2 0.0031 0.0036 0.00470.48 ≤ η < 0.96 0.096 3.4 5.7 6.6 0.0032 0.0055 0.00630.96 ≤ η < 1.44 0.12 2.9 4.6 5.5 0.0036 0.0058 0.00681.44 ≤ η < 1.92 0.16 2.5 6 6.5 0.0041 0.01 0.0111.92 ≤ η < 2.4 0.22 1.6 4.5 4.8 0.0035 0.0099 0.011

Table 8.12: Statistic, systematic and total error on lepton asymmetry withRQCD=32±4.8% and RQCD=12±3% as a function of |ηl| .

ηPseudorapidity 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

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5% error band10% error band20% error band

Figure 8.18: Lepton asymmetry at Atlas as a function of absolute pseudorapidity, |ηl|for two different cut scenarios. Statistical, statistical and systematical errors excludingQCD background as well as the total error to be expected for the measurement atAtlas are shown as different errors bars on full black markers. Coloured error bandsindicated relative uncertainties of 5, 10 and 20 %.

sets are so large, that their error bands do not even overlap for most of the |ηl| binsinvestigated here. The simulated data is shown with light and dark error bars, indi-cating the standard and the optional set of cuts with RQCD = 32% and RQCD = 12%.It agrees better with the CTEQ66 prediction, which is not surprising. The data wasgenerated using the CTEQ6LL5 PDF set.

The main reason for the large differences between CTEQ and MSTW PDF pre-dictions in figure 8.19 are the distributions of u and d valence quarks, where there isno specific experimental data available for x < 10−2, so that the shapes of the valence

5Global PDF fit carried out with leading order DGLAP evolution using leading order values ofαs

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ton

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CTEQ66 NLO 90% C.L.

MSTW08 NLO 90% C.L.

=12%, CTEQ6LL, LOQCD

sim. data, R

=32%, CTEQ6LL, LOQCD

sim. data, R

η absolute rapidity 0 0.5 1 1.5 2 2.5

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io A

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EQ

66)

0.7

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1

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CTEQ66 NLO 90% CL.MSTW2008 NLO 90% CL.average PDF uncertaintyaverage PDF uncert. (centered)

Figure 8.19: On the left hand side the prediction for the lepton asymmetry at√s =14

TeV is shown for the NLO PDF sets CTEQ66 (black), MSTW08 (red) and NNPDF(yellow), with the errors indicated as bands. On the right hand side, the MSTW08and CTEQ66 predictions for the asymmetries are shown normalised to the CTEQ66prediction. When presented like this, it becomes even more obvious that the centralvalues of the two PDF sets differ by 10-15% partly outside their respective error bands.The blue line shows the envelope enclosing the upper error of the CTEQ66 PDF setand the lower errors of the MSTW08 PDF. The yellow error shows the same, but iscentered on 1 and is used to determine the average PDF uncertainty steming from theindividual PDF error sets as well as from the differences between the central valuesof the different PDF sets.

quarks in the kinematic region of the W production at the LHC depend very cruciallyon the input parametrisation and specifics of the global PDF fit [41, 101]. In view ofdifferences between the central values of the CTEQ and MSTW PDF predictions, itwould be an underestimation, just to take the PDF uncertainty of one of the PDFsets or just the average value of the uncertainties of CTEQ66 and MSTW08.

The PDF uncertainty on the lepton asymmetry measurement is therefore eval-uated using an approach illustrated in figure 8.19, right plot. Here, the ratio ofboth, CTEQ66 and MSTW08 central value PDF asymmetries, are normalised to theCTEQ66 central value PDF. The CTEQ66 ratio is shown as black squares, while theMSTW08 results are indicated by red triangles. Their error bands are also normalisedto the CTEQ66 central value PDF and shown as error bars on the markers. Now theenvelope of these two predictions is taken and called the ”average PDF uncertainty”,which is indicated by a blue line. Since the normalisation to one specific PDF set tocalculate the uncertainties is a somewhat random choice, the average PDF uncertaintyis centred at unity with symmetric errors, indicated as a yellow error band in figure8.19. It is rather this yellow error band, corresponding to about ±10 − 15% relativeuncertainty, which corresponds to the systematic bias on the lepton asymmetry whenone takes into account the global differences between the CTEQ66 and MSTW08 PDFsets.

Comparing the size of this systematic bias with the expected experimental error onthe lepton asymmetry allows an estimation of just how much the lepton asymmetrymeasurement will constrain the PDFs. Figure 8.20 depicts on the left hand sidethe PDF uncertainty as open triangles with a yellow error band, that represents a

129


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Rat

io R

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0

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0.6

0.8

1

1.2

=32%, standard cuts, av. PDFQCD

, Rexpσ

=12%, additional isolation cuts, av. PDFQCD

, Rexpσ

Figure 8.20: Comparison of PDF uncertainties with experimental errors of a prospec-tive lepton asymmetry measurement at Atlas as a function of |ηl| for the stan-dard cuts and RQCD = 32 ± 4.8% as well as for the additional isolation cut andRQCD = 12 ± 3%, shown as black squares and black triangles respectively. The PDFuncertainty, shown as open triangles, are larger than the experimental errors over thewhole range of |ηl|. The error bars and the yellow band indicate an assumed 20%uncertainty on the experimental as well as on the PDF errors. On the right handside the ratio of the experimental uncertainties to the PDF errors is shown for thestandard cuts as black squares and for RQCD = 12± 3% as black triangles – this ratiois an estimation of the factor by which PDF uncertainties might be reduced whenusing including a measurement of the lepton asymmetry into the PDF fits.

20% uncertainty on the PDF uncertainty itself. Also shown in the same plot are theexperimental uncertainties of the standard cuts (RQCD = 32± 4.8%) as black squaresand of the measurement conducted using the additional isolation cut (RQCD = 12±3%)as open circles. Here again the error bars represent a 20% uncertainty on the depictedvalues. The 20% error on the PDF and the experimental uncertainties is meantto express that these uncertainties themselves are the result of an estimation usingsimulated data. The size of the PDF uncertainties depend crucially on the choice,how the predictions of the CTEQ and MSTW and possibly other collaborations is tobe combined. The size of the systematical uncertainties depend on measurements andestimations from statistically limited samples, therefore they cannot exactly matchwhat will be observed for a statistically independent and also statistically limited realdata sample. The 20% are an estimation of this uncertainty, meant to be a neithertoo optimistic nor too pessimistic guess of how different the uncertainties could be.

Figure 8.20 shows that while the PDF uncertainties decrease from 15.6% at central|ηl| to 9.6%, the experimental errors from both variations of the measurement lie with8-9% and 5-6.5% significantly below. For convenience, the numbers in the single |ηl|bins are also compared binwise in table 8.13.

On the right hand side of figure 8.20 the ratios of the experimental uncertaintieswith the PDF uncertainty is shown, σexp/σPDF. In first approximation, the PDFdescription of the u and d valence quark ratio, uV /dV will improve by the same factoras σexp/σPDF. For the standard cuts the expected improvement factor is then 0.7-0.8 as shown in figure 8.20 with black squares. For a measurement with additionalisolation cuts, the PDF errors are expected to be halved. It should be noted that

130

η region total error total error total errorRQCD=32% RQCD=12% PDF uncertainty (envelope)

0.00 ≤ η < 0.48 8.1 5.2 14.440.48 ≤ η < 0.96 9.0 6.6 15.590.96 ≤ η < 1.44 8.2 5.5 12.761.44 ≤ η < 1.92 9.0 6.5 12.061.92 ≤ η < 2.40 7.8 4.8 9.62

Table 8.13: Comparison of total experimental errors with PDF uncertainties as afunction of |ηl|.

these improvement factors significantly differ from 1 for most of the |ηl| bins, evenif an error of 20% is assumed on experimental as well as PDF uncertainties. Thisdemonstrates the importance of the lepton charge asymmetry measurement for thePDFs used in the LHC kinematic region.

8.3 Presentation of Results of the Lepton Asym-

metry Measurement

In the previous section, the measured reconstructed asymmetry with its associatederrors was presented and these errors were compared to the uncertainties of PDFpredictions. In this section, a closer look shall be taken at how the measured recon-structed asymmetry relates to the true asymmetry and how it could be published.

8.3.1 Relation between True and Reconstructed Lepton Asym-

metry

The relation between the true lepton asymmetry, Atruel , and the reconstructed lepton

asymmetry, Arecol , when only the detector resolution has to be accounted for and once

corrections for backgrounds and misidentification are applied, is:

Arecol = Atrue

l ⊗ Detector Resolution (8.15)

The Detector Resolution can be described using resolution functions, R. Theseresolution functions describe, how the reconstructed values of the variables depend onthe true values and how these dependencies change as a function of the true values:

R(variableltrue) =

variablereco

variabletrue (variableltrue) (8.16)

R should be evaluated for the relevant cut variables of the analysis, namely 6ET ,pl

T and ηl .

8.3.2 Resolution Functions of the Atlas Detector

The knowledge of the resolution functions of leptons and 6ET will be crucial for theextraction of the true lepton asymmetry based on the lepton asymmetry as measured

131

with the reconstructed leptons in the detector. In this section, the resolution functionsfor 6ET , pl

T and ηl are evaluated.The resolution functions are extracted using the fully simulated W → eν data

sample, described in section 6.1. In the signal sample, the generated truth lepton ofthe W → eν decay is matched to the reconstructed lepton with the condition that∆R =

√

∆φ2 + ∆η2 < 0.2. Both truth and reconstructed lepton are required to fulfila set of relaxed cuts:

• plT > 15 GeV

• 6ET> 15 GeV

• |ηl| < 1.37 and 1.55 < |ηl| < 2.4

• medium ID cuts (reconstructed lepton only) [see section 6.1 and [67]]

Where these cuts are fulfilled, the resolution functions variablereco

variabletrue are calculated inbins of ηl , pl

T and 6ET of the truth level lepton. As an example the resolution functionsare shown in figure 8.21 for 6ET , pl

T and ηl for 0.0 < ηl < 0.48 for four bins of 6ET andpl

T respectively. For both, 6ET and plT , the lower energy bins depict an asymmetric

resolution function with a bias towards reconstructed plT that are higher than the

true plT . This is in part due to the minimum pl

T and 6ET cuts on reconstructed andtrue values.Another factor for leptons is bremsstrahlung that affects the energy ofthe reconstructed lepton. The pl

T resolution is much better than the 6ET resolution.The 6ET resolution functions show a peculiar feature as 6ET increases. Their meansget shifted from above 1.0 towards 1.0 while at the same time the widths of thedistributions get smaller as 6ET

true increases. The shift in the mean values of thereconstructed 6ET is likely to be caused by soft particles not reaching the calorimeterand thus not being considered in the 6ET calculation. This has been studied in moredetail elsewhere [92].

Figure 8.22 and figure 8.23 depict the means (linearity) and the widths (resolution)of the resolution functions as function of 6ET and pl

T respectively for three differentηl bins and for positrons and electrons separately. The ηl bins shown cover the veryforward endcap-region of 1.92 < |ηl| < 2.4, marked by a full circle, the crack region,1.44 < |ηl| < 1.92, shown as full rectangles as well as the central region, 0 < |ηl|< 0.48, denoted by open circles. Positron distributions are shown in red, while electrondistributions are shown in blue. In these figures, the shifts of the mean and thedecrease of the RMS of the 6ET resolution functions with increasing 6ET become evenmore apparent. The linearity drops smoothly from an overcompensation of 1.4 at15 GeV of 6ET to a linearity of 1.0 at around 40 GeV, while above it undershoots.However for pl

T the linearity is much flatter. Above 25 GeV, the plT linearity is flat as

a function of plT . However, there is a significant amount of undercompensation for

leptons in the crack region, -1.92 < ηl < -1.44, where only 95% of the true lepton plT

is reconstructed. This is due to energy leaking into dead material in the detector andnot being recovered. For ηl the linearity is flat as a function of pl

T for all ηl regions.The resolutions are shown in figure 8.23. The 6ET resolution varies from just below

30% to 15% as a function of 6ET . Again, the performance is worse in the crack region,where the resolution is almost 40% at 6ET =15 GeV. The lepton resolution is better andvaries from 15% to 4% as a function of pl

T . Again, the resolution is worse in the crack

132

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true

TE 85 <=

a) 6ETreco/ 6ET

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c) ηl reco/ηl true

Figure 8.21: Resolution functions fora) 6ET for 0.0 < ηl < 0.48 and for four6ET bins of 13≤ 6ET <25 GeV, 37≤6ET <49 GeV, 61≤ 6ET <73 GeV, 85≤6ET <97 GeV and resolution functionfor b) pl

T and c) ηl for 0.0 < ηl < 0.48and for four pl

T bins of 13≤ plT <19

GeV, 19≤ plT <25 GeV, 31≤ pl

T <37GeV and 43≤ pl

T <49 GeV respec-tively.

[GeV]TE 10 20 30 40 50 60 70 80

line

arity

TE

0.95

1

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1.1

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< 1.92η2.4 < < 1.44η1.92 < < 0η0.48 <

a)

[GeV]Tl P

10 20 30 40 50 60 70

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arity

TlP

0.95

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< 1.92η2.4 < < 1.44η1.92 < < 0η0.48 <

b)

[GeV]Tl P

10 20 30 40 50 60 70 80

line

arity

η

0.9992

0.9994

0.9996

0.9998

1

1.0002

1.0004

PositronsElectrons

< 1.92η2.4 < < 1.44η1.92 < < 0η0.48 <

c)

Figure 8.22: Linearity for a) 6ET , b) plT

and c) ηl for 0.0 <|ηl| <0.48, 1.44<|ηl|<1.92 and 1.92<ηl <2.4 as a func-tion of 6ET and pl

T respectively. For1.44<|ηl| <1.92 there is a notable shiftvisible in the linearity of the leptons,

defined asplT

reco

plT

true . This is due to the

fact that there is still some energylost around the crack region (1.37<|ηl|<1.52), that is not recovered for thereconstructed lepton. The bias in theηl distribution is still under investiga-tion.

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[GeV]TE 10 20 30 40 50 60 70 80

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< 1.92η2.4 < < 1.44η1.92 < < 0η0.48 <

a)

[GeV]Tl P

10 20 30 40 50 60 70

res

olut

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TlP

0.02

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< 1.92η2.4 < < 1.44η1.92 < < 0η0.48 <

b)

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olut

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η

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

PositronsElectrons

< 1.92η2.4 < < 1.44η1.92 < < 0η0.48 <

c)

Figure 8.23: Resolution for a) 6ET ,b) pl

T and c) ηl for 0.0 <|ηl| <0.48,1.44<|ηl| <1.92 and 1.92<ηl <2.4as a function of 6ET and pl

T respec-tively.

region, 1.37< |ηl| <1.52, where fluctuations are larger due to undetectable energydeposited in dead material. It is interesting to note, that the worse reconstruction ofthe lepton in the crack region also significantly affects the 6ET reconstruction. The6ET reconstruction also suffers worse linearity and resolution whenever the lepton isdetected in the crack region. The ηl resolution is flat as a function of pl

T , howeverit is strongly dependent on ηl itself. The reason is that here the relative resolutions,

σ(

ηlreco

ηltrue

)

, are considered. The absolute differences between ηl ltrue and ηl lreco are

roughly the same and directly related to the geometrical size of the calorimeter cells.By normalizing the resolution, for small values of ηl

true ∼ 0, the relative resolution willnaturally be larger than for large values of ηl

true ∼ 2.4.The linearity and the resolution presented here is what is expected to be achieved

for leptons at Atlas . The detector linearity and resolution for leptons can be deter-mined using data-driven measurements [67, 92], but only with finite precision.

8.3.3 Restoring the True Asymmetry

There are two principle methods of restoring the true asymmetry from the measuredreconstructed asymmetry.

Using the Resolution Functions

The resolution functions can be determined using MC or data-driven methods. Theycan then be used to study the relation between the true and the reconstructed asym-metry, which is smeared due to the inherent resolution of the detector.

The resolution functions can be used in unfolding techniques to extract the truefrom the measured asymmetry distribution. Alternatively, in a global PDF fit the

134

c(ηl) =Atrue,MC

l(ηl)

Areco,MC+simulation

l(ηl)

σ(c) σ(c) [%]

-2.4 < |η| < -2 1.02 0.053 5.2-1.9 < |η| < -1.5 0.955 0.058 6.1-1.4 < |η| < -0.99 0.968 0.074 7.6-0.93 < |η| < -0.51 1.01 0.093 9.1-0.45 < |η| < -0.032 0.948 0.091 9.60.032 < |η| < 0.45 0.964 0.088 9.10.51 < |η| < 0.93 1.04 0.099 9.50.99 < |η| < 1.4 1.03 0.076 7.41.5 < |η| < 1.9 0.976 0.092 9.42 < |η| < 2.4 1.04 0.055 5.3

Table 8.14: Size of correction factor c to correct from reconstructed to true asymmetrywith its statistical uncertainties given as absolute values as well as given in %.

deviation of the predicted from the measured asymmetry could be evaluated onlyafter the prediction has been smeared using the resolution functions.

Using MC Correction Factors

Instead of using a fullblown unfolding technique based on the (data-driven) resolutionfunctions, one could employ correction factors derived from MC in order to extractfrom the measured the true asymmetry. The correction factors c would be determinedbased on MC and detector simulation using the following relations:

c(ηl) =Atrue,MC

l (ηl)

Areco,MC+simulationl (ηl)

(8.17)

The size of these correction factors are shown in figure 8.24 as a function of ηl forthe data sample used here. None of them is larger than 5% from unity and they are infact all compatible with unity. The mean size of the correction factors is 0.995±0.003.Their numerical values alongside the absolute as well as the percentage errors are alsolisted in table 8.14.

The deviation of the reconstructed from the true asymmetry is thus much smallerthan the statistical error which is of the order of 3.5-8%. The errors on the correctionfactors shown here are purely statistical, since this is the dominant component dueto the size of our sample. Here it is assumed that to first order the correction factorsare independent of the PDFs even though the correction factors are obtained fromMC using a specific PDF set. For the present analysis this assumption is justifiedsince the statistical errors on this correction dominate. For analysis using real data,the correction factors should be obtained using NLO Monte Carlo, rather than LOPythia, to check again that the agreement between measured and true asymmetry isgood.

135

η pseudorapidity -2 -1 0 1 2

trut

h)→

cor

rect

ion

fact

or (

reco

0.85

0.9

0.95

1

1.05

1.1

1.15

Figure 8.24: The correction factor to correct from a given reconstructed asymmetryto the true value. It is extracted using Monte Carlo and should be investigated usingdifferent PDFs. Here, however due to the small size of the sample, statistical effectsare dominant and are the only ones regarded here.

Publication of the Lepton Asymmetry

There are three possibilities to publish a measurement of the lepton asymmetry atAtlas.

Firstly, the values of the reconstructed asymmetry could be given alongside theabove extracted resolution functions in parametrised form, published for Atlas e.g.in [61], to allow PDF fitters and phenomenologists to extract the true asymmetryusing an unfolding technique.

Secondly, an alternative method or a simplified version of the unfolding is applyingcorrection factors in bins of ηl correct the reconstructed asymmetry back to the truelepton asymmetry.

Thirdly a combination of both could be chosen: Publish the resolution functionsas well as the correction factors, so that PDF fitters could decide for themselves, whatthey wanted to do.

8.4 Conclusion

In this chapter, the expected size of the experimental errors on the measurement ofthe lepton asymmetry at

√s =14 TeV centre-of-mass energy was investigated using

MC data with full simulation of the ATLAS detector. The main sources of systemat-ical uncertainties were covered, namely those stemming from electroweak and QCDbackgrounds, trigger and electron ID cut uncertainty, charge misidentification, reso-lution and scale uncertainties. The total systematic and statistical uncertainties fora data sample of 100 pb−1 were extracted as a function of |ηl| for two different cutscenarios.

136

The two cut scenarios explored were the standard cuts of plT >25 GeV, 6ET>25

GeV, 1.52<|ηl| <2.4 and |ηl| <1.37 as well as a cut scenario, with an additionalisolation cut of etcone20

plT

< 0.1. The total relative error for the standard cuts are

between 8-10%, while the total relative error of the lepton asymmetry obtained usingisolation cuts has 5-7.5% total relative error, measured in 5 bins of |ηl|.

The comparison between 7, 10 and 14 TeV centre-of-mass energy MC generatedsamples showed differences of about 30% between each of the centre-of-mass energiesfor one specific PDF set (fig. 2.9). With the experimental uncertainties being expectedto be less than 10%, this implies that each measurement of the lepton asymmetry ata different center of mass energies will have the power to provide additional input forPDF fits. Furthermore, the measured asymmetry agrees well with the true asymmetry,so that no corrections need to be applied in order to correct for the resolution of thedetector.

Comparing the expected experimental uncertainties to the PDF uncertainties esti-mated with MSTW08 and CTEQ66 PDFs at

√s =14 TeV, shows that the experimen-

tal errors are up to a factor of 0.5 (isolation cut scenario) to 0.8 (standard cuts) smallerthan the PDF uncertainties. These values indicate to first order also by what factorthe PDF uncertainties are reduced, if a lepton asymmetry measurement at ATLASwere used in global PDF fits. This shows that the W asymmetry and its measurementas the lepton asymmetry are crucial ingredients for PDF fits in the kinematic regionof the LHC.

Chapter 9

Conclusions

The charge asymmetry in the production of W bosons at the LHC is a crucial mea-surement to constrain PDFs in the kinematic region of Q2= M2

W = (80.4 GeV)2 and3 × 10−4 < x < 1 × 10−1 (at

√s =14 TeV) and 6 × 10−4 < x < 2 × 10−1 (at

√s =7

TeV). No data constraining u and d valence quark distributions are as of yet availablein that region and the existing PDF parametrisations of the CTEQ and MSTW col-laborations differ significantly by up to 35% for the W asymmetry and up to 15% forthe lepton asymmetry, which is smeared due to the W decay. A possible extension ofthe measurement, that would be interesting and possible with a larger luminosity, isthe measurement of the lepton asymmetry in W+jet events as a function of variousjet variables. It is described in appendix A.

A method to measure the W asymmetry directly using a statistical unfoldingmethod that has been successfully developed [50] and used at the TeVatron [49] hasbeen tested for the LHC conditions using MC truth level information. In this methodtwo solutions to the W rapidity are calculated using a constrain on MW . If both thesesolutions are physical, this ambiguity is then resolved using a statistical unfoldinginvolving a weighting procedure, acceptance corrections and an iterative feedbackloop. It is found, that the weighting procedure is inherently very unreliable at theLHC because of two reasons. Firstly, the W± differential cross sections are quiteflat over a broad range of ηl, therefore yielding the same weight for most rapiditysolutions. Secondly, the ratio of q/q, used in order to construct a weight based on thedecay angle cos θ∗W,emp, is close to unity and therefore does not give strong handle todecide between solutions either. Most of the weights are found to be close to 0.5. Thisdestroys the correlation between the MC input weighting tables and the W rapiditiesreconstructed from the pseudo data. Therefore, the method relies to a large extendon the acceptance corrections.

The iterative procedure is tested out for√s =14 TeV using MSTW08 PDF and

Pythia to generate MC input and CTEQ66 and Pythia to generate the ‘pseudo-data’ used to reconstruct the W asymmetry. The procedure is also tested for

√s =10

TeV using a LO MC input sample and a NLO ‘pseudo-data’ sample, both generatedusing MSTW08 PDFs. The iterative procedure is found to converge after the firstiteration, but to suffer from random walks induced by statistical fluctuations in theinput MC, even though the input MC samples consists in both cases of 8 millionevents. Also, it is found, that the crucial acceptance corrections cannot be iteratedand corrected for in the iterative feedback loop, if there are significant differences

137

138

from the actual pseudo-data acceptance. Therefore, the acceptances need to be ofhigh accuracy and can only be used in a W asymmetry measurement with confidenceafter both, PDFs and higher-order calculations of W production, have been confirmedwith LHC data. Last but not least the acceptance corrections include the detectorresolution. It can not be expected that the detector simulation of the Atlas detectorwill be able to describe the early data with sufficient accuracy. The extraction of thedirect W asymmetry is not a promising approach at the LHC.

As a consequence a measurement of the lepton asymmetry with the Atlas de-tector is investigated. On of the main systematic uncertainties is the backgrounddue to QCD dijet and γ+jet processes in which one of the jets mimics an electronsignature in the detector and is therefore reconstructed as a so-called ”fake elec-tron”. Several data-driven methods to estimate these backgrounds to a W → eν-like signal have been presented: the ” 6ET vs. Iso” , Photon Extrapolation Fit andthe template fit method. They are tested to extract the QCD background fractionRQCD =

NQCD

NQCD+Nsignal. In this study, a QCD sample of 0.08pb−1 at 10 TeV centre-

of-mass energy with a full simulation of the Atlas detector is used. The combinedestimations of RQCD=27.4%±4.4% (template fit with calo-based Failed ID Cut Selec-tion and template fit with Photon Selection) and RQCD=26.2%±3.8% (template fitwith track-based Failed ID Cut Selection and template fit with Photon Selection),agree well with the true value of 28.8%±2.4% using the standard cuts for W → eνanalysis. When an additional isolation cut is applied, the background fraction RQCD isslightly underestimated with RQCD=5.3%±1.5% (template fit with calo-based FailedID Cut Selection and template fit with Photon Selection) and RQCD=5.5%±1.4%(template fit with track-based Failed ID Cut Selection and template fit with PhotonSelection) compared to the true value of RQCD=8.7%±1.7. This is partly due to thesmall statistics of the QCD sample used in order to test these methods. The rel-ative uncertainties on RQCD are 15% (standard cuts) and 25% (additional isolationcuts). These numbers are subsequently used as the relative uncertainty on the QCDbackground fraction.

In the last chapter of this thesis, the prospects of a measurement of the leptonasymmetry with an integrated luminosity of 100 pb−1 at

√s =14 TeV are analysed.

Two cut scenarios are explored, the standard cuts of plT >25 GeV, 6ET>25 GeV,

1.52<|ηl| <2.4 and |ηl| <1.37 as well as a cut scenario, where on top of these standardcuts an additional isolation cut of ET,iso

frac < 0.1, suppressing the QCD background, isapplied. All relevant systematic effects are accounted for. This includes reconstructionand trigger efficiencies, electroweak and QCD backgrounds, charge misidentification,measurement of the lepton position and energy and of 6ET . For the uncertainty on theQCD background, the actual QCD background fraction is determined for the 14 TeVsample and then the relative uncertainties as determined in chapter 7 are applied.

The total relative error for the standard cuts are found to be between 8-11%, whilethe total relative error of the asymmetry obtained using isolation cuts has 5-7.5% totalrelative error, measured in 5 bins of |ηl| . A direct comparison with the differencesbetween the PDF predictions of CTEQ66 and MSTW08 show that the experimentalerrors lie below the PDF errors. A measurement of the lepton asymmetry with 100pb−1 with the Atlas detector will be able to constrain PDFs and reduce errors inthe parametrization. An analysis of the impact the lepton asymmetry measurementwith this predicted uncertainty would have on PDF fits is underway [41].

Appendix A

W Charge Asymmetry in thePresence of Jets

In the presence of additional jets, W bosons are no longer produced in Drell-Yanqq-annihilation processes. The above discussed relation of Q2 and x become morecomplicated than in simple Drell-Yan production. However, investigating W+jetevents can help to gain additional insight inside into PDFs by choosing a specificregion in Q2-x phase space and by gaining sensitivity also directly to the g(x) PDF.As shown in figure A.1, where the two LO diagrams for W+1 jet production aredepicted, the W+1 jet process also involves qg initial states and is therefore moredirectly sensitive to g(x). The estimated contributions of qq, qg and gg initial statesto W+n jet production are listed in table A.1 after [102]. Additional jets producedalongside the W boson enhance the contribution of g initial states and can thus beused to sample different PDFs in W+jet production.

Also, in fact, W+jet production probes a different kinematic region compared toW+0 jet production. If you consider for example the outgoing final states and theirfour-momenta in W+1 jet production:

W

g

q

q q

W

q

g

Figure A.1: Feynman-Diagrams for W+ 1 jet production in LO.

139

140

% qq % qg % ggW+0 100 0 0W+1 75 25 0W+2 18 75 7W+3 18 72 10

Table A.1: Percentage contribution of different initial states to total W+n jet pro-duction. With a higher jet multiplicity the fraction of initial states involving gluonsincreases (taken from [102]).

P1 =

√s

2(x1, 0, x1) (A.1)

P2 =

√s

2(x2, 0,−x2)

PW = (EW , pWT , p

Wz )

PJ = (EJ , pJT ,−pJ

z )

Using these four-vectors, the x values of the incoming partons can be derived usingenergy and momentum conservation [103]:

x1 =1√s(√

M2W + (pW

T )2eyW + pJT e

−yJ ) (A.2)

x2 =1√s(√

M2W + (pW

T )2e−yW + pJT e

yJ ) (A.3)

Then Q2 = −t can be calculated as:

Q2 = −t = −(P1 − PW )2 (A.4)

= −(P2 − PJ)2

= (pWT )2 + (pJ

T )√

M2W + (pW

T )2e−(yW +yJ )

= (pJT )2 + (pJ

T )√

M2W + (pW

T )2e−(yW +yJ)

One has to consider here also the u-channel process, that introduces a change ofsign:

Q2 = −u = −(P1 − PJ)2 (A.5)

= −(P2 − PW )2

= (pJT )2 + (pJ

T )√

M2W + (pW

T )2e+(yW +yJ)

The average for the Q2 values for W+1 jet production for the t and u-channelprocesses, that are indistinguishable, are shown in figure A.2 on the left hand plot.

141

[GeV]TW =PT

jet P

20 30 40 50 60 70 80 90 100

) je

t +

yw

(y

-5

-4

-3

-2

-1

0

1

2

3

4

5

[GeV

]2

Q

410

510

J

Rapidity y-4 -3 -2 -1 0 1 2 3 4

x

-310

-210

-110

= -3.0 W

y = +3.0 W

y

= 0.0 W

y

Figure A.2: On the left hand side, the Q2 values for W+1 jet production is shownas a function of pW

T = pJT and (yW + yJ); the values are obtained as the average for

the t and u-channel processes, that are indistinguishable. The closer the jet and theW in y-space and the smaller their pT , the smaller their Q2. Also shown as a blackline is Q2 = M2

W . The right hand side plots depicts the values for x1 (solid line) andx2 (dotted line) as a function of yJ for different values of yW , yW = -3.0 (black), 0.0(blue), +3.0 (red). The values for x1 and x2 for yW = 0 are symmetric with regardto yJ = 0. The x values for yW = +3.0 are also symmetric to those for yW = −3.0with regard to yJ = 0. The larger the jet-W separation in rapidity y, the moreextreme x values can be sampled, e.g. for yJ = 4.0 and yW = −3.0, xmin ∼4×10−4

and xmax ∼0.08.

Here Q2 is shown as a function of pWT = pJ

T and (yW + yJ). The closer the jet and theW in y-space and the smaller their pT , the smaller their Q2. Also shown as a blackline is Q2 = M2

W , the Q2 for Drell-Yan W -production.On the right hand side of figure A.2 the reach of the x values is shown. This is

done for x1 (solid line) and x2 (dotted line) as a function of yJ for different values ofyW , yW = -3.0 (black), 0.0 (blue), +3.0 (red). The values for x1 and x2 for yW = 0are symmetric with regard to yJ = 0. The x values for yW = +3.0 are also symmetricto those for yW = −3.0 with regard to yJ = 0. The larger the jet-W separationin rapidity y, the more extreme x values can be sampled, e.g. for yJ = 4.0 andyW = −3.0, xmin ∼4×10−4 and xmax ∼0.08.

Investigating W boson production and its charge asymmetry as a function ofjet multiplicity or invariant mass can deliver additional information to an inclusivemeasurement of the W asymmetry. This is due to its sensitivity to gluon initialstates and due to the fact, that a different kinematic phase space can be sampled,allowing to restrict oneself to regions of phase space, where the PDFs are less or in factbetter known. For example, checking whether the measured asymmetry in a W+n jetsample in a well-constrained kinematic region matches the expected asymmetry, wouldallow to cross-check the amount of tt background in the data for a W+n jet crosssection measurement, where significant tt contributions would lower the observed Wasymmetry..

Further investigations into a PDF measurement involving W+jets as a functionof jets or invariant mass would be therefore beneficial. A measurement of this kindrequires however a larger integrated luminosity than a conventional, inclusive mea-

142

surement of the W asymmetry, and will not be appropriate for early data analysis atthe LHC.

Appendix B

Electron and Photon IdentificationCuts

This chapter summarises the cuts values used to identify electrons and photons. Thevariables used to distinguish electrons and photons from hadrons and mesons in thedetector are described in section 5.1.2, table 5.1. Most cut values are applied in bins ofη and ET . This appendix lists the numerical cut values of the different ID variables.

B.1 Electron Identification Cuts

The pseudorapidity of the EM cluster is always required to be |ηEMcluster| < 2.47 (L1).L1 refers to the naming scheme of the ID cuts, where the letter indicates, which setof cuts the variable belongs to (loose, medium or tight). The numbers is a uniqueidentifier.

B.2 Photon Identification Cuts

EM clusters are only reconstructed as photons, if they cannot be matched to a trackwithin a window of ∆η × ∆φ = 0.05×0.10. Therefore, for photons only calorimeterbased ID cuts are defined and used (L1-M5, T8).

143

144Hadronic Leakage Cut (L2)

ET ranges ηl ranges0 < |η| < 0.8 0.8 < |η| < 1.37 1.37 < |η| < 1.52 1.52 < |η| < 1.81 1.81 < |η| < 2.01 2.01 < |η| < 2.35 2.35 < |η| < 2.47

0 < ET < 7.5 GeV 0.025 0.018 0.020 0.045 0.030 0.025 0.0157.5 < ET < 15 GeV 0.020 0.018 0.020 0.045 0.030 0.025 0.015

15 < ET GeV 0.018 0.018 0.020 0.045 0.030 0.025 0.015Lateral shower shape in η, R77 (L3)


0 < ET < 7.5 GeV 0.750 0.750 0.600 0.650 0.890 0.890 0.8907.5 < ET < 15 GeV 0.770 0.770 0.600 0.750 0.910 0.910 0.910

15 < ET GeV 0.800 0.800 0.600 0.850 0.910 0.910 0.910Lateral shower shape in η, R37 (L4)


0 < ET GeV always set to passLateral width in η, wη2 (L5)


0 < ET < 7.5 GeV 0.0150 0.0150 0.025 0.0160 0.0140 0.0140 0.01257.5 < ET < 15 GeV 0.0140 0.0145 0.025 0.0155 0.0140 0.0140 0.0125

15 < ET GeV 0.0140 0.0140 0.020 0.0150 0.0140 0.0140 0.0125Difference between second energy maximum and energy minimum ∆ES (M1)

if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeter


0 < ET GeV 0.15 GeV 0.15 GeV 0.1 GeV 0.3 GeV 0.2 GeV 0.15 GeV 0.15 GeVSecond largest energy maximum in strips normalised to cluster energy Rmax2 (M2)if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeter


0 < ET GeV 0.25 0.45 0.45 0.53 0.40 0.40 0.30Total shower width, wstot (M3)



0 < ET < 7.5 GeV 4.00 4.00 3.50 4.10 2.50 1.55 1.407.5 < ET < 15 GeV 4.00 4.00 3.30 4.00 2.50 1.55 1.40

15 < ET GeV 4.00 4.00 3.00 3.10 2.10 1.55 1.40

Table B.1: Cuts values of loose and medium electron ID cuts (L2-L4, M1-M3).

145

Shower width ws3 (M4)if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeter


0 < ET < 15 GeV 0.80 0.80 0.80 0.80 0.78 0.70 0.6515 < ET GeV 0.80 0.80 0.75 0.75 0.68 0.65 0.60

Fside, Fraction of energy outside three central strips, but within 7 strips (M5)if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeter


0 < ET < 7.5 GeV 0.60 0.65 0.70 0.80 0.45 0.25 0.207.5 < ET < 15 GeV 0.45 0.65 0.60 0.70 0.40 0.25 0.20

15 < ET GeV 0.35 0.48 0.47 0.48 0.27 0.25 0.20

NhitsPi (M6)


0 < ET GeV 1 1 1 1 1 1 1Nhits

Pi+Si (M7)


0 < ET GeV 9 9 9 9 9 9 9Transverse impact parameter, D0 (M8)


0 < ET GeV 1 1 1 1 1 1 1Nhits

BL (T1)


0 < ET GeV 1 1 1 1 1 1 1Cut on ∆η (T2)


0 < ET GeV 0.005 0.005 0.005 0.005 0.005 0.005 0.005

Table B.2: Cuts values of medium and tight electron ID cuts (M4 - T2).

146

Cut on ∆φ (T3)ET ranges ηl ranges

0 < |η| < 0.8 0.8 < |η| < 1.37 1.37 < |η| < 1.52 1.52 < |η| < 1.81 1.81 < |η| < 2.01 2.01 < |η| < 2.35 2.35 < |η| < 2.470 < ET GeV 0.02 0.02 0.02 0.02 0.02 0.02 0.02

Cut on E/p (T4)


0 < ET < 30 GeV 0.8 < E/p < 2.5 0.8 < E/p < 2.5 0.8 < E/p < 2.5 0.8 < E/p < 3.0 0.8 < E/p < 3.0 0.8 < E/p < 3.0 0.8 < E/p < 3.030 < ET < 40 GeV 0.7 < E/p < 3.0 0.7 < E/p < 3.0 0.7 < E/p < 3.0 0.7 < E/p < 3.0 0.7 < E/p < 4.0 0.7 < E/p < 4.0 0.7 < E/p < 3.040 < ET < 50 GeV 0.7 < E/p < 3.0 0.7 < E/p < 3.0 0.7 < E/p < 3.0 0.7 < E/p < 4.0 0.7 < E/p < 5.0 0.7 < E/p < 5.0 0.7 < E/p < 4.0

50 < ET GeV 0.7 < E/p < 5.0 0.7 < E/p < 5.0 0.7 < E/p < 5.0 0.7 < E/p < 5.0 0.7 < E/p < 5.0 0.7 < E/p < 5.0 0.7 < E/p < 5.0Number of hits in TRT, NTRT (T5)

ET ranges ηl ranges0 < |η| < 0.1 0.1 < |η| < 0.625 0.625 < |η| < 1.07 1.07 < |η| < 1.304 1.304 < |η| < 1.752 1.752 < |η| < 2.0 N.A.

0 < ET GeV -15. -15. -15. -15. -15. -15.

Fraction of high threshold hits of total hits, fTRT =N

TRThigh

NTRT(T6 & T7)

ET ranges ηl ranges0 < |η| < 0.1 0.1 < |η| < 0.625 0.625 < |η| < 1.07 1.07 < |η| < 1.304 1.304 < |η| < 1.752 1.752 < |η| < 2.0 N.A.

0 < ET GeV 0.08 0.085 0.085 0.115 0.13 0.1550 < ET GeV 0.10 0.10 0.125 0.13 0.13 0.13

tightend cut, ǫ=90%

Cut on isolation, Ratio of ET in a cone of ∆R = 0.45 to EEM clusterT (T8)


0 < ET < 7.5 GeV 0.8 0.8 0.8 0.8 0.8 0.8 0.87.5 < ET < 15 GeV 0.5 0.5 0.5 0.5 0.5 0.5 0.515 < ET < 30 GeV 0.3 0.3 0.3 0.3 0.3 0.3 0.330 < ET < 40 GeV 0.25 0.25 0.25 0.25 0.25 0.25 0.25

40 < ET GeV 0.20 0.20 0.20 0.20 0.20 0.20 0.20

Table B.3: Cuts values of tight electron ID cuts (T5 - T8).

147

Hadronic Leakage Cut (L2)ET ranges ηl ranges

0 < |η| < 0.7 0.7 < |η| < 1.0 1.0 < |η| < 1.5 1.5 < |η| < 1.8 1.8 < |η| < 2.0 2.0 < |η| < 2.50 < ET GeV 0.006 0.003 0.003 0.008 0.009 0.007

Lateral width in η, R77 (L3)

ET ranges ηl ranges0 < |η| < 0.7 0.7 < |η| < 1.0 1.0 < |η| < 1.5 1.5 < |η| < 1.8 1.8 < |η| < 2.0 2.0 < |η| < 2.5

0 < ET < 30 GeV 0.925 0.925 0.920 0.905 0.925 0.91530 < ET < 40 GeV 0.935 0.925 0.925 0.905 0.930 0.92040 < ET < 50 GeV 0.941 0.932 0.930 0.910 0.93 0.9250 < ET < 60 GeV 0.943 0.937 0.932 0.910 0.93 0.92260 < ET < 70 GeV 0.946 0.94 0.935 0.916 0.93 0.92270 < ET < 80 GeV 0.946 0.94 0.937 0.91 0.94 0.928

80 < ET GeV 0.952 0.946 0.943 0.925 0.94 0.93Lateral width in η, R37 (L4)



80 < ET GeV 0.92 0.92 0.9 0.915 0.926 0.925Lateral width in η, wη2 (L5)



80 < ET GeV 0.0097 0.0102 0.0105 0.0125 0.0108 0.0114

Table B.4: Cuts values of loose photon ID cuts (L2-L5).

148

Difference between second energy maximum and energy minimum ∆ES (M1)if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeter


0 < ET < 25 GeV 100.MeV 75.MeV 90.MeV -1000.MeV 200.MeV 130.MeV 140.MeV25 < ET < 30 GeV 100.MeV 75.MeV 90.MeV -1000.MeV 150.MeV 140.MeV 155.MeV30 < ET < 40 GeV 130.MeV 130.MeV 135.MeV -1000.MeV 150.MeV 190.MeV 145.MeV40 < ET < 50 GeV 140.MeV 110.MeV 185.MeV -1000.MeV 150.MeV 320.MeV 400.MeV50 < ET < 60 GeV 300.MeV 260.MeV 190.MeV -1000.MeV 460.MeV 540.MeV 550.MeV60 < ET < 70 GeV 280.MeV 400.MeV 190.MeV -1000.MeV 250.MeV 500.MeV 400.MeV70 < ET < 80 GeV 320.MeV 280.MeV 280.MeV -1000.MeV 360.MeV 500.MeV 460.MeV

80 < ET GeV 200.MeV 200.MeV 200.MeV -1000.MeV 600.MeV 500.MeV 600.MeVSecond largest energy maximum in strips normalised to cluster energy Rmax2 (M2)if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeter


0 < ET < 25 GeV 0.13 0.162 0.22 -1000. 0.357 0.28 0.325 < ET < 30 GeV 0.135 0.15 0.2415 -1000. 0.315 0.2425 0.2530 < ET < 40 GeV 0.175 0.265 0.27 -1000. 0.4 0.46 0.2740 < ET < 50 GeV 0.22 0.26 0.28 -1000. 0.6 0.5 0.750 < ET < 60 GeV 0.367 0.55 0.395 -1000. 0.7 0.7 0.760 < ET < 70 GeV 0.3 0.4 0.4 -1000. 0.5 0.5 0.470 < ET < 80 GeV 0.28 0.28 0.42 -1000. 0.5 0.4 0.37

80 < ET GeV 0.46 0.34 0.4 -1000. 0.65 0.5 0.46Total shower width, wstot (M3)



0 < ET < 25 GeV 2.15 2.55 2.65 0. 2.85 1.75 1.325 < ET < 30 GeV 2.05 2.3 2.45 0. 2.65 1.6 1.330 < ET < 40 GeV 2.35 2.6 2.62 0. 2.95 1.82 1.3540 < ET < 50 GeV 2.4 2.6 2.8 0. 3.0 1.9 1.450 < ET < 60 GeV 2.55 2.75 2.95 0. 2.9 2.2 1.560 < ET < 70 GeV 2.15 2.8 2.75 0. 2.8 2.4 1.5570 < ET < 80 GeV 2.4 2.4 2.65 0. 3.0 2.0 1.6

80 < ET GeV 2.3 2.6 2.8 0. 2.9 2.2 1.6

Table B.5: Cuts values of medium photon ID cuts (M1-M3).

149

Shower width ws3 (M4)if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeter


0 < ET < 25 GeV 0.65 0.68 0.68 0. 0.72 0.64 0.6225 < ET < 30 GeV 0.65 0.68 0.68 0. 0.68 0.64 0.6230 < ET < 40 GeV 0.64 0.68 0.7 0. 0.72 0.64 0.640 < ET < 50 GeV 0.68 0.7 0.72 0. 0.74 0.68 0.6250 < ET < 60 GeV 0.68 0.7 0.7 0. 0.72 0.64 0.6260 < ET < 70 GeV 0.64 0.655 0.7 0. 0.7 0.7 0.6470 < ET < 80 GeV 0.62 0.68 0.7 0. 0.74 0.68 0.68

80 < ET GeV 0.66 0.66 0.68 0. 0.74 0.655 0.62Fside, Fraction of energy outside three central strips, but within 7 strips (M5)

if 5% of energy is reconstructed in the calo strips, the 1st layer of the calorimeterET ranges ηl ranges

0 < |η| < 0.7 0.7 < |η| < 1.0 1.0 < |η| < 1.37 1.37 < |η| < 1.52 1.8 < |η| < 2.0 2.0 < |η| < 2.370 < ET < 25 GeV 0.262 0.342 0.402 0. 0.462 0.231 0.1825 < ET < 30 GeV 0.262 0.342 0.402 0. 0.452 0.231 0.1830 < ET < 40 GeV 0.255 0.340 0.385 0. 0.45 0.230 0.1840 < ET < 50 GeV 0.25 0.340 0.385 0. 0.45 0.23 0.1850 < ET < 60 GeV 0.245 0.34 0.38 0. 0.45 0.23 0.1860 < ET < 70 GeV 0.245 0.34 0.40 0. 0.45 0.23 0.1870 < ET < 80 GeV 0.25 0.35 0.40 0. 0.44 0.25 0.19

80 < ET GeV 0.25 0.35 0.40 0. 0.45 0.25 0.19

Cut on isolation, Ratio of ET in a cone of ∆R = 0.45 to EEM clusterT (T8)


0 < ET < 7.5 GeV 0.8 0.8 0.8 0.8 0.8 0.8 0.87.5 < ET < 15 GeV 0.5 0.5 0.5 0.5 0.5 0.5 0.515 < ET < 30 GeV 0.3 0.3 0.3 0.3 0.3 0.3 0.330 < ET < 40 GeV 0.25 0.25 0.25 0.25 0.25 0.25 0.25

40 < ET GeV 0.20 0.20 0.20 0.20 0.20 0.20 0.20

Table B.6: Cuts values of medium and tight photon ID cuts (M4-M5, T8).

Appendix C

Distorted Material

In the simulated data samples used in this thesis, a geometrical configuration of simu-lation of the Atlas detector was used, which is different from the nominal geometricalconfiguration. In the samples, additional material budgets were added to the detectorfor positive values of φ only in order to study systematic effects from incorrect descrip-tions of the detector in the simulation. Figures C.1 and C.2 depict the extra materialadded into the detector expressed as percentage increase compared to the nominalmaterial budget. It should be noted, that the added material is not symmetric inz. Figure C.3 shows the additional material in the misal1 sample normalised to thenominal material distributions in terms of radiation length X0 for A and C side asfunction of |η| (red and blue).

150

151

Figure C.1: Location of the additional material added into the detector for the specificdata sample used, shown for the A side (+η).

Figure C.2: Location of the additional material added into the detector for the specificdata sample used, shown for the C side (-η).

152

η rapidity 0 1 2 3 4 5

addi

tiona

l mat

eria

l X/X

0

0.5

1

1.5

2

2.5 )ηratio of additional / nominal material (

)ηratio of additional / nominal material (-

Figure C.3: The additional material in the misal1 sample is shown normalised tothe nominal material distributions in terms of radiation length X0 for A and C sideas function of |η| (red and blue).

Appendix D

Derivation of the MisidentificationCorrection

The actual lepton asymmetry is defined as

Aactual =Nactual

+ −Nactual−

Nactual+ −Nactual

−(D.1)

With N± being the number of electrons and positrons respectively. The termactual here refers to the actual or true number of leptons, not the the measurednumber of leptons in the detector. These measured numbers are different from theactual numbers due to charge misidentification:

Nmeasured+ = Nactual

+ (1 − f+) +Nactual− (f−)

Nmeasured− = Nactual

− (1 − f−) +Nactual+ (f+) (D.2)

Here, f− and f+ are the charge specific misidentification rates. f− for example isthe probability that a true positrons is identified as an electron. The lepton asymmetrymeasured in the detector is:

Ameasured =Nactual

+ (1 − f+) +Nactual− (f−) −Nactual

− (1 − f−) −Nactual+ (f+)

Nactual+ (1 − f+) +Nactual

− (f−) +Nactual− (1 − f−) +Nactual

+ (f+)(D.3)

This equation can be rearranged to get the Aactual, we are interested in, as afunction of the measured asymmetry, Ameasured, and the measured fake rate f±:

153

154

Ameasured =Nactual

+ (1 − 2f+) −Nactual− (1 − 2f−)

Nactual+ +Nactual

−

=Nactual

+ − 2Nactual+ f+ −Nactual

− + 2Nactual− f−

Nactual+ +Nactual

−

=Nactual

+ −Nactual+ f+ −Nactual

+ f− −Nactual− +Nactual

− f+

Nactual+ +Nactual

−

+Nactual

− f− −Nactual+ f+ − f+Nactual

− +Nactual+ f− +Nactual

− f−

Nactual+ +Nactual

−

=(Nactual

+ −Nactual− )(1 − f+ − f−) + (−f+ + f−)(Nactual

+ +Nactual− )

Nactual+ +Nactual

−

=(Nactual

+ −Nactual− )(1 − f+ − f−)

Nactual+ +Nactual

−− f+ + f−

Ameasured + f+ − f− =(Nactual

+ −Nactual− )(1 − f+ − f−)

Nactual+ +Nactual

−

Ameasured + f+ − f− = Aactual(1 − f+ − f−)

Aactual =Ameasured + f+ − f−

(1 − f+ − f−)

Aactual =Ameasured + ∆f

(1 −∑ f)(D.4)

(D.5)

The last line this eq. D.5 is used in section 8.1.4 to correct the measured leptonasymmetry in order to reconstruct the actual or true asymmetry.

List of Figures

2.1 Partonic cross section at the LHC . . . . . . . . . . . . . . . . . . . . . 52.2 MSTW PDFs at Q2 =10 and 104 GeV . . . . . . . . . . . . . . . . . . 72.3 Kinematic phase space in Q2 and x . . . . . . . . . . . . . . . . . . . . 92.4 Feynman diagram for W boson production . . . . . . . . . . . . . . . . 112.5 Accessible xmin at TeVatron and LHC . . . . . . . . . . . . . . . . . . . 132.6 Comparison of MSTW08 and CTEQ6.5M PDFs at Q2 = 104GeV2 and

W asymmetry predictions for√s = 14TeV. . . . . . . . . . . . . . . . . 15

2.7 qq →W → e−νe decay: Angular relations . . . . . . . . . . . . . . . . . 162.8 The reconstructed lepton rapidity, pl

z = pWz + pl∗

z . . . . . . . . . . . . . 182.9 W and the lepton asymmetries for three different centre-of-mass energies 19

3.1 Probability density functions for cos θ∗W+,e+ weighting . . . . . . . . . . 223.2 cos θ∗W+,e+ PDFs at the TeVatron . . . . . . . . . . . . . . . . . . . . . 243.3 Flow chart of the reconstruction of the direct W rapidities . . . . . . . 253.4 Weight of solution closest to true W− rapidity at the TeVatron . . . . . 273.5 Calculated and true yW− distributions at the TeVatron . . . . . . . . . 283.6 Fully kinematically reconstructed and true yW− distributions at the

TeVatron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.7 Fully kinematically reconstructed and true yW− (without cuts) distri-

butions at the TeVatron . . . . . . . . . . . . . . . . . . . . . . . . . . 293.8 Asymmetry at the TeVatron . . . . . . . . . . . . . . . . . . . . . . . . 303.9 Problems of the weighting procedure at the LHC . . . . . . . . . . . . 313.10 cos θ∗e,W distributions at the LHC . . . . . . . . . . . . . . . . . . . . . 323.11 Weight given to correct rapidity solution at the LHC . . . . . . . . . . 323.12 Calculated and true yW distributions at the LHC . . . . . . . . . . . . 333.13 Kinematically fully reconstructed and true yW distributions at the LHC 343.14 Kinematically fully reconstructed and true yW distributions at the LHC 353.15 Asymmetry at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . 363.16 Iterations of the weighting procedure at the LHC . . . . . . . . . . . . 393.17 Acceptance corrections at LHC and ratios of acceptances for ‘data’ and

MC input samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.1 Overview of the Atlas detector . . . . . . . . . . . . . . . . . . . . . . 434.2 The Atlas trigger system . . . . . . . . . . . . . . . . . . . . . . . . . 444.3 Geometrical layout of the Atlas tracking system . . . . . . . . . . . . 464.4 Material distribution of the inner detector . . . . . . . . . . . . . . . . 474.5 Geometrical layout of the Atlas calorimeter system . . . . . . . . . . 484.6 Layout of an Atlas LAr-EM calorimeter module . . . . . . . . . . . . 49

155

156

5.1 Trigger towers for electron and photon triggers . . . . . . . . . . . . . . 52

7.1 An example of a ” 6ET vs. Iso” 2-D histogram . . . . . . . . . . . . . . . 677.2 Isolation distribution for different 6ET regions . . . . . . . . . . . . . . 697.3 Dependence of the background estimate on the ” 6ET vs. Iso” boundaries 717.4 a) Agreement between control sample and background. b) Extrapola-

tion fit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757.5 Comparison of extrapolation fit with fake electron sample . . . . . . . . 767.6 Photon Extrapolation Fit method: Result of the fit . . . . . . . . . . . 777.7 Source of fake electrons and respective 6ET distributions . . . . . . . . . 807.8 Template fit results using a Photon Selection and 6ET as template variable 847.9 Template Fit Method with calo-based Failed ID Cut Selection and 6ET . 887.10 Template fit results, obtained using a calo-based Failed ID Cut Selec-

tion , ET,isofrac as template distribution . . . . . . . . . . . . . . . . . . . 90

7.11 Template fit results of the track-based Failed ID Cut Selection method,ET,iso

frac distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

8.1 QCD efficiency scaling to smoothen ηl plot . . . . . . . . . . . . . . . . 978.2 Lepton asymmetry with all background included . . . . . . . . . . . . . 988.3 Lepton asymmetry of backgrounds . . . . . . . . . . . . . . . . . . . . 998.4 PDF uncertainties and uncertainties caused by the QCD background . 1018.5 Correlations for the RQCD, its relative uncertainty and σAsy . . . . . . . 1028.6 Z → ee tag & probe method trigger efficiencies . . . . . . . . . . . . . 1088.7 Selection & monitor trigger method trigger efficiencies . . . . . . . . . . 1088.8 Lepton ID efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1128.9 Misidentification rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 1158.10 Difference and sum of misidentification rates, ∆f and

∑

f . . . . . . . 1158.11 Ratio NPHOTOS/NBorn for pl

T . . . . . . . . . . . . . . . . . . . . . . . 1188.12 Lepton rapidities with and without electroweak corrections . . . . . . . 1198.13 Lepton asymmetry with and without electroweak corrections . . . . . . 1198.14 Uncertainties on lepton asymmetry as function of ηl . . . . . . . . . . 1238.15 Lepton asymmetry at Atlas as function of ηl . . . . . . . . . . . . . . 1248.16 Uncertainties on lepton asymmetry as function of |ηl| (linear scale) . . 1258.17 Uncertainties on lepton asymmetry as function of |ηl| (log scale) . . . . 1268.18 Lepton asymmetry at Atlas as function of |ηl| . . . . . . . . . . . . . 1278.19 Lepton asymmetry for CTEQ66 and MSTW08 PDFs and errors bands 1288.20 Comparison of PDF uncertainties with experimental errors . . . . . . . 1298.21 Resolution of cut variables . . . . . . . . . . . . . . . . . . . . . . . . . 1328.22 Linearity of cut variables . . . . . . . . . . . . . . . . . . . . . . . . . . 1328.23 Resolution of cut variables . . . . . . . . . . . . . . . . . . . . . . . . . 1338.24 Correction factors for lepton asymmetry . . . . . . . . . . . . . . . . . 135

A.1 W+1 jet production . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139A.2 Q2 and x phase space for W+1 jet production . . . . . . . . . . . . . . 141

C.1 Additional Material – A Side . . . . . . . . . . . . . . . . . . . . . . . . 151C.2 Additional Material – C Side . . . . . . . . . . . . . . . . . . . . . . . . 151C.3 Additional material in A and C side . . . . . . . . . . . . . . . . . . . . 152

List of Tables

2.1 Processes included in the global PDF analysis of the MSTW group . . 102.2 Parton-x values for W production at various rapidities yW . . . . . . . 13

4.1 Main parameters of the Atlas tracking systems . . . . . . . . . . . . . 45

5.1 Electron Identification cuts . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.1 Selection Cuts employed in the W Asymmetry analysis . . . . . . . . . 626.2 Number of events selected in the W analysis by dataset . . . . . . . . . 626.3 Efficiency of cumulative cuts for each dataset . . . . . . . . . . . . . . . 62

7.1 Datasets used for QCD background studies . . . . . . . . . . . . . . . . 657.2 Kolmogorov-Probabilities for iso distributions in various 6ET regions . . 707.3 ” 6ET vs. Iso” estimations for QCD background . . . . . . . . . . . . . . 727.4 ” 6ET vs. Iso” estimations for QCD background: systematic errors . . . 737.5 Contributions of W → eν events to the QCD control sample . . . . . . 757.6 Photon Extrapolation Fit : Estimate for QCD bkg, 6ET extrapolation fit 787.7 Photon Extrapolation Fit method: Systematic errors, 6ET extrapol. fit . 797.8 Settings tested for the template fitting . . . . . . . . . . . . . . . . . . 837.9 RQCD estimation: Template fit, Photon Selection, 6ET . . . . . . . . . . 857.10 Systematic errors: Template fit, Photon Selection, 6ET . . . . . . . . . . 857.11 RQCD estimation: Template fit, calo-based Failed ID Cut Selection, 6ET 887.12 Systematic errors: Template fit, calo-based Failed ID Cut Selection, 6ET 897.13 RQCD estimation: Template fit, calo-based Failed ID Cut Selection, ET,iso

frac 91

7.14 System. errors: Template fit, calo-based Failed ID Cut Selection, ET,isofrac 91

7.15 RQCD estimat.: Template fit, track-based Failed ID Cut Selection, ET,isofrac 92

7.16 System. errors: Template fit, track-based Failed ID Cut Selection, ET,isofrac 93

7.17 Overview of the fake rate estimations for the different methods. . . . . 947.18 Combined fake rate RQCD. The increased error is given in parathesis. . 95

8.1 Uncertainty on asymmetry due to Z → ee , tt and W → τν backgrounds1008.2 Distortions of the lepton asymmetry due to resolution and scale effects 1048.3 Trigger efficiencies for leptons and positrons . . . . . . . . . . . . . . . 1118.4 Uncertainties due to biases in the trigger selection . . . . . . . . . . . . 1118.5 Misidentification correction factor ∆f . . . . . . . . . . . . . . . . . . . 1168.6 Relative error due to charge misidentification . . . . . . . . . . . . . . . 1168.7 Used datasets for W boson studies . . . . . . . . . . . . . . . . . . . . 1178.8 Difference due to the electroweak corrections . . . . . . . . . . . . . . . 1208.9 Relative uncertainty on lepton asymmetry . . . . . . . . . . . . . . . . 121

157

158

8.10 Absolute uncertainty on lepton asymmetry . . . . . . . . . . . . . . . . 1228.11 Errors on lepton asymmetry with RQCD=32±4.8% as a function of ηl . 1228.12 Errors on lepton asymmetry as a function of |ηl| for both RQCD scenarios1278.13 Comparison of experimental errors with PDF uncertainties . . . . . . . 1308.14 Correction factor and statistical uncertainty . . . . . . . . . . . . . . . 134

A.1 Contribution of different initial states to W+n jet production . . . . . 140

B.1 Cuts values of loose and medium electron ID cuts (L2-L4, M1-M3) . . . 144B.2 Cuts values of medium and tight electron ID cuts (M4 - T2) . . . . . . 145B.3 Cuts values of tight electron ID cuts (T5 - T8) . . . . . . . . . . . . . . 146B.4 Cuts values of loose photon ID cuts (L2-L5) . . . . . . . . . . . . . . . 147B.5 Cuts values of medium photon ID cuts (M1-M3) . . . . . . . . . . . . . 148B.6 Cuts values of medium and tight photon ID cuts (M4-M5, T8) . . . . . 149

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