The dependence of the energy reconstruction in the ECAL-CMS calorimeter …xoomer.virgilio.it/danilosmess/elaborati/relazione... · 2005. 10. 25. · on a test beam to measure the

UNIVERSITA DEGLI STUDI MILANO BICOCCA

Laurea Triennale in Fisica

Relatore: Prof. Marco Paganoni

The η-φ dependence of the energyreconstruction in the ECAL-CMS

calorimeter calibration

Danilo Piparo

Matricola: 048316

Anno Accademico 2004-2005

2

Contents

1 The CMS detector 71.1 The LHC Physics programme . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 The CMS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2.1 Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.2 ECAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.2.3 HCAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.2.4 Muon chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 The energy reconstruction 132.1 The η-φ dependence of the energy reconstruction . . . . . . . . . . . . . . . 132.2 An improvement for reconstruction . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 The η correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.2 The φ correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.3 The correction check . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Some results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 The ECAL calorimeter Calibration 233.1 The calibration procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 The calibration algorithm . . . . . . . . . . . . . . . . . . . . . . . . 233.1.2 The ECAL segmentation . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.3 The miscalibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.1.4 Events selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 The accurate energy reconstruction influence on calibration . . . . . . . . . . 263.2.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3

4 CONTENTS

Introduction

The aim of this work is to improve the energy reconstruction of the CMS electromagneticcalorimeter ECAL by means of the Monte Carlo information study, to help refining theW → eν calibration procedure. The Monte Carlo information can help in getting rid ofthe geometrical effects due to the holding structure of ECAL, and to the effects of thebremsstrahlung induced by the presence of the silicon tracker inside the ECAL.

In the first chapter of this relation a very concise description of the CMS experiment willbe presented, with more details on ECAL.

Chapter 2 deals with the study of the energy reconstruction from the CMS tracker andECAL information with particular attention to the reconstruction of electrons with a fixedarray of crystals. A procedure to eliminate the effects due to the detector structure isexposed. The study concentrates on the barrel part (|η| < 1.479).

In chapter 3 a calibration algorithm of ECAL is exposed. The algorithm allows theintercalibration of the crystals using the electron energy information coming both from thetracker and from the electromagnetic calorimeter. Its main routine consists in a simplematrix inversion procedure. Then the effects of the energy reconstruction improvement onthe calibration accuracy are presented. A comparison is made between the results of thecalibration before and after the implementation of the energy reconstruction improvement.

5

6 CONTENTS

Chapter 1

The CMS detector

1.1 The LHC Physics programme

Hadron colliders are up to now the most promising tool to extend the discovery in the searchof new Physics beyond the Standard Model (SM).

The Large Hadron Collider (LHC) [1] is a proton proton collider with very ambitiousgoals in terms of luminosity and centre-of-mass energy:

∫L dt = 100 pb−1 in one year and√

s = 14 TeV. Moreover it is a remarkable effort in term of costs, human effort, complexityand size of the experiments.

Figure 1.1: An LHC overview: old CERN accelerators are used as injectors.

Figure 1.1 shows the four big experiments at LHC: CMS, ATLAS, LHCb and ALICE.The Higgs Boson(s) will be searched throughout a range of energies from the ∼ 120 GeV/c2

lower limit set by LEP and Tevatron up to ∼ 1 TeV/c2. By combining CMS (Compact MuonSolenoid) and ATLAS (A Toroidal LHC ApparatuS) experiments, it will be possible to dis-cover a signal from an H decay (with a significance S√

N> 5) after two years of operation

over the whole spectrum of the Higgs mass.

7

8 CHAPTER 1. THE CMS DETECTOR

At LHC precise measurements of some fundamental parameters of the SM will be per-formed and a further investigation of phenomena such as the CP-violation will be carriedout [2]. W bosons will be copiously produced with a rate of ∼15 Hz at low luminosity.This statistics will allow precise measurements of the W bosons mass. Detailed studiesof B hadrons and CP-violation in the B-hadron system will be performed at the LHC-bexperiment where also new top-physics effects will be searched for.

LHC will also allow studies of phenomena beyond the SM such as the presence of extra-dimensions. Furthermore the final word about the manifestation of SUSY at the energy scaleof ∼ 1 TeV will be stated.

The efforts of ALICE (A Large Ion Collider Experiment) will be dedicated to the studyof the phase transition from hadronic matter to plasma of deconfined quarks and gluons viathe collisions of heavy ions.

1.2 The CMS detector

The CMS multi purpose detector (see fig. 1.2) will be installed at the interaction point nb. 5.Its structure is cylindrical around the beam line following a barrel-endcap scheme [3].

A built-in superconductive coil will produce a very intense uniform magnetic field of4 T parallel to the beam axis to allow high precision momentum measurements for chargedparticles. Such a field will also literally sweep away low momentum particles.

The expected production rate of about 109 evt/s is far higher than the 100 evt/s ac-quisition rate. In order to reduce the events rate, a three-levels triggering system has beenimplemented.

Compact Muon Solenoid

Pixel DetectorSilicon Tracker

Very-forwardCalorimeter

Electromagnetic Calorimeter

HadronicCalorimeter

Preshower

Muon Detectors

Superconducting Solenoid

Figure 1.2: The CMS detector.

1.2. THE CMS DETECTOR 9

The sub-detectors necessary to measure the proprieties of the particles produced in theinteraction vertex, starting from the inside, are organised as follows, both for the barrel andthe endcaps (see fig. 1.3):

• The Tracker.

• The electromagnetic calorimeter (ECAL).

• The hadronic calorimeter (HCAL).

• The Muon chambers.

Figure 1.3: A CMS slice. The figure shows the organisation of the sub-detectors and thetracks of different types of particles.

1.2.1 Tracker

The CMS tracker [4] is composed by silicon devices. Surrounding the beam line, the SPD(Silicon Pixel Detector) is meant to reconstruct secondary vertexes. A second subdetector,the SSD (Silicon Strip Detector), surrounds the SPD. It is composed by silicon microstripsarranged in 10 cylindrical layers and 10 endcap disks per side. Its volume is 24.4 m3 and itsrunning temperature will be −10◦ C. Its role is to let the high PT tracks reconstruction withan elevated efficiency. Since it is a solid state device with a thickness between 0.4 X0 and 1.4X0 (see fig. 1.4), its presence determines a non negligible effect on the particle trajectory.


Figure 1.4: CMS Tracker budget material as a function of η in units of radiation lengthsX0.

1.2.2 ECAL

The CMS electromagnetic calorimeter will measure with high precision the electrons andphotons energy. The joint action of its high granularity and excellent energy resolution isoptimised for the Higgs discovery in the channel H → γγ with an Higgs mass in the rangefrom 115 GeV/c2 to 150 GeV/c2.

It is made of 82, 728 PbWO4 scintillating crystals among which 61, 200 located in thebarrel (see fig. 1.5). They are compact to fit inside the coil, radiation hard to survive in theLHC harsh environment and characterised by a fast response to follow the high repetitionrate of the events. The single crystals are assembled into submodules of dimension 5 × 2units, in an aluminium and glass fibre structure. Submodules are grouped in the number of40 or 50 to form a module: each of them is surrounded by a metallic cross-plate. The biggeststructure is the supermodule: composed of 4 modules, its extension is 20 ◦ over φ and 1.479over η. Thus the whole calorimeter is made of 36 supermodules.

Crystals are off-pointing with respect to the primary interaction vertex with a 3 ◦ tilt bothin φ and η to prevent particles from escaping through the dead holding structures betweenthe crystals.

Each crystal is coupled to two Avalanche Photo Diodes (APDs), two solid state photodetectors with a high quantum efficiency, radiation hardness and capability to operate inan intense magnetic field. They have been chosen to operate at a gain of 50 to compensatethe small light output of the PbWO4 crystals, an average of 4.2 photoelectrons/MeV (seefig. 1.6). The current signal coming from the APDs of a crystal is converted by an MGPA

1.2. THE CMS DETECTOR 11

Figure 1.5: A ECAL overview with the representation of its sub-units.

(MultiGain PreAmplifier) based on the 0.25 µm CMOS technology. One preamplifier isfollowed by three amplifiers. Then the outputs are sent in parallel to a compound ASICADC composed of 4 12-bits ADC. This design is considerably simple and in particular onlyone power supply voltage is required [5].

The ECAL detector has to be calibrated because the response of each single crystal isdifferent. The calibration procedure can be divided into two logical steps:

• The intercalibration, which equalises all the crystals with respect to an arbitraryfixed point

• The absolute calibration, that aligns the fixed point to a physical reference

Before the installation inside the CMS detector, the fully equipped supermodules can be puton a test beam to measure the response of all their crystals to particles with known energyand impinging direction. This procedure allows to achieve a precision of 0.5% in the energyreconstruction that is compatible with the CMS requirements. Unfortunately, the tight CMSschedule forbids the beam calibration of all the supermodules.

Cosmic ray calibration will be performed instead. The cosmic rays impinging into thecrystals are mostly minimum ionising muons leaving in the crystal an average of 250 MeV.In order to see a clear signal above the pedestal, it is necessary to raise the APD gain bya factor of 4. Moreover the direction of the impinging particles and their path inside thecrystal are not under strict control as for the beam calibration.

During the LHC data taking, the in situ calibration will be performed. In the very firstperiod it will be possible to rely on Z → ee channel, by using the precise measurement ofthe Z mass performed at LEP, being none of the other sub-detectors as calibrated as ECAL.After the calibration and alignment of the tracker the higher statistics channel W → eν willbe accessible for a more precise ECAL calibration.

Because of the harsh radiation environment (15 rad/h), the crystals behaviour during theLHC runs will be affected by the radiation damage, losing transparency in a short periodof exposure to the beams. The in situ calibration strategies have a time scale of the orderof weeks and cannot monitor such fast variations of the crystal behaviour. To follow thedamaging curve over a short period, a laser monitoring system has been designed and tested.Indeed, by measuring the crystal transmittance it is possible to follow up and correct theeffects due to radiation damage during the data taking. The monitoring system will inject


laser light of two different wavelengths in every crystal by means of optical fibres: 440 nmand 800 nm. The 440 nm laser will measure the loss in transmittance: the light collected bythe APDs from the crystal is compared to the measurement of a reference diode put aftereach fanout that distributes the light to the single crystals.

The 800 nm one will act as a reference benchmark, because the crystal is not losingtransparency at that wavelength. In this way, variations that are measured by the 440 nmlight, but not due to modifications in transmittance of the crystal, can be identified.

Figure 1.6: The distribution of the light yield of 100 different crystals measured during the2002 test beam.

1.2.3 HCAL

HCAL will measure the energy and the direction of hadronic jets. It will also carry out thetask of the transverse missing energy measurement, a distinctive signature of neutral longliving particles escaping previous detection. To accomplish these goals, the detector musthave a high granularity and a good hermeticity, covering the largest possible solid angle.The dynamic range of HCAL is between 20 MeV and 3 TeV, to allow the measurement fromsingle muons to large energies deposited by jets.

1.2.4 Muon chambers

Only muons and neutrinos survive outside the magnetic return yoke. Muon chambers willendow CMS to detect muons. They are placed outside the calorimeters and the coil andconsist of 4 layers interleaved with the iron return yoke plates. The charge assignmentperformed by means of the magnetic field effect is correct for a particle up to 7 TeV. Thedetector will perform an unambiguous bunch crossing identification.

Chapter 2

The energy reconstruction

2.1 The η-φ dependence of the energy reconstruction

The electrons coming from the W± → e±νe decay can be used for ECAL calibration, sincetheir energy is measured both by the tracker and ECAL and the two measurements can becompared.

The W± → e±νe Monte Carlo dataset used to study the η-φ dependence of the energyreconstruction has been published at the end of the last year. It covers 1

8of ECAL and

contains about 2, 450, 000 events, among which 60% fall into the ECAL barrel (see fig. 2.1).This amount of data has been generated by means of PYTHIA [6] and eventually stored inROOT-files. It corresponds to ∼ 75 days of data acquisition at low luminosity (2 · 1033 fb−1)or to ∼ 21.5 days of data acquisition at high luminosity (1034 fb−1).

Figure 2.1: The region of the calorimeter where the Monte Carlo events have been gener-ated, shown in a ECAL exploded view.

The tracker detector measures the electrons momentum (ptracker). The study of the MonteCarlo simulation of the electrons hitting ECAL showed the confinement of the generatedshowers in a 5 × 5 crystals cluster. During this work the estimator of the electron energywill be the sum of the energies measured by these 25 crystals (EECAL). This choice hasalso the advantage not to involve the corrections present in the algorithm which producessuper-clusters.

The study performed on the EECAL/ptracker (referred as EoP in the following) distributionalong η and φ pointed out a sharp dependence on these coordinates (see fig. 2.3).

13

14 CHAPTER 2. THE ENERGY RECONSTRUCTION

The main effects determining this non uniformity are:

• The presence of metallic crossplates embedding each module and each supermodule.

• The tracker material budget (see fig. 1.3).

Each crossplate alters the E measurement for those crystals in its immediate neighbour-hood. Indeed the showers generated by electrons and positrons hitting the crystals canpartially develop inside the metallic structure (see fig 2.2). This phenomenon determines asystematically lower estimation of E (see fig. 2.3).

Figure 2.2: The pattern of the PbWO4 crystals and the shape of the shower generated byan impinging electron. Part of the energy of the shower is lost in the holding structure atcritical η and critical φ. The label “critical” is referred to coordinates in the proximity ofcrossplates.

The material of the tracker causes electrons to loose energy throughout a Bremsstrahlungprocess. This phenomenon, combined with the presence of an high axial magnetic field (4 T),causes the energy to be spread on the ECAL surface the higher the η coordinate, around theφ coordinate. Because of this, a large part of the irradiated photons, which carry away a nonnegligible amount of energy, does not hit the 5 × 5 cluster reached by the electron. Thus,due to the geometrical structure of the material in front of ECAL, the EoP values decreaseat increasing η (see fig. 2.3).

2.2 An improvement for reconstruction

Since the procedure that will be described in this section provides a correction factor for eachsingle crystal, they will be identified by two discrete indexes: η and φ, ranging from 85 to170 and from 180 to 270 respectively, to cover the whole ECAL region hit by the producedelectrons.

2.2. AN IMPROVEMENT FOR RECONSTRUCTION 15

Figure 2.3: The EoP map before the correction. The “grid” is the effect of the holdingstructures. The decrement of EoP at increasing η is clearly observable.

As illustrated in the previous section, showers can develop in the metallic structuresupporting the crystals. Thus the EoP ratio is altered for those crystals next to thecrossplates: their coordinates will be called critical (i.e. η = 109, 110, 129, 130 . . . andφ = 190, 191, 210, 211 . . . See fig. 2.2).

The correction has been implemented in two separated steps: one pertaining the η coor-dinate and the other the φ coordinate.

The basic assumption is that the energy loss due to cross-plates and bremsstrahlungemission is proportional to the measured energy. The first position can be understood if thedynamic of the shower development near the crossplate is considered. An energy quantityproportional to EMEAS is lost in the dead holding structure. The second assumption statesthat the photons emitted through bremsstrahlung, not hitting the 5 × 5 cluster reached bythe electron, carry away a percentage of the measured energy. Thus, for η and φ:

EηLOST = EMEAS(cη − 1) Eφ

LOST = EMEAS(dφ − 1) (2.1)

Eventually it is necessary to merge the η and the φ correction. The way to accomplish thisgoal is simply to sum them (see fig. 2.2):

ELOST = EηLOST + Eφ

LOST = EMEAS(cη − 1) + EMEAS(dφ − 1) (2.2)

Since ETOT = EMEAS + ELOST , it follows that:

ETOT = EMEAS(cη + dφ − 1), (2.3)

where cη and dφ are the coefficients to be determined.


2.2.1 The η correction

The correction for this coordinate has been computed not considering crystals labelled by acritical φ. ECAL has been imagined as composed by “circular” crystals (see fig. 2.4). Theevents characterised by the same η were accumulated as they had been detected by one ofthese bigger crystals.

Two effects have to be removed by the η correction: the decreasing EoP at high η andlower EoP for critical crystals. Decreasing tendency at increasing η has been quantified byfitting EoP against ηnon−Critical values with a parabola: f(η) = aη2 + bη + c. For the criticalη the same tendency has to be expected but f(η) must be multiplied by a fixed factor A,which quantifies the portion of energy released in the crossplate by the shower. Thus thefunction interpolating EoP for critical η is f(η) = Af(η), where f is meant to have alreadya,b,c parameters fixed by the fit (see fig. 2.7).

Eventually two functions are determined: f and f . The correction coefficients are:

cη ={ 1

f(η)for critical η

1f(η)

for non critical η(2.4)

Figure 2.4: The modularity of ECAL as used for the η correction.

2.2.2 The φ correction

This second step was performed by exploiting the ECAL symmetry.For each non-critical η an average of EoP values over both critical and non-critical φ was

carried out. The ratio < EoPcritical > / < EoPnon−critical > is almost constant over the wholeη range. That value has been interpolated with a function g(φ) = R, where R was estimatedto a value R = 1.012 ± 0.008 (see fig. 2.5). The complete set of φ correction coefficients is:

dφ ={ R for critical φ

1 for non critical φ(2.5)

With this set of coefficients it is possible to fix the lower energy estimation for crystals atcritical φ.

2.2. AN IMPROVEMENT FOR RECONSTRUCTION 17

Eta80 90 100 110 120 130 140 150 160 170

Rat

io

1.004

1.006

1.008

1.01

1.012

1.014

1.016

1.018

<Critical>/<NonCritical> Vs Eta

Figure 2.5: The < EoPnc > / < EoPc > against η.

Figure 2.6: The modularity of ECAL as used for checking the φ correction.


2.2.3 The correction check

To calculate the cη and dφ coefficients the 75% of the full available Monte Carlo dataset wasprocessed, corresponding to ∼ 56 days of data taking at low luminosity or to ∼ 16 daysat high luminosity. Eventually the correction was applied to an independent data samplecomposed by the remaining 25% of the dataset, corresponding to ∼ 19 days of data taking atlow luminosity. This way the effectiveness of the correction could be tested. The summaryof the separated corrections on η and on φ is displayed in figures 2.7 and 2.8. In order tocheck the results of the φ correction ECAL has been considered formed by “stick” crystals(see fig. 2.6). In analogy with the procedure described in section 2.2.1, events characterisedby the same φ – and by a non critical η – were accumulated as they had been detected byone of these “stick” crystals.

Figure 2.7: The η corrections. Observe (plot 1 and 4) the reduction of the value of theparameter p2 – the coefficient of the second degree term – after the correction. The functionfitting the corrected dataset (plot 4) is almost constant. Fit parameters are the index of theeffectiveness of the correction technique. Note also the significant reduction of the range inwhich the points are concentrated in plot 1 and 4. The correction has realigned the detachedvalues of EoP present at critical η.

2.3. SOME RESULTS 19

Figure 2.8: The φ correction. The critical values, initially apart from the non critical ones,have been realigned (plot 1 and 4). The value of the parameters resulting from the secondand the last fit is the proof of the removal of the lower EoP estimation issue at critical φ.

2.3 Some results

This section shows the results obtained with the implementation of the correction.

The data show many benefits from the applied correction. The pattern in the EoP mapdue to the presence of the dead holding structure is no more present (see fig. 2.9 and 2.10).Moreover the values of EoP do not decrease as a function of η (see fig. 2.13). Both the goalslisted in sections 2.2.1 and 2.2.2 have been accomplished.

Anyway the correction implies other benefits. Figures 2.11 and 2.12 stress the reductionof the spreading of the EoP values. Figure 2.11 shows the EoP RMS over η at fixed φ, whileFigure 2.12 shows the EoP RMS over φ at fixed η. The figure 2.13 represents the summaryof the joint η and φ correction effects.


Figure 2.9: The EoP map before correction

Figure 2.10: The EoP map after correction. The pattern due to the holding structuresdisappeared and the decreasing EoP tendency at increasing η has been removed. Here therange has been set equal to the one of fig. 2.5 to ease the comparison between the two maps.Indeed the EoP range after the correction is reduced by a factor of 4.

2.3. SOME RESULTS 21

Figure 2.11: RMS Vs φ: effects of the correction. Each entry in the histograms representthe EoP RMS over η at fixed φ.A clear RMS reduction is observable.

Figure 2.12: RMS Vs η: effects of the correction. Each entry in the histograms representthe EoP RMS over φ at fixed η.


Figure 2.13: 3D graph of the effect of the correction. Lower estimation of EoP at criticalcoordinates clearly visible in the first plot is not present in the second one, created processingthe corrected dataset. Both corrected and uncorrected datasets were fitted with a surfacez = p0 + p1 · η + p2 · η2. Since there is no reason to foresee a φ dependence because of theECAL symmetry, z is only function of η. The parameters of the fits point out the removalof the EoP decreasing tendency as a function of η.The coefficients of the second and first degree term of the surface fitting the corrected datasetare compatible with 0.

Chapter 3

The ECAL calorimeter Calibration

3.1 The calibration procedure

3.1.1 The calibration algorithm

An electron that hits the ECAL surface deposits its energy in a cluster of crystals. Theenergy deposited in a single crystal crystal is:

Ei = αidi , (3.1)

where di is the output in ADC counts coming from the APD of the i-th crystal after pedestalsubtraction and αi is the corresponding calibration factor [7].

In order to find the set of calibration coefficients {αj} during the data taking at LHC,the event W± → e±νe can be used with the assumption that the momentum measured bythe tracker (ptracker) is an unbiased estimator of the energy deposited in ECAL (EECAL):

ptracker = EECAL =∑

i ε xtals

(αidi) . (3.2)

This assumption corresponds to the minimisation of:

χ2 =∑

m ε Events

(

(α1d1 + . . . + αNdN)(m) − p(m)tracker

)2

σ2m

, (3.3)

where σ2m is the combined error of the momentum and the energy. Since:

∂χ2

∂αj

= 2∑

m

1

σ2m

(

(α1d1 + . . . + αNdN)(m) − p(m)tracker

)

d(m)j , (3.4)

the requirements for the minimisation:

∂χ2

∂αj

= 0 (3.5)

23

24 CHAPTER 3. THE ECAL CALORIMETER CALIBRATION

produce a set of N equations, with {αj}j=1...N unknown.Starting from (3.5) and (3.4), it follows:

∑

m

((α1d1 + . . . + αNdN)(m)d(m)j )

σ2m

=∑

m

(p(m)trackerd

(m)j )

σ2m

, (3.6)

α1

∑

m

(d(m)1 d

(m)j )

σ2m

+ . . . + αN

∑

m

(d(m)N d

(m)j )

σ2m

=∑

m

(p(m)trackerd

(m)j )

σ2m

. (3.7)

In terms of matrices:

∑

i ε xtals

αi

∑

m

(d(m)i d

(m)j )

σ2m

︸︷︷︸

Aji

=∑

m

(p(m)trackerd

(m)j )

σ2m

︸︷︷︸

bj

, (3.8)

that is:A α = b . (3.9)

The set of calibration coefficients is obtained by inverting the matrix A:

α = A−1 b . (3.10)

The matrix A has N×N elements, where N is the number of crystals in the ECAL barrel(amounting to 61,200) – or in the sub-region of ECAL under investigation.

3.1.2 The ECAL segmentation

A shower generated by an electron involves only a limited number of crystals. This meansthat only a block along the diagonal of the A will be different from zero. In order to simplifythe problem of inverting A, it is convenient to segment ECAL in subregions Mi, where theblock Ai is calculated.

Ai 0 0

0

a11 . . . a1k

......

ak1 . . . akk

0

0 0 Ai+2

α i

α1...

αk

α i+2

=

b i

b1...bk

b i+2

(3.11)

Using this diagonal block matrix system, to find the {αi}i=1...N it is not necessary toinvert a N × N matrix, but only N/k matrices of dimensions k × k, finding a subset of thetotal solution:

a11 . . . a1k

......

ak1 . . . akk

︸︷︷︸

Ai

α1...

αk

︸︷︷︸

α i

=

b1...bk

︸︷︷︸

b i

. (3.12)

3.1. THE CALIBRATION PROCEDURE 25

3.1.3 The miscalibration

The simulated events have been reconstructed with a perfectly calibrated calorimeter, hencethe differences among crystals are only due to geometrical reasons.To study the calibration procedure it was necessary to miscalibrate the calorimeter in ad-vance. The artificial miscalibration has been introduced with a Gaussian distribution aroundthe calibrated value, with different widths. The miscalibration factors αi have been mul-tiplied by the calibrated energies E i to give the miscalibrated energies Ei used to test thealgorithm, as shown in equation 3.13:

Ei = αi Ei . (3.13)

The algorithm returns the calibration factors ci, which are needed to reconstruct the cali-brated energy Ecalib

i :Ecalib

i = ci Ei = ci αi Ei . (3.14)

Since theoretically:Ecalib

i = Ei , (3.15)

it follows that:ci αi = 1 (3.16)

and therefore the two variables 1/ci and αi are linearly correlated. The precision of thecalibration coefficients is given by the width of the distribution which plots, for each crystal,the quantity:

∆ci =1

ci

− αi . (3.17)

The algorithm precision has been estimated by fitting this distribution with a Gaussian.The width of the initial miscalibration was fixed at the level of 4% to reproduce the

expected situation at the beginning of the LHC data taking. The crystals lying outside thetotal region of interest – that can be smaller than the entire ECAL barrel – where the eventsare collected, but still involved in the shower development generated by particles impingingat the borders of the area, have not been miscalibrated, to avoid biases.

3.1.4 Events selections

To refine the events selection and get rid of events that broaden the distribution 3.3, anappropriate event selection can be applied on variables related to the electron track or theshape of the electron shower1.

• The χ2 of the fit of the particle in the Tracker can be used to select only well recon-structed tracks, and therefore to suppress the electrons with large bremsstrahlung.

• The number of valid hits in the tracker is proportional to the length of the track beforeany hard bremsstrahlung radiative process, and can be used, together with the trackχ2, to select only particles radiating in the outermost part of the Tracker.

1For a complete dissertation see [7].


• The 3.3 itself can be used as a cut variable, by avoiding events which give a too largecontribution to the χ2 used to calibrate.

• Shower shape variables inside ECAL, as the E3×3/E5×5 ratio, help in identifying theelectrons that emitted large angle bremsstrahlung photons.

The test of the energy reconstruction improvement on the ECAL calibration has beencarried out implementing two kinds of cuts. The first considering the χ2 by degree of freedom(χ2/dof)of the particle track fit and the second evaluating the number of the valid hits inthe track reconstruction (n◦ Hits). More quantitatively:

• 0.5 < χ2/dof < 2.

• 8 < n◦ Hits < 15.

3.2 The accurate energy reconstruction influence on

calibration

In this last section we discuss the effects of the energy reconstruction improvement (seechapter 2) on the ECAL calibration performed with the matrix inversion algorithm. Thealgorithm was tested both on datasets without and with the correction for the energy re-construction, each time with 50 different (Gaussian) induced miscalibrations, to simulate50 independent calibration trials. For each crystal, an histogram filled with 50 ∆c valuescould be created and fitted with a Gaussian distribution. The peak of this Gaussian can beconsidered an estimator of the accuracy of the calibration algorithm.

The results coming from the calibration were improved by the better energy reconstruc-tion as expected.

The values of the Gaussian peaks for each crystal can be organised in matrices. We plotthe matrices both with uncorrected data (fig. 3.1) and with the corrected data (fig. 3.2).In fig. 3.2 the pattern which can be observed in fig. 3.1 disappeared. The value of the ∆cdistribution peak in the neighbourhood of the crossplates is reduced due to the improvedcalibration accuracy.

Figures 3.3 and 3.4 represent the η profile of ∆c peak as a function of η and φ. Of coursethere are different values, corresponding to different φ, for the same η coordinate. Again onecan observe the removal of the crossplate effects (η=110,111,130. . . ) on the ∆c peak due tothe energy reconstruction improvement. The lower accuracy obtained with the uncorrecteddataset is stressed by the higher values of the peak at critical η in fig. 3.3. An overallreduction of the smearing of the values can be observed too.

All the peak values can be organised in the same histogram to obtain a global distribution.Figures 3.5 and 3.6 point out one of the most important benefits brought by the energyreconstruction improvement. The structures embedding each module determine the ∆cpeak distribution to be broader, effect clear in fig. 3.5 where a significant contribution tothe global histogram came from critical peak values. In fig. 3.6, created with the correcteddataset, the widening effect due to critical ∆c peak has been removed.

3.2. THE ACCURATE ENERGY RECONSTRUCTION INFLUENCE ON CALIBRATION27

3.2.1 Conclusions

In this work we have simulated the in-situ calibration procedure of the ECAL barrel detector,with W → eν events.

The accuracy of this procedure is sharply enhanced by imposing the energy reconstructioncorrection for the dead regions due to the presence of holding structures.

The most significant results are clearly visible by comparing fig. 3.5 and 3.6, where theright tail in the distribution of calibration coefficients precision disappears after the correctionhas been applied.


Eta90 100 110 120 130 140 150 160

Phi

0

10

20

30

40

50

60

70

80

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Peak

Figure 3.1: The ∆c distribution peak map resulting from uncorrected data. The patternis an index of the inability of the algorithm to reconstruct the miscalibration coefficients inproximity of the crossplates.

Eta90 100 110 120 130 140 150 160

Phi

0

10

20

30

40

50

60

70

80

-0.04

-0.02

0

0.02

0.04

0.06Peak

Figure 3.2: The ∆c distribution peak map resulting from corrected data. The improvementof energy reconstruction determined the disappearing of the pattern of fig. 3.1. Afterthe correction the algorithm is able to reconstruct with high accuracy the miscalibrationcoefficients near the crossplates.

3.2. THE ACCURATE ENERGY RECONSTRUCTION INFLUENCE ON CALIBRATION29

eta90 100 110 120 130 140 150 160

reso

lutio

n (p

eak)

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08RingRing

Figure 3.3: All the ∆c distribution peaks as a function of η before the correction. Theholding structures cause the peaks to have an higher value.

eta90 100 110 120 130 140 150 160

reso

lutio

n (p

eak)

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08RingRing

Figure 3.4: All the ∆c distribution peaks as a function of η after the correction. Theimprovement determines a realignment of the peak values and an overall reduction of thespreading of the values.


Figure 3.5: The global ∆c peak distribution: uncorrected data. A non negligible contribu-tion to the histogram comes from critical regions of ECAL and affects the fitted distributioncausing its broadening.

Figure 3.6: The global ∆c peak distribution: corrected data. The contribution comingfrom critical ECAL regions, does not cause the distribution broadening anymore.

Bibliography

[1] D. Boussard et al., The Large Hadron Collider Conceptual Design, CERN/AC/95-05(1995).

[2] F. Gianotti, Collider physics : LHC, proceedings of the 1999 european school of highenergy physics, CERN 2000-07 (2000).

[3] CMS Collaboration, CMS Technical Proposal, CERN/LHCC/94-38 (1994).

[4] CMS Collaboration, The Tracker Project Technical Design Report,CERN/LHCC/98-6 (1998).

[5] CMS Conference Report, The CMS PbWO4 Electromagnetic Calorimeter, CMS CR2003/0042.

[6] T. Sjostrand et al., PYTHIA 6.3 Physics and Manual, arXiv:hepph/0308153.

[7] Pietro Govoni et al., CMS ECAL intercalibration using the Inverted Matrix technique:progress and plans. Roma, 2005.

[8] Pietro Govoni, PhD Thesis, Universita degli studi diMilano-Bicocca, 2005.

31

32 BIBLIOGRAPHY

List of Figures

1.1 An LHC Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 The CMS detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 A CMS slice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 CMS Tracker budget material . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 An ECAL overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.6 Distribution of crystals light yield . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 The region of the barrel where the MC events are generated . . . . . . . . . 132.2 Scheme a the developing shower in ECAL . . . . . . . . . . . . . . . . . . . 142.3 The EoP map before the correction . . . . . . . . . . . . . . . . . . . . . . . 152.4 The modularity of ECAL as used for the η correction . . . . . . . . . . . . . 162.5 < EoPnc > / < EoPc > against η . . . . . . . . . . . . . . . . . . . . . . . . 172.6 The modularity of ECAL as used for checking the φ correction . . . . . . . . 172.7 The η correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.8 The φ correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.9 The EoP map before correction . . . . . . . . . . . . . . . . . . . . . . . . . 202.10 The EoP map after correction . . . . . . . . . . . . . . . . . . . . . . . . . . 202.11 RMS Vs φ: effects of the correction . . . . . . . . . . . . . . . . . . . . . . . 212.12 RMS Vs η: effects of the correction . . . . . . . . . . . . . . . . . . . . . . . 212.13 A 3D overview of EoP corrections . . . . . . . . . . . . . . . . . . . . . . . . 22

3.1 The ∆c distribution peak map resulting from uncorrected data . . . . . . . . 283.2 The ∆c distribution peak map resulting from corrected data . . . . . . . . . 283.3 ∆c distribution peaks before the correction . . . . . . . . . . . . . . . . . . . 293.4 ∆c distribution peaks after the correction . . . . . . . . . . . . . . . . . . . . 293.5 The global ∆c peak distribution: uncorrected data . . . . . . . . . . . . . . 303.6 The global ∆c peak distribution: corrected data . . . . . . . . . . . . . . . . 30

33

Documents

The dependence of the energy reconstruction in the ECAL-CMS calorimeter …xoomer.virgilio.it/danilosmess/elaborati/relazione... · 2005. 10. 25. · on a test beam to measure the