WichitaStateUniversity Seminar Spring2016 · (2013) Higgs Discovery: The Power of Empty Space , Bodley Head. é S ample, I. (2013) Massive: The Higgs Boson and the Greatest Hunt in

MULTI-JET HIGGS

Terrance FigyAssistant Professor

WSU Physics

March 9, 2016WSU Physics Seminar

OUTLINE

• Introduction

• Jet Algorithms

• Higgs boson Production in Association of Jets

A. Salam S. Weinberg S. Glashow

D. Gross F. Wilczek D. Politzer

):

The Standard Model

SU(2)L ⇥ U(1)Y :

SU(3)c:

Standard Electroweak(EW) gauge theory

Quantum Chromo Dynamics (QCD)

How is mass generated?

30 December 2013 Physics Today www.physicstoday.org

Higgs boson

Goldstone boson. Superconductors also exhibit thefamous Meissner effect, the expulsion of externalmagnetic fields that makes possible magnetic levi-tation. Anderson started with the simple Londontheory of the Meissner effect, rewrote the equationsin a relativistic form more palatable to particlephysicists, and showed that they describe what is,in effect, a massive photon; he called it a plasmon.Being a massive spin-1 boson, the plasmon has anextra longitudinal polarization compared with apropagating photon, which also is a spin-1 bosonbut with only two transverse polarizations. Wheredid the extra degree of freedom come from? It’s theGoldstone mode! Anderson concluded that “thesetwo types of bosons [the massless Goldstone bosonand the massless gauge boson] seem capable of ‘can-celling each other out’ and leaving finite mass bosonsonly.” Anderson’s work made it clear that gauge the-ories and symmetry breaking have a special rela-tionship; what remained was to understand it.

In his first paper of 1964, Peter Higgs pointed outa loophole in the Goldstone, Salam, and Weinbergtheorem: The proof assumes explicit Lorentz invari-ance in relating broken symmetries to particles.6

Due to the necessity of fixing a gauge, that assump-tion is violated when electromagnetism or any othergauge theory is quantized.

Gauge symmetries, in fact, are not symmetriesin the usual sense of relating seemingly distinctphysical processes or configurations. Instead, gaugesymmetry is a redundancy; you can formulate thequantum theory in a way that is manifestly Lorentzinvariant and manifestly gauge invariant, but thatformulation actually represents an infinite numberof copies of the same physical system. In quantizingthe theory, you need to choose arbitrarily one of theequivalent quantum descriptions of the physics;that’s what is meant by fixing a gauge. The Lorentz

and gauge symmetries that are built into the classi-cal theory still control the quantum physics, butthey do so through a delicate choreography. Justhow gauge fixing invalidates the Goldstone, Salam,and Weinberg theorem was shown in a paper byGerald Guralnik, Carl Hagen, and Tom Kibble,7

published shortly after the Higgs loophole paper.

Mass effectsEven with the theorem by Goldstone and companyevaded, the question remains as to how a masslessgauge boson can obtain mass. To answer the ques-tion, in his second paper of 1964, Higgs reconsid-ered Goldstone’s Mexican-hat model and added aphoton.8 Once the boson field, also called the Higgsfield, acquires a vacuum expectation value (particlephysicists refer to “turning on the Higgs field”) andthe theory is quantized, the gauge symmetry of elec-tromagnetism imposes two new interactions notpresent in ordinary electrodynamics. One of thoseis a mass term for the photon; the other is a couplingof the photon to the would-be Goldstone boson (seePHYSICS TODAY, September 2012, page 14).

Early in 1964 Robert Brout and François Englertshowed that those two interactions work together toallow a gauge invariant quantum theory with a mas-sive gauge boson.9 The gauge invariance, already ex-plicitly broken by gauge fixing in quantization andseemingly again by the new mass term, is restoredin the quantum theory by the coupling between thephoton and the Goldstone boson. For one particularchoice of gauge fixing called the Coulomb gauge, thephysical degrees of freedom are manifest and thetwo interactions show that the would-be Goldstoneboson becomes the longitudinal polarization neededto turn a massless gauge boson into a massive one.It has become customary to say that the masslessGoldstone boson is “eaten” to give the gauge boson

Figure 1. Yoichiro Nambu, Jeffrey Goldstone, and Philip Anderson penned important early chapters in thestory of the Higgs boson. Beginning in 1960, particle physicists Nambu (left) and Goldstone (center) adaptedideas from condensed-matter physics to explore the relationship of symmetry breaking to the generation ofmassive particles. Two years later, condensed-matter physicist Anderson (right) argued that two types of troubling massless particles—Goldstone bosons and gauge bosons—could together yield a massive particle.(Nambu photo courtesy of the AIP Emilio Segrè Visual Archives, Marshak Collection. Goldstone and Andersonphotos courtesy of the AIP Emilio Segrè Visual Archives, PHYSICS TODAY Collection.)

This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:97.94.124.63 On: Sat, 30 Nov 2013 21:29:53

Condensed Matter Physics

Yoichiro Nambu, Jeffrey Goldstone, and Philip Anderson

The 1964 Physical Review Letters

Kibble GuralnikHagen

Englert

Brout Higgs

2010 J.J. Sakurai Prize

Overview H0 production via VBF Results Concluding Remarks

SM Higgs bosonSpontaneous Symmetry Breaking: SU(2)L × U(1)Y → U(1)em

SM Higgs Doublet

Φ = U(x)1√2

!

0v + H

"

The remormalizable Lagrangian

L = |DµΦ|2 + µ2Φ†Φ− λ(Φ†Φ)2

leads to the vacuum expectiation value v =#

µ2

λfor the Higgs

field H.

T. Figy H0 production via VBF

https://www.youtube.com/watch?v=JBhAjTpx_Os


SM Higgs bosonHiggs couplings to gauge bosons

Kinetic energy term of the Higgs doublet field:

(DµΦ)† (DµΦ) =1

2∂µH∂µH +

!

"gv

2

#2W µ+W−

µ

+1

2

(g2 + g ′2)v2

4ZµZµ

$%

1 +H

v

&2

W ,Z mass generation: m2W =

'

gv2

(2,m2

Z =(g2+g ′2)v2

4

WWH and ZZH couplings are generated:couplingstrength = 2m2

V/v ≈ g 2v within SM



SM Higgs bosonHiggs couplings to fermions

Fermion masses arise from Yukawa couplings via

Φ† →!

0, v+H√2

"

.

LYukawa = −#

f

mf f f

$

1 +H

v

%

Test SM prediction: f fH Higgs coupling strength = mf /v

Observation of Hf f Yukawa coupling is no proof that av.e.v exists


CERN LARGE HADRON COLLIDER


Happy Higgsdependence Day!”I think we have it” -Rolf-Dieter Heuer, 4 July 2012

ATLAS-CONF-2012-170

CMS-PAS-HIG-12-045


https://www.youtube.com/watch?v=ggsS8BUvP8w

The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2013 to François Englert and Peter W. Higgs “for the theoretical discovery of a mechanism that contributes to our understanding of the origin of mass of subatomic particles, and which recently was confirmed through the discovery of the predicted fundamental particle, by the ATLAS and CMS experiments at CERN’s Large Hadron Collider”.

FURTHER READING! More information on the Nobel Prize in Physics 2013: http://kva.se/nobelprizephysics2013 and http://nobelprize.org REVIEW ARTICLES: Rose, J. (2013) I mörkret bortom Higgs, Forskning & Framsteg, nr 6 (Swedish). Llewellyn-Smith, C. (2000) The Large Hadron Collider, Scientific American, July. Weinberg, S. (1999) A Unified Physics by 2050?, Scientific American, December. BOOKS: Randall, L. (2013) Higgs Discovery: The Power of Empty Space, Bodley Head. Sample, I. (2013) Massive: The Higgs Boson and the Greatest Hunt in Science, Virgin Books. Carroll, S. (2012) The Particle at the End of the Universe, Dutton. Close, F. (2011) The Infinity Puzzle, Oxford University Press. Wilczek, F. (2008) The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books. LINKS: Link TV (2012) CERN Scientists Announce Higgs Boson: The Moment: http://www.youtube.com/watch?v=0CugLD9HF94 CERN (2010) CERN LHC Brochure: http://cds.cern.ch/record/1278169?In=en Cham, J. (2012) The Higgs Boson Explained. (animation): http://www.phdcomics.com/comics/archive.php?comicid=1489 Higgs, Peter W. (2010) My Life as a Boson. (transcribed speech): http://www.kcl.ac.uk/nms/depts/physics/news/events/MyLifeasaBoson.pdf More references can be found in the Scientific Background: http: //kva.se/nobelprizephysics2013

The Nobel Prize 2013 in Physics

Editors: Lars Bergström, Lars Brink and Olga Botner, The Nobel Committee for Physics, The Royal Swedish Academy of Sciences; Sara Strandberg and Oscar Stål, Stockholm University; Joanna Rose, Science Writer; Victoria Henriksson, Editor and Linnéa Wallgren, Nobel Assistant, The Royal Swedish Academy of Sciences. Graphic design: Ritator Illustrations: Johan Jarnestad/ Swedish Graphics Print: Åtta45

Phot

o: p

ortr

ait o

f Fra

nçoi

s En

gler

t: Je

an D

omin

ique

Bur

ton;

por

trai

t of P

eter

Hig

gs: C

allu

m B

enne

tts.

Printing anddistributionmade possible by

© The Royal Swedish Academy of SciencesBox 50005, SE-104 05 Stockholm, SwedenPhone: +46 8 673 95 00e-mail: [email protected], http://kva.sePosters may be ordered free of charge at http://kva.se/posters or by phone.

Nob

el P

rize

® a

nd th

e N

obel

Pri

ze®

med

al

desi

gn m

ark

are

regi

ster

ed tr

adem

arks

of

the

Nob

el F

ound

atio

n.

Here, at last! François Englert and Peter W. Higgs are jointly awarded the Nobel Prize in Physics 2013 for the theory of how particles acquire mass. In 1964, they proposed the theory independently of each other (Englert did so together with his now-deceased colleague Robert Brout). In 2012, their ideas were confirmed by the discovery of a so-called Higgs particle, at the CERN laboratory outside Geneva in Switzerland.

The awarded mechanism is a central part of the Standard Model of particle physics that describes how the world is constructed. According to the Standard Model, everything – from flowers and people to stars and planets – consists of just a few building blocks: matter particles which are governed by forces mediated by force particles. And the entire Standard Model also rests on the existence of a special kind of particle: the Higgs particle.

The Higgs particle is a vibration of an invisible field that fills up all space. Even when our universe seems empty, this field is there. Had it not been there, nothing of what we know

would exist because particles acquire mass only in contact with the Higgs field. Englert and Higgs proposed the existence of the field on purely mathematical grounds, and the only way to discover it was to find the Higgs particle.

The Nobel Laureates probably did not imagine that they would get to see the theory confirmed in their lifetimes. To do so required an enormous effort by physicists from all over the world. Almost half a century after the proposal was made, on July 4, 2012, the theoretical prediction could celebrate its biggest triumph, when the discovery of the Higgs particle was announced.

Broken Symmetry The Higgs mechanism relies on the concept of spontaneous symmetry breaking. Our universe was probably born symmetrical (1), with a zero value for the Higgs field in the lowest energy state – the vacuum. But less than one billionth of a second after the Big Bang, the symmetry was broken spontaneously as the lowest energy state moved away (2) from the symmetrical zero-point. Since then, the value of the Higgs field in the vacuum state has been non-zero (3).

The Field Matter particles acquire mass in contact with the invisible field that fills the whole universe. Particles that are not affected by the Higgs field do not acquire mass, those that interact weakly become light, and those that interact strongly become heavy. For example, electrons acquire mass from the field, and if it suddenly disappeared, all matter would collapse as the suddenly massless electrons dispersed at the speed of light. The weak force carriers, W and Z particles, get their masses directly through the Higgs mechanism, while the origin of the neutrino masses still remains unclear.

François Englert Belgian citizen. Born 1932 in Etterbeek, Belgium. Professor emeritus at Université Libre de Bruxelles, Brussels, Belgium.

Peter W. Higgs British citizen. Born 1929 in Newcastle upon Tyne, United Kingdom. Professor emeritus at University of Edinburgh, United Kingdom.

The Particle Collider LHCProtons – hydrogen nuclei – travel at almost the speed of light in opposite directions inside the circular tunnel, 27 kilometres long. The LHC (Large Hadron Collider) is the largest and most complex machine ever constructed by humans. In order to find a trace of the Higgs particle, two huge detectors, ATLAS and CMS, are capable of seeing the protons collide over and over again, 40 million times a second.

top quark

Heavier Lighter

bottom quark

tau

charm quark

muon

strange quark

down quark

up quark

electron

electron neutrino

muon neutrino

tau neutrino

The PuzzleThe Higgs particle (H) was the last missing piece in the Standard Model puzzle. But the Standard Model is not the final piece in the cosmic puzzle. One of the reasons for this is that the Standard Model only describes visible matter, accounting for one sixth of all matter in the universe. To find the rest – the mysterious so-called dark matter – is one of the reasons why scientists continue to chase unknown particles at CERN.

Potential energy of the Higgs field

CMS A short-lived Higgs particle is created in the collision and decays into four muons (tracks in red).

ATLAS In the collision, a short-lived Higgs particle is created, which decays into two muons (tracks in red) and two electrons (tracks in green).

1. 2. 3.

ATLAS

LHC

CMS

Pseudo-Rapidity, Azimuthal Angle, and Transverse Momentum

Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0

dx1dx2 fh1,a(x1, µ2

F ) fh2,b(x2, µ2

F )×σab(x1p1, x2p2, αS(µ2

R);µ2

F )

Computing Scattering Cross sections

Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )

Framework: QCD factorization

Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )


Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )

Framework: QCD factorization Parton Distribution Functions

Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )


Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )


Partonic cross section

Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )


Hx1

x2

h2

h1

a

b X

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )


Partonic cross sectionHx1

x2

h2

h1

a

b X

Precise predictions for depend on good knowledge of BOTH and

σ

σab fh,a(x, µ2

F )

σ(p1, p2;MH) =!a,b

" 1

0


F ) fh2,b(x2, µ2


R);µ2

F )

Juan Rojo University of Oxford, 28/04/2014

QCD calculations are provided in terms of quarks and gluons in the final state

After hard scattering, quarks and gluons follow a branching process and then hadronize, leading to a collimated bunch of hadrons as characteristic signal n the detector: a QCD jet

A quantitative robust mapping between final state hadrons, observed in the detector, and partons from the hard-scattering, is required to compare theory with data: a jet algorithm

We already saw a first example of jet algorithm: the Sterman-Weinberg jets in electron-positron annihilation ( which however in collinear unsafe at O(!S2) )

Here we explore modern jet reconstruction algorithms with enfasis on LHC phenomenology

A jet is a fundamentally ambiguous conceptA jet algorithm is required to provide a jet definitionGood jet algorithms can be applied to partons, hadrons and calorimeter cells

JETS IN HADRON COLLISIONS

• QCD calculations are provided in terms of quarks and gluons.

• After hard scattering, quarks and gluons following a branching process and then hadronize, leading to a collimated bunch of hadrons as a characteristic signal in the detector: a QCD jet

• A quantitative robust mapping between final state hadrons, observed in the detector, and partons from the hard scattering, is required to compare theory with data: a jet algorithm

JET ALGORITHMS

• The mapping between quarks and gluons/ hadrons/ calorimeter towers and jets is provided by the so called jet algorithms

• In addition, we need to specify which four-momenta is assigned to the combination to two particles when forming the jets: this is known as the recombination scheme

• The jet algorithm with its corresponding parameters, like jet radius, together with the recombination scheme, fully determine the jet definition

• In 1990, the Snowmass accord was set out to specify the desirable properties of good jet algorithms


The mapping between quarks and gluons / hadrons / calorimeter towers and jets is provided by the so called jet algorithms

In addition, we need to specify which four-momenta is assigned to the combination of two particles when forming the jet: this is known as the recombination scheme

The jet algorithm with its corresponding parameters, like jet radius, together with the recombination scheme, fully determine the jet definition

In 1990, the Snowmass accord was set out to specify the desirable properties of good jet algorithms

A crucial property of a jet algorithm is that it should be infrared safe, to avoid depending on the unknown, long-distance properties of QCD where perturbation theory breaks downs

Many of the jet algorithms in the last 20 years were infrared unsafe. Fortunately, this is not the case at the LHC anymore

JET ALGORITHMS

• A crucial property of a jet algorithm is that is should be infrared safe, to avoid depending on the unknown, long-distance properties of QCD where perturbation theory breaks down

• Surprisingly, many of the jet algorithms in the last 20 or so years were infrared unsafe. Today, we are using infrared safe algorithms to analyze LHC data.

JET ALGORITHMS

• In the particular case of jet algorithms , infrared safety can be formulated as the requirement that if the final state particles are modified by a soft emission or a collinear splitting then the set of hard jets found should be unchanged

• Failing this criterion, a jet definition with produce infinite results at some point in the perturbative expansion because of the lack of cancellation of infrared divergences


In the particular case of jet algorithms, infrared safety can be formulated as the requirement that if the final state particles are modified by a soft emission or a collinear splitting then the set of hard jets found should be unchanged

Failing this criterion, a jet definition will produce infinite results at some point in the perturbative expansion because of the lack of cancellation of infrared divergences

Jet pT

Jet rapidity

In the IRC unsafe algorithm, a collinear splitting leads to a different set of final state jets and thus to the lack of cancellation of soft and collinear divergences (KLN theorem)

JET ALGORITHMS

• In the particular case of jet algorithms , infrared safety can be formulated as the requirement that if the final state particles are modified by a soft emission or a collinear splitting then the set of hard jets found should be unchanged

• Failing this criterion, a jet definition with produce infinite results at some point in the perturbative expansion because of the lack of cancellation of infrared divergences


In the particular case of jet algorithms, infrared safety can be formulated as the requirement that if the final state particles are modified by a soft emission or a collinear splitting then the set of hard jets found should be unchanged

Failing this criterion, a jet definition will produce infinite results at some point in the perturbative expansion because of the lack of cancellation of infrared divergences

In the IRC unsafe algorithm, a soft emission leads to a different set of final state jets and thus to the lack of cancellation of soft and collinear divergences (KLN theorem)


Total SM Higgs cross sections at the LHC

H

H

H

W,Z

t

t

H



Total SM Higgs cross sections at the LHC

H

H

H

W,Z

t

t

H


[GeV] HM100 200 300 400 500 1000

H+X

) [pb

]

→(p

p σ

-110

1

10

210= 14 TeVs

LHC

HIG

GS

XS W

G 2

010

H (NNLO+NNLL QCD + NLO EW)

→pp

qqH (NNLO QCD + NLO EW)

→pp

WH (NNLO QCD + NLO EW)

→pp

ZH (NNLO QCD +NLO EW)

→pp

ttH (NLO QCD)

→pp

0.1 1 1010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

103

104

105

106

107

108

109

σσσσZZ

σσσσWW

σσσσWH

σσσσVBF

MH=125 GeV

WJS2012

σσσσjet

(ET

jet > 100 GeV)

σσσσjet

(ET

jet > √√√√s/20)

σσσσggH

LHCTevatron

eve

nts

/ s

ec f

or L

= 1

03

3 c

m-2s

-1

σσσσb

σσσσtot

proton - (anti)proton cross sections

σσσσW

σσσσZ

σσσσt

σ

σ

σ

σ

(( ((nb

)) ))

√√√√s (TeV)

{

arXiv:1504.05833


Vector Boson Fusion

Event Characteristics

Energetic jets in the forward and backward directions(pT > 20 GeV)

Higgs decay products between tagging jets

Little gluon radiation in the central-rapidity region, due tocolorless W /Z exchange (central jet veto: no extra jetswith pT > 20 GeV and |η| < 2.5)



Vector Boson FusionCentral Jet Veto

Example: Gluon fusion vs vector boson fusion

JHEP 05 (2004) 064

yrel = yvetoj − (y tag 1j + y

tag 2j )/2



Hjjj via VBF at NLO (only t-channels)Total Cross section

µ0 = 40 GeV

ξ = 2∓1 scale variations:

LO: +26% to −19%

NLO: less than 5%

JHEP 0802 (2008) 076 [arXiv:0710.5621]


role of the polarization vector for the weak boson is taken by a current, hµ, which, for the

first two diagrams in Fig. 1, is given by

hµ(pbτb, p2τ2) = δτ2τb(−e)gHV V gV f2fb

τ2 DV [p2a13]DV [p2

b2]ψ(p2)γµPτ2ψ(pb) (2.4)

with pijk = pi − pj − pk and pij = pi − pj, while DV [q2] = 1/[q2 − M2V ] is the weak boson

propagator, which, in our calculation, only occurs with space-like momentum. In terms of

the Compton amplitude of Eq. (2.3) the A3 are then given by

A3(1q, 3g, aq; 2Q, bQ) = MB(p1, p3, pa13; ϵ3, h(pbτb, p2τ2)),

A3(2Q, 3g, bQ; 1q, aq) = MB(p2, p3, pb23; ϵ3, h(paτa, p1τ1)). (2.5)

The gQ → qqQH subprocess is obtained by crossing the initial state quark q(pa) with

the final state gluon in Eq. (2.2) and dropping the s-channel graphs which result from

crossing the diagrams in the second line of Fig. 1. The 3-parton matrix elements M3 have

been computed using the helicity amplitude method of Ref. [23].

The real emission corrections to VBF Hjjj production consist of four subprocess

classes with four final state partons. These classes are (a) qQ → qQggH, (b) qQ →

qQq′q′H, (c) gQ → qqQgH, and (d) gg → qqQQH. The generalization to the crossed

processes with q → q and/or Q → Q is straightforward.

Figure 2: The dominant virtual QCD corrections. The “blobs” correspond to the sum of all virtualcorrections to the basic Q → QgV Compton amplitude and are given more explicitly in Fig. 6. Thefirst diagram and the second pair of diagrams in each line form gauge invariant subsets.

The above subprocesses lead to soft and collinear singularities when integrated over

the phase space of the final state partons. We use the Catani-Seymour dipole subtraction

method to regulate these divergences [26] and to cancel them against those originating from

the virtual corrections. The virtual corrections can be divided into two classes of gauge

– 5 –

No pentagon or hexagon diagrams included.

Approximate as two DIS reactions.

HJETS++

• Our aim was to compute the missing pieces (s, t,and u-channel one-loop amplitudes) in H+3 Jets production where the Higgs boson is produced via the HVV coupling (a.k.a VBF+Jet).

• Virtuals: Hexagons, Pentagons, Boxes, and Triangles

• Reals: H+6 parton amplitudes (6 quark + H, 4 quark + 2 gluons +H)arX

iv:1

308.

2932

v2 [

hep-

ph]

12 S

ep 2

013

DESY 13-144, FTUV-13-1308, IFIC/13-55, LPN13-055, LU-TP 13-28, MAN/HEP/2013/17

Electroweak Higgs plus Three Jet Production at NLO QCD

Francisco Campanario,1 Terrance M. Figy,2 Simon Platzer,3 and Malin Sjodahl4

1Theory Division, IFIC, University of Valencia-CSIC, E-46100 Paterna, Valencia, Spain2School of Physics and Astronomy, University of Manchester

3Theory Group, DESY Hamburg4Dept. of Astronomy and Theoretical Physics, Lund University, Solvegatan 14A, 223 62 Lund, Sweden

We calculate next-to-leading order (NLO) QCD corrections to electroweak Higgs plus three jetproduction. Both vector boson fusion (VBF) and Higgs-strahlung type contributions are includedalong with all interferences. The calculation is implemented within the Matchbox NLO frameworkof the Herwig++ event generator.

PACS numbers: 12.38.Bx

I. INTRODUCTION

Higgs production via vector boson fusion (VBF) is anessential channel at the LHC for disentangling the Higgsboson’s coupling to fermions and gauge bosons. The ob-servation of two tagging jets is crucial to reduce the back-grounds. Furthermore, the possibility to identify Higgsproduction via VBF is enhanced by being able to increasethe signal to background ratio by vetoing additional softradiation in the central region [1–7], since this suppressesimportant QCD backgrounds, including Hjj via gluonfusion.

To exploit the central jet veto (CJV) strategy for Higgscoupling measurements, the reduction factor caused bythe CJV on the observable signal must be accuratelyknown. The fraction of VBF Higgs events with at leastone additional veto jet between the tagging jets providesthe relevant information, i.e., we need to know the ratioof Hjjj production to the inclusive cross section of Hjjproduction via VBF. Gluon fusion NLO QCD correctionsfor Hjjj within the top effective theory approximationhave been recently computed in [8], a validation of theeffective theory approximation at LO for this process canbe found in [9].

At present, the NLO QCD corrections of Hjjj viaVBF were calculated [10] with several approximationsand without the inclusion of five- and six-point functiondiagrams (Fig. 1, second row) and the corresponding realemission cuts, which were estimated to contribute at theper mille level. However, some studies [5] suggest thatthe contribution of the missing pieces can be larger. Dueto the importance of the process to Higgs measurements,a full calculation is necessary to ensure that integratedcross sections and kinematic distributions are not under-estimated.

In this letter, we present results for electroweak Higgsplus three jet production at NLO QCD. In Section II,we present technical details of our computation. In Sec-tion III, we present numerical results and the impactof the NLO QCD corrections on various differential dis-tributions. Finally, we summarize our findings in Sec-tion IV.

H H

H H

FIG. 1. Representative examples of diagrams of Hjjj pro-duction via vector boson fusion.

II. CALCULATIONAL DETAILS

For the calculation of the LO matrix elements for Higgsplus two (we have performed the Hjj calculation in par-allel within the same framework), three and four jets,we have used the builtin spinor helicity library of theMatchbox module [11] to build up the full amplitude fromhadronic currents. For the Born-virtual interference thehelicity amplitude methods described in [12] have beenemployed. Both methods resulted in two different im-plementations of the tree level amplitudes which havebeen validated against each other, including color cor-related matrix elements. The LO implementation hasfurther been cross checked against Sherpa [13, 14] andHawk [15, 16]. The dipole subtraction terms [17] havebeen generated automatically by the Matchbox mod-ule [11], which is also used for a diagram-based mul-tichannel phase space generation. For the virtual cor-rections, we have used in-house routines, extending thetechniques developed in [18]. The amplitudes have beencross checked against GoSam [19]. A representative setof topologies contributing are depicted in Fig. 1.For electroweak propagators, we have introduced finite

width effects following [20], using complex gauge bosonmasses and a derived complex value of the sine of theweak mixing angle. We used the OneLoop library [21]

page 1/6

Diagrams made by MadGraph5

u1

u3

g

d5

d~

u2 u 4

zh 7

zd~ 6

diagram 1 QCD=2, QED=3

u1

u3

g

d~6

d

u2 u 4

zh 7

zd 5


u2 u 4

gd 5

d

u1

u3

z

h7

z

d~ 6


u2 u 4

g d~ 6

d~

u1

u3

z

h7

z

d 5


u1

u3

g

u4

u~

u2 d 5

w-h 7

w-d~ 6


u1

u3

g

d~6

d

u2 d 5

w-h 7

w-u 4


DIPOLE SUBTRACTION


Higgs Production via Vector Boson Fusion at NLODipole subtraction method

Catani and Seymour, hep-ph/9605323

NLO cross section:

σNLOab (p, p) = σNLO{4}

ab (p, p) + σNLO{3}ab (p, p)

+

! 1

0

dx [σNLO{3}ab (x , xp, p) + σNLO{3}

ab (x , p, xp)]

σNLO{3}ab (p, p) =

!

3

[dσVab(p, p) + dσB

ab(p, p)⊗ I]ϵ=0





NLO cross section:



+

! 1

0


ab (x , p, xp)]

σNLO{3}ab (p, p) =

!

3


ab(p, p)⊗ I]ϵ=0





NLO cross section:



+

! 1

0


ab (x , p, xp)]

σNLO{3}ab (p, p) =

!

3


ab(p, p)⊗ I]ϵ=0





NLO cross section:



+

! 1

0


ab (x , p, xp)]

! 1

0dx σNLO{3}

ab (x , xp, p) ="

a′

! 1

0dx

!

3{dσB

a′b(xp, p)

⊗ [P(x) +K(x)]aa′

}ϵ=0





NLO cross section:



+

! 1

0


ab (x , p, xp)]

σNLO{4}ab (p, p) =

!

4

[dσRab(p, p)ϵ=0 − dσA

ab(p, p)ϵ=0]


For the H+2,3, and 4 jet amplitudes we use the in-house spinor library of Matchbox.

HJETS++

• Matchbox [S. Platzer and S. Gieseke, arXiv:1109.6256]

• Catani-Seymour Dipole subtraction [hep-ph/9605323]

• Subtractive and POWHEG style matching to parton shower

• ColorFull [M. Sjodahl, arXiv:1211.2099, http://home.thep.lu.se/~malin/ColorMath.htm#ColorMath, ColorFull will soon be public.]

• Tensorial Reduction [F. Capanario, arXiv:1105.0920]

• Scalar Loop Integrals: OneLOop [A. van Hameren arXiv:1007.4716 ]

THE RESULTS

• Input parameters and selection cuts.

• Scale variations for total cross section.

• Kinematic distributions.

INPUT PARAMETERS

• Ecm=14 TeV (proton - proton LHC)

• At least three anti-KT D=0.4 (E-scheme recombination) of 20 GeV and rapidity within -4.5 and 4.5 using FastJet [arXiv:0802.1189, arXiv:1111.6097]

• PDF choices: CT10 for NLO and CTEQ 6L1 for LO [arXiv:hep-ph/0201195, arXiv:1007.2241]

• Scales: W-boson mass (MW) and sum of transverse momentum of reconstructed jets (HT)

yi: rapidity�i: azimuthal angle

�yij = |yi � yj |: absolute rapidity di↵erence between i and j

��ij = |�i � �j |: absolute azimuthal angle di↵erence between i and j

mij =p(pi + pj)2: invariant mass of i and j

pi: four momentum vector of i

2

which supports complex masses to calculate the scalarintegrals. For the reduction of the tensor coefficients upto four-point functions, we apply the Passarino-Veltmanapproach [22], and for the numerical evaluation of the fiveand six point coefficients, we use the Denner-Dittmaierscheme [23], following the layout and notation of [18].To ensure the numerical stability of our code, we have

implemented a test based on Ward identities [18]. TheseWard identities are applied to each phase space point anddiagram, at the expense of a small additional computingtime and using a cache system. If the identities are notfulfilled, the amplitudes of gauge related topologies areset to zero. The occurrence of these instabilities are atthe per-mille level, and therefore well under control. Thismethod was also successfully applied in other two to fourprocesses [24, 25]. In the present work, it is applied forthe first time to a process which involves loop propagatorswith complex masses.The color algebra has been performed using ColorFull

[26] and double checked using ColorMath [27]. Withinthe same framework, we have implemented the corre-sponding calculation of electroweak Hjj production andperformed cross checks against Hawk [15, 16].

III. NUMERICAL RESULTS

In our calculation, we choose mZ = 91.188GeV,mW = 80.419002GeV, mH = 125GeV and GF =1.16637 × 10−5GeV−2 as electroweak input parametersand derive the weak mixing angle sin θW and αQED fromstandard model tree level relations. All fermion masses(except the top quark) are set to zero and effects fromgeneration mixing are neglected. The widths are calcu-lated to be ΓW = 2.0476 GeV and ΓZ = 2.4414 GeV.We use the CT10 [28] parton distribution functions withαs(MZ) = 0.118 at NLO, and the CTEQ6L1 set [29] withαs(MZ) = 0.130 at LO.We use the five-flavor scheme andthe center-of-mass energy is fixed to

√s = 14TeV.

To study the impact of the QCD corrections, we useminimal inclusive cuts. We cluster jets with the anti-kT algorithm [30] using FastJet [31] with D = 0.4, E-scheme recombination and require at least three jets withtransverse momentum pT,j ≥ 20 GeV and rapidity |yj | ≤4.5. Jets are ordered in decreasing transverse momenta.In Figure 2, we show the LO and NLO total cross-

sections for inclusive cuts for different values of the fac-torization and renormalization scale varied around thecentral scale, µ for two scale choices, MW /2, and thescalar sum of the jet transverse momenta, µR = µF =µ = HT /2 with HT =

!j pT,j . In general, we see a

somewhat increased cross section and - as expected - de-creased scale dependence in the NLO results. We alsonote that the central values for the various scale choicesare closer to each other at NLO. The uncertainties ob-tained by varying the central value a factor two up anddown are around 30% (24%) at LO and 2% (9%) at NLOusing HT /2 (MW /2) as scale choice. At µ = HT /2, we

1300

1400

1500

1600

1700

1800

1900

2000

2100

σ/fb

0.81

1.2

0.25 0.4 0.6 0.8 1.0

K

ξ

LO, µ = ξHT

LO, µ = ξMW

NLO, µ = ξHT

NLO, µ = ξMW

HJets++

FIG. 2. The Hjjj inclusive total cross section (in fb) at LO(cyan) and at NLO (blue) for the scale choices, µ = ξMW

(dashed) and µ = ξHT (solid). We also show the K-factor,K = σNLO/σLO for µ = ξMW (dashed) and µ = ξHT (solid).

obtained σLO = 1520(8)+208−171 fb σNLO = 1466(17)+1

−35

fb. Studying differential distributions, we find that thesegenerally vary less using the scalar transverse momentumsum choice, used from now on.In the following, we show some of the differential dis-

tributions which characterize the typical vector boson fu-sion selection cuts and central jet veto strategies as wellas the pT spectrum of the Higgs.For the leading jets (defined to be the two jets with

highest transverse momenta pT,1 and pT,2), we show therapidity difference in Fig. 3. Generally, we find smalldifferences in shape compared to the LO results.In Figure 4, the differential distribution for the pT of

the Higgs is shown. The NLO corrections are moderateover the whole spectrum and the scale uncertaities areclearly smaller.In Figure 5, the differential distribution of the third jet,

the vetoed jet for a CJV analysis, is presented. Here wefind large differences in the high energy tail of the trans-verse momentum distribution. Such high energy jets aresignificantly enhanced at NLO.We also study the normalized centralized rapidity dis-

tribution of the third jet w.r.t. the tagging jets, z∗3 =(y3 − 1

2(y1 + y2))/(y1 − y2). This variable beautifully

displays the VBF nature present in the process. Oneclearly sees how the third jet tends to accompany one of

µR = µF = HT /2 (MW /2):30% (24%) at LO and 2% (8%) at NLO

⇠ = µ/µ0

µ0 = HT (MW )

HT =P

j pT,j

K = �NLO/�LO

Scale Variations on Integrated Cross-sections

�LO = 1520(8)+208�171 fb �NLO = 1466(17)+1

�35 fb

JET DISTRIBUTIONS

z?3 = (y3 �1

2(y1 + y2))/(y1 � y2)

HJets++

LONLO

10−2

10−1

1

10 1

10 2

Transverse momentum of the third jet

dσ/dp⊥,3[fb/GeV

]

20 40 60 80 100 120 140 160 180 2000.5

1

1.5

2

2.5

3

3.5

p⊥,3 [GeV]

K

HJets++

LONLO

1

10 1

10 2

Rapidity of the third jet

dσ/dy3[fb]

-4 -2 0 2 4

0.6

0.8

1

1.2

1.4

y3

K

NLO QCD Corrections to EW H j j j Production at the LHC Terrance M. Figy

HJets++

LONLO

10−2

10−1

1

10 1

10 2


dσ

/d

pT

,3[f

b/

GeV

]

20 40 60 80 100 120 140 160 180 2000.5

1

1.5

2

2.5

3

3.5

pT,3 [GeV]

K

HJets++

LONLO

10 2

10 3

Relative position of the third jet

dσ

/d

z∗ 3[f

b]

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0.6

0.8

1

1.2

1.4

z∗3

K

Figure 3: Differential cross section and K factor for the pT of the third hardest jet (left) and the normalizedcentralized rapidity distribution of the third jet w.r.t. the tagging jets (right). Cuts are described in the text.The bands correspond to varying µF = µR by factors 1/2 and 2 around the central value HT/2.

HJets++

LONLO

10−4

10−3

10−2

10−1

1

10 1


dσ

/d

pT

,3[f

b/

GeV

]

20 40 60 80 100 120 140 160 180 200

0.6

0.8

1

1.2

1.4

pT,3 [GeV]

K

HJets++

LONLO

10−1

1

10 1

10 2

Relative position of third jet

dσ

/d

z∗ 3[f

b]

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0.6

0.8

1

1.2

1.4

z∗3

K

Figure 4: Differential cross section and K factor for the pT of the third hardest jet (left) and the normalizedcentralized rapidity distribution of the third jet w.r.t. the tagging jets (right) with µR = µF = HT . Beyondthe inclusive cuts described in the text, we include the set of VBF cuts: m12 =

!

(p1+ p2)2 > 600 GeV and|∆y12|= |y1− y2|> 4.0.

On the left-hand side of Figure 3, the differential distribution of the third jet, the vetoed jetfor a CJV analysis, is shown. Here we find large K factors in the high energy tail of the transversemomentum distribution. However, when VBF cuts 1 are included the K factor is almost flat forthe transverse momentum of the third jet (see the left-hand side of Figure 4). On the right-handside of Figure 3, we show the normalized centralized rapidity distribution of the third jet w.r.t. thetagging jets, z∗3 = (y3− 1

2(y1+ y2))/(y1− y2). This variable beautifully displays the VBF nature

1For the VBF cuts we have chosen to include the following cuts in addition to the inclusive cuts described in themain text : m12 =

!

(p1+ p2)2 > 600 GeV and |∆y12|= |y1−y2|> 4.0

5

HJets++

LONLO

1

10 1

10 2

Rapidity difference of first and second jet

dσ/d

∆y12

[fb]

0 2 4 6 8 10

0.6

0.8

1

1.2

1.4

∆y12

K

HJets++

LONLO

1

10 1

10 2

10 3Rapidity difference of first and third jet

dσ/d

∆y13

[fb]

0 2 4 6 8 10

0.6

0.8

1

1.2

1.4

∆y13

K

HJets++

LONLO

1

10 1

10 2

10 3Rapidity difference of second and third jet

dσ/d

∆y23

[fb]

0 2 4 6 8 10

0.6

0.8

1

1.2

1.4

∆y23

K

Rapidity separation

Higgs Boson Distributions

Transverse momentum Rapidity

HJets++

LONLO

10−3

10−2

10−1

1

10 1

10 2

Rapidity of the H

dσ/dyH[fb]

-4 -2 0 2 4

0.6

0.8

1

1.2

1.4

yH

K

HJets++

LO

NLO

10−1

1

10 1

Transverse momentum of the H

dσ/dp⊥,H

[fb/GeV

]

0 50 100 150 200 250 300 350 400

0.6

0.8

1

1.2

1.4

p⊥,H [GeV]

K

HJets++

LONLO

10 2

Azimuthal angle separation of H and third jet

dσ/d

∆φh3[fb]

-3 -2 -1 0 1 2 3

0.6

0.8

1

1.2

1.4

∆φh3

K

HJets++

LONLO

1

10 1

10 2

Rapidity separation of H and third jet

dσ/d

∆y h

3[fb]

0 2 4 6 8 10

0.6

0.8

1

1.2

1.4

∆yh3

K

Higgs Boson Distributions

Jet Masses

HJets++

LONLO

10−3

10−2

10−1

1

10 1

10 2

Mass of the second jet

dσ/dm

2[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

m2

K

HJets++

LONLO

10−5

10−4

10−3

10−2

10−1

1

10 1

10 2

Mass of the first jet

dσ/dm

1[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

m1

K

HJets++

LONLO

10−6

10−5

10−4

10−3

10−2

10−1

1

10 1

10 2

Mass of the third jet

dσ/dm

3[fb/GeV

]

0 20 40 60 80 100

0.6

0.8

1

1.2

1.4

m3

K

Here we see fat jets.

Distributions with VBF cutsLONLO

10−2

10−1

1

Mass of first and third jet

dσ/dm

13[fb/GeV

]

0 500 1000 1500 2000

0.6

0.8

1

1.2

1.4

m13 [GeV]

Ratio

LONLO

10−1

Mass of first and second jet

dσ/dm

12[fb/GeV

]

0 500 1000 1500 2000

0.6

0.8

1

1.2

1.4

m12 [GeV]

Ratio

LONLO

10−2

10−1

1

Mass of second and third jet

dσ/dm

23[fb/GeV

]

0 500 1000 1500 2000

0.6

0.8

1

1.2

1.4

m23 [GeV]

Ratio

• mj1j2 > 600 GeV

• �yj1j2 > 4.0

Distributions with VBF cutsLONLO

10−1

1

10 1

10 2

Rapidity difference of first and third jet

dσ/d

∆y13

[fb]

0 2 4 6 8 10

0.6

0.8

1

1.2

1.4

∆y13

Ratio

LONLO

10−1

1

10 1

10 2

Rapidity difference of first and second jet

dσ/d

∆y12

[fb]

0 2 4 6 8 10

0.6

0.8

1

1.2

1.4

∆y12

Ratio

LONLO

10−1

1

10 1

10 2

Rapidity difference of second and third jet

dσ/d

∆y23

[fb]

0 2 4 6 8 10

0.6

0.8

1

1.2

1.4

∆y23

Ratio

• mj1j2 > 600 GeV

• �yj1j2 > 4.0

Distributions with VBF cuts

LONLO

10−1

1

10 1

10 2

Relative position of third jetd

σ/dz∗ 3[fb]

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

0.6

0.8

1

1.2

1.4

z∗

3

K

LONLO

10−4

10−3

10−2

10−1

1

10 1


dσ/dp⊥,3[fb/GeV

]

20 40 60 80 100 120 140 160 180 200

0.6

0.8

1

1.2

1.4

p⊥,3 [GeV]

Ratio

LONLO

10−1

1

10 1

Rapidity of the third jet

dσ/dy3[fb]

-4 -2 0 2 4

0.6

0.8

1

1.2

1.4

y3

Ratio

• mj1j2 > 600 GeV

• �yj1j2 > 4.0

COMPARISONS TO OTHER CODES

mjj > 130 GeV

�yjj > 3.0

|yj | < 5.0

• Compared HJETS++ with POWHEG BOX.

• Discovered deviations between the results of HJETS++ and POWHEG BOX due the various approximations implemented in POWHEG BOX

pS = 13 TeV

Herwig 7 & HJets++ NLOHerwig 7 & HJets++ NLO ⊕ PSPOWHEG-BOX & Herwig 7

10−4

10−3

dσ

/d

p ⊥,h

×G

eV/

pb

0 50 100 150 200

0.6

0.8

1

1.2

1.4

p⊥,h / GeV

#/

NL

O


10−7

10−6

10−5

10−4

10−3

10−2

10−1

dσ

/d

y h×

1/p

b

-4 -2 0 2 4

0.6

0.8

1

1.2

1.4

yh

#/

NL

O


10−5

10−4

10−3

dσ

/d

p⊥

,1×

GeV

/p

b

0 50 100 150 200 250 300 350 400

0.6

0.8

1

1.2

1.4

p⊥,1 / GeV

#/

NL

O


10−2

10−1

dσ

/d

y1×

1/p

b

-4 -2 0 2 4

0.6

0.8

1

1.2

1.4

y1

#/

NL

O


10−7

10−6

10−5

10−4

10−3

10−2

dσ

/d

p⊥

,2×

GeV

/p

b

0 50 100 150 200 250 300

0.6

0.8

1

1.2

1.4

p⊥,2 / GeV

#/

NL

O


10−2

10−1

dσ

/d

y2×

1/p

b

-4 -2 0 2 4

0.6

0.8

1

1.2

1.4

y2

#/

NL

O


10−5

10−4

10−3

10−2

dσ

/d

p⊥

,3×

GeV

/p

b

0 20 40 60 80 100 120 140

0.6

0.8

1

1.2

1.4

p⊥,3 / GeV

#/

NL

O


10−2

10−1

dσ

/d

y3×

1/p

b

-4 -2 0 2 4

0.6

0.8

1

1.2

1.4

y3

#/

NL

O

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100 120 140 160 180 200d m

/d p

T,3 (

fb/G

eV)

pT,3(GeV)

VBF cuts

LO VBFNLOLO HJets++

-2

0

2

4

6

8

10

12

0 20 40 60 80 100 120 140 160 180 200

d m

/d p

T,3 (

fb/G

eV)

pT,3(GeV)

VBF cuts

NLO VBFNLONLO HJets++

Comparison to VBFNLO

Documents

WichitaStateUniversity Seminar Spring2016 · (2013) Higgs Discovery: The Power of Empty Space , Bodley Head. é S ample, I. (2013) Massive: The Higgs Boson and the Greatest Hunt in