msci report

MSci Project Report: Looking for New Physics at the LHC Using

Tau Leptons

Sophie Middleton

Supervised by Dr David Colling

Assessed by Dr Morgan Wascko

April 30, 2012

Abstract

The following report presents a search for the standard model Higgs boson in real CMS data taken duringthe 2011A run with an integrated luminosity of 2094 pb�1. The search aims to look for the di-tau decay ofa neutral Higgs boson prodcued via vector boson fusion using the e⌧had and µ⌧had tau decay channels.

Initially, work is done to establish accurate estimates of backgrounds to this process including the Z ! ⌧⌧decay, W+Jets and QCD backgrounds. Estimates of the Z ! ⌧⌧ are derived from the Z ! ee, µµ data;

cross-sections are derived from data for all three processes and are shown to be consistant with each otherand theoretical predictions.

No excess is found in the observed tau-pair invarient mass for either tau decay channel. This results inupper limits being placed on Higgs boson production cross section at a 95 % confidence level for Higgs

masses in the range 115-140 GeV/C2.

Declaration

The majority of the work within this report is my own, however, specific credit must go to my fellow MScistudents: David Kirkpatrick and Edward Evans who helped with calculations of the Z ! µµ and ee cross-sections which were used in the final analysis. Everything else unless explicitly referenced is my own workand interpretation of the results provided.

The data used is 2011A CMS data which was taken at CERN during the first half of 2011 and the ntu-ple ROOT trees used for the analysis as well as the Monte Carlo simulations were provided by Mike Cutajarwho I must acknowledge for his assistance in the statistical analysis as well as for providing sections ofexample code.

Sophie Middleton

I

Acknowledgments

First of all I would like to thank my supervisor, Dr David Colling, for giving me the opportunity to work onone of the most revolutionary experiments every built and for his guidance throughout; work on my MSciproject has given me a great insight into the world of particle physics research at its most sophisticated leveland has inspired me to pursue further study in this field.

I must also thank Mike Cutajar for his assistance and expertise in the use of LandS which was used toestablish limits on the Higgs cross-section.

II

Contents

1 Introduction: Standard Model and Higgs Phenomenology 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Quantum Field Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4.1 QED:Quantum Electro-Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4.2 QCD: Quantum Chromo-Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4.3 Unifying the EM and Weak Forces: Electroweak Theory . . . . . . . . . . . . . . . . . 4

1.5 Spontaneous Symmetry Breaking and The Higgs Mechanism . . . . . . . . . . . . . . . . . . 51.6 Higgs Production at the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 The CMS Detector Design 72.1 The Large Hadron Collider ( LHC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 CMS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 The Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 The ECAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.3 The HCAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.4 The Muon System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.5 Tau Triggers and Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Current Limits and Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Software 123.1 The ROOT Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 RooFit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 LandS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.4 Event Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Results and Analysis 134.1 Z ! µ+µ� analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1.1 Z Production, Initial and Final State Radiation . . . . . . . . . . . . . . . . . . . . . . 134.1.2 Muon Quality Cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.1.3 Background and Other Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.2.1 Jets Selection and VBF Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.2.2 VBF cutflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.3 Z ! e+e� analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.3.1 Correction Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.3.2 Calculation of E�ciency and Acceptances for the di-electron and di-muon cases . . . 214.3.3 Observed di-electron and di-muon Cross-sections . . . . . . . . . . . . . . . . . . . . . 21

4.4 Z ! ⌧+⌧� analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.4.1 Kinematic Selection and Hadronic Tau Ideintification . . . . . . . . . . . . . . . . . . 224.4.2 ⌧had + µ Event Reconstruction and Background analysis . . . . . . . . . . . . . . . . . 234.4.3 Method of Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4.4 W+jets background in µ⌧had Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4.5 QCD Background in the µ⌧had Channel . . . . . . . . . . . . . . . . . . . . . . . . . . 254.4.6 tt̄, Di-boson and Z ! l+l� background in the µ⌧had channel . . . . . . . . . . . . . . 264.4.7 ⌧had+e Event Reconstruction and Background analysis . . . . . . . . . . . . . . . . . . 264.4.8 � +jets Background in the e⌧had Channel . . . . . . . . . . . . . . . . . . . . . . . . . 27

III

4.4.9 Systemic, Statistical and Theoretical Uncertainty . . . . . . . . . . . . . . . . . . . . 294.4.10 Signal Events and Z ! ⌧⌧ cross section . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.5 Statistical Analysis: Is there a Higgs Decay in the Data? . . . . . . . . . . . . . . . . . . . . . 304.5.1 Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.5.2 Are ee and µµ data samples consistent with ⌧⌧? . . . . . . . . . . . . . . . . . . . . . 304.5.3 Probability of there being a Higgs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.5.4 Predicting Z ! ⌧⌧ from MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.5.5 Predicting Z ! ⌧⌧ from Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.5.6 Statistical Significance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.5.7 Shape Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.5.8 Inclusive Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5 Conclusions 36

Bibliography 37

A Appendix 39A.1 Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39A.2 Di-muon and di-jet Contol Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39A.3 Triggers and E�ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

A.3.1 ee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41A.3.2 µµ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41A.3.3 e⌧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41A.3.4 µ⌧ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

A.4 Higgs Expected Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42A.5 Higgs Exclusion For individual channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

IV

Chapter 1

Introduction: Standard Model andHiggs Phenomenology

1.1 Introduction

The project is focused on the use of the Compact Muon Solenoid (CMS) detector, based at the LHC inCERN, for detecting charged leptons, particularly, tau leptons and their use in the search for the standardmodel Higgs boson. The di-tau decay channel of the standard model Higgs has a moderate branching fractionof ⇡10% in the low mass region this along with the low levels of background when compared to heavy quarkprocesses make it a good channel for discovery.

From the latter part of the twentieth century research into particle physics has taken place using highenergy accelerators, these allow subatomic particle to be collided at high energy e↵ectively ‘recreating theconditions shortly after the Big Bang.’ This allows analysis of the particles and forces that have shaped theuniverse since. The LHC is currently the highest energy collider every built, with a design centre-of-massenergy of 14TeV, making it incredibly useful, not just in Higgs searches but for SUSY searches as well asanalysis of CP violation and searches for even more exotic physics.

CMS is one of two general purpose detectors (the second being ATLAS) which is primarily focused onHiggs searches. This builds on decades of previous research at CERN, with experiments such as LEP in the1990’s, as well as the Tevatron experiments. These experiments combined have already made huge steps inexcluding, at a 95 % confidence level, Higgs masses below 114GeV/c2 and above 200GeV/c2 as well as aregion around 150� 160GeV/c2 .The CMS and ATLAS experiments have already provided huge amounts ofdata leading to further mass regions been excluded at a 95 % confidence level.

The Higgs Boson is a result of the Higgs Mechanism which was hypothesized to introduce spontaneoussymmetry breaking to account for the fact that the weak force bosons (W±, Z0) posses mass while thestrong and electromagnetic force carriers do not. Finding (or excluding) the standard model Higgs boson is,therefore, of extreme importance to our understanding of the universe.

1.2 Aims

• To familiarize oneself with the ROOT Framework and C++ as a language for interpreting data fromhigh energy physics experiments in a LINUX environment

• To Understand the mathematical derivation of concepts within the standard model formulation includ-ing: QED, QCD, Electroweak theory and the Higgs Mechanism

• To apply e↵ective analytical techniques to real and simulated data

• To compare and inspect results from detector data and Monte Carlo to estimate signal and backgroundyields

• To carry out statistical analysis using LandS to put limits on the probability of there being a Higgsparticle in the 2011A CMS data

1

Project Report Introduction: The Higgs Boson 2

1.3 The Standard Model

The standard model of particle physics brings together two major extant theories: electroweak theory, whichproposes that the electromagnetic and weak forces are manifestations of the same fundamental process , andquantum chromo-dynamics (QCD), the theory of strong interactions. The standard model proposes thatthese forces are a result of the exchange of force mediating gauge bosons (s=1). Strong interactions aremediated by gluons, electromagnetic interactions by the photon and the weak force by the W± and Z bosons.The standard model is a quantum field theory formulated on the SU(2)c ⇥ SU(2)L ⇥ U(1)Y gauge group,where SU(3)c represents QCD and SU(2)L ⇥ SU(3)Y represents the electroweak theory. C defines colour,the strong equivalent of charge, L defines a left-handed current and Y defines weak hyper-charge involved inelectroweak interactions.[1][2]

Photons and gluons are massless, however, the weak gauge bosons must posses mass otherwise the crosssection of the weak interaction would diverge to infinity. This presented somewhat of a problem in thecourse of electroweak unification and to account for weak boson mass spontaneous symmetry breaking wasintroduced and proposes that all massive particles acquire their mass via the Higgs Mechanism (section 1.5).

The table below summarizes the fundamental particles in the standard model:

Fermion/Boson Type Particles Spin Charge InteractionsFermion Lepton ⌫e, ⌫µ, ⌫⌧ 1/2 0 weak

e, µ, ⌧ 1/2 -1 weak, EMFermions Quarks u,c,t 1/2 +2/3 EM, weak, strong

d,s,b 1/2 -1/3 EM, weak, strong

Fermion/Boson Interaction Particles Spin Charge Mass(GeV/c2)Boson EM � 1 0 0Boson Strong 8 gluons 1 0 0Boson Weak W+ 1 +1 80.4

W� 1 -1 80.4Z0 1 0 91.2

Boson Higgs 0 0 ???

In the standard model there are two types of fundamental half-integer spin fermions: leptons, quarksas well as the described spin-1 force mediating bosons. Quarks may be distinguished from leptons by therestrong interactions; each quark must posses a “strong charge” named after one of three colours: red, blueor green. In total the SM predicts 61 elementary particles: 36 quarks, 12 leptons, 12 force mediator and 1Higgs.

Although, to date, the SM has proven successful in terms of experimental proof it is, however, not a fullyunified theory in that it is not built around a single representation with one coupling constant as well asbeing unable to fully account for neutrinos masses and the extent of CP-violation in the universe as well asnot providing a viable dark matter candidate or accounting for the Higgs heirarchy problem. [3][4]

1.4 Quantum Field Theories

Quantum Field Theory, or QFT, was initially proposed by Paul Dirac in the late 1920’s; QFT builds quan-tum mechanics into a theory of canonically quantized fields operating on a vacuum thus correcting severallimitations to quantum mechanics such as the possibility of particle creation/annihilation and the negativeprobabilities which arise when special relativity is incorporated [3]. The standard model formulation relies onquantum field theories constructed upon gauge invariant Lagrangian. In field theory the Euler-Lagrangianequations of motion is expressed as:

@µ(@L

@(@µ�))� @L

@�= 0 (1.1)

where @µ is the space-time four vector and the field � is a function of xµ. The Lagrangian density L forboson fields is given by the Klein-Gordon Lagrangian:

LKG =1

2(@µ�)(@

µ�)� 1

2m2�2 = 0 (1.2)

Applying the Euler-Lagrange eqn. gives:

@µ@µ�+m2� = 0 (1.3)


This is the expected Lorenz covariant Klein-Gordon eqn.Similarly, one can derive the Lagrangian density for a free fermion field which is given by the Dirac

Lagrangian:

LDirac = �(̄i�µ@µ �m)� (1.4)

At the heart of the standard model is the principle of local gauge invariance: the idea that the lawsof physics are invariant under certain local phase transformations. Imposing local gauge invariance onthe Lagrangian gives the interaction between particles and introduces gauge fields as mediators of theseinteractions. This will be shown in the next section for QED, QCD and the Electroweak cases.[1]

1.4.1 QED:Quantum Electro-Dynamics

Quantum Electro-Dynamics (QED) was developed to explain electromagnetic interactions in terms of bosonexchange. This was the first successful gauge theory and is based on the U(1) gauge group. The Lagrangiandensity for the Dirac equation describing spin-1/2 fermions may be written as:

LD = i ̄�µ@µ �m ̄ (1.5)

which comprises of a kinetic term and a mass term, where and ̄ are the spinor and its adjoint fieldsand �µ are the Dirac gamma matrices. This Lagrangian is invariant under global U(1) gauge transformation,however, it is not invarient under local gauge transformation, which may be written as:

! 0 = eiq✓(x) (1.6)

where ✓ is a space-time dependent function with constant coupling factor q. Local gauge invariance canbe restored by introducing the covariant derivative:

Dµ = @µ + iqAµ (1.7)

where q is the electromagnetic coupling constant and Aµ is commonly known as the gauge field, acompensating vector field necessary to balance the gauge freedom of [1]. Aµ has gauge freedom such thatit transforms as:

Aµ ! Aµ + @µ✓(x) (1.8)

Therefore, by enforcing that QED is invariant under local gauge (U(1)) transformation we have introduceda new field , Aµ, which mediates the EM force.Aµ may be interpreted as the electromagnetic vector potentialmeaning EM interactions can be understood in terms of photon exchange.

The Dirac Lagrangian (1.5) may now be written in the form of a new ’gauged’ Lagrangian:

LD = i ̄�µDµ �m ̄ = i ̄�µ@µ � q ̄�µAµ �m ̄ (1.9)

which is invariant under the local gauge transformation.The gauge invariant kinetic term for the field Aµ can be introduced using a field tensor:

Fµ⌫ = @µA⌫ � @µAµ (1.10)

meaning the complete QED Lagrangian may be written as:

LQED = i ̄�µ@µ � q ̄�µAµ �m ̄ � 1

4Fµ⌫F

µ⌫ (1.11)

where the third term describes the photon field interacting with fermions with strength q which is equiv-alent to the electric charge of the fermion.

1.4.2 QCD: Quantum Chromo-Dynamics

QCD is the strong force equivalent of QED and can be formulated in an analogous way by requiring gaugeinvariance. Beginning with a free Lagrangian denoted by:

L0 = i ̄j�µ@µ j �m ̄j j (1.12)

where j describes the quark field with color index j=1,2,3 (from now onward the j is dropped). However,we are no longer looking at the U(1) gauge group, strong force is instead formulated on the non-abelianSU(3)c group so the local transformation is given by:


! 0 = ei✓a(x)Ta (1.13)

where ✓a(x) is the space-time dependent phase and Ta are the eight Gell-Mann matrices. A covariantderivative which maintains the invariance of the theory can be constructed to compensate the local phasetransformation of :

Dµ = @µ + igstrongTaGaµ (1.14)

where Gaµ corresponds to 8 new gauge fields which mediate the strong interaction via gluon exchange.

Due to SU(3)c been an non-abelian group the gauge field now transforms as:

Ga0

µ = Gaµ =

1

@µ✓a � fabc✓bG

cµ (1.15)

where fabc are the structure constants of the group defined by the commutation relation of SU(3) gener-ators:

[Ta, Tb] = fabcTc (1.16)

The complete Lagrangian density for QCD may be written as:

LQCD = i ̄j�µ@µ j �m ̄j j � gs ̄�

µTaGaµ � 1

4Ga

µ⌫Gµ⌫a (1.17)

where the tensor field is given by:

Gaµ⌫ = @µG

a⌫ � @⌫G

aµ � gstrongfabcG

bµG

c⌫ (1.18)

The last term does not appear in QED and arises from the non-abelian structure of the SU(3)c groupwhere the generators are matrices which do not commute. The third term of the QCD Lagrangian isinterpreted as gluon field Ga

µ interacting with the quarks. The quadratic term GµG⌫ describes how gluonsself-interact. Such self-interaction accounts for the divergent nature of the strong force which results in onlyconfined states of quarks being visible in nature.

1.4.3 Unifying the EM and Weak Forces: Electroweak Theory

Electroweak theory was originally formulated by Glashow, Weinberg and Salam in the 1960s and unifiesthe electromagnetic and weak interactions. Electroweak theory is formulated under SU(2)c ⇥ U(1)Y gaugeinvariance where Y describes the weak hyper-charge and is related to EM charge(Q) and weak Isospin (I3)by the following relation:

Q = I3 +Y

2(1.19)

The covariant derivative which makes the Lagrangian invariant under SU(2)c⇥U(1)Y gauge transforma-tion takes the form:

Dµ = @µ + ig⌧

2Wµ + i

1

2g0Y Bµ (1.20)

This achieves the required local invariance when ⌧ § are the generators of SU(2) and Wµ and Bµ are thegauge fields associated with SU(2) i.e fields associated with the weak and electromagnetic forces respectively.The electro-weak field tensors are given by:

Waµ⌫ = @µ Wa

⌫ � @⌫ Wµ � g✏abc Wbµ Wc

⌫ (1.21)

Bµ⌫ = @µB⌫ � @⌫Bµ (1.22)

This leads to an Electroweak Lagrangian density of the form:

LEW = iL�̄µ(@µ + ig⌧

2Wµ + i

1

2g0Y Bµ)L+ iR�̄µ(@µ + i

1

2g0Y Bµ)R� 1

4Wµ⌫ W⌫µ � 1

4Bµ⌫B

µ⌫ (1.23)

where L and R describe left handed doublets and right handed singlets of fermionic fields.The use of left handed doublets and right handed singlets accounts for the fact that the weak force

violating parity meaning only left-handed chirality fermion states interact with the SU(2) gauge field.


Wµ = (W 1µ ,W

2µ ,W

3µ) is a three component vector field. The physical electroweak fields associated with

the W±, Z0 and � are therefore defined as a combination of these four EM and weak gauge fields:

W± =

r1

2(W 1

µ ⌥ iW 2µ) (1.24)

Zµ = Bµsin✓w �W 3µcos✓w (1.25)

Aµ = Bµcos✓w +W 3µsin✓w (1.26)

where ✓w describes the Weinberg angle, defined as tan�1( g0

g ).

1.5 Spontaneous Symmetry Breaking and The Higgs Mechanism

In the previous formulation all gauge bosons appear massless since a mass term of the form an integer-spinfield of the form m2AµA

µ is not invariant under the SU(2)L⇥U(1)Y gauge transformation. However, It hasbeen experimentally observed that the weak gauge bosons posses mass, therefore, to allow a massless photonthe symmetry of the electroweak theory needs to be broken. The Higgs Mechanism finds away to introducespontaneous symmetry breaking without destroying the gauge invariance of the electroweak theory and thusprovides a way for bosons to acquire mass by requiring that the symmetry of a system be spontaneouslybroken when the vacuum state of the system is not invariant under local gauge transformation but theLagrangian density is.[1]

This may be accomplished by introducing a scalar field, ‘The Higgs field’, defined as a SU(2) doublet withtwo complex scalar terms:

� =

✓�+

�0

◆=

✓�1 + i�2�3 + i�4

◆(1.27)

The Lagrangian density for this field is given as:

LHiggs = (Dµ�)†(Dµ�)� VHiggs(�

†�) (1.28)

where Dµ is the electroweak covariant derivative described in equation 1.20 and V is the vacuum potentialwhich we assume has the form:

VHiggs = µ2�†�+ �(�†�)2 (1.29)

By requiring that µ2 < 0 and � > 0 the symmetry is no longer unique but takes the form of a continuousring in the complex plane.The vacuum expectation value for � will occur at a potential minimum i.e. when@V

@�†� = 0 and is given by:

�vacuum =1p2

✓0

v + h(x)

◆, v =

r�µ2

�(1.30)

where v is the vacuum expectation value(vev) and h(x)is the Higgs field expressed as a quantum fluctuationabout this vev. This is zero for the charged component and therefore preserves EM symmetry but non-zerofor the neutral component and therefore breaks electroweak gauge invariance this may be referred to asspontaneous symmetry breaking.

If the expressions in 1.20,1.29 and 1.30 are substituted into the Higgs Lagrangian density and the covariantderivative expanded the Higgs Lagrangian density after symmetry breaking is obtained:

@µh@µh+

1

8(v + h)2g2(W 1

µ + iW 2µ)(W

1µ � iW 2µ) +1

8(v + h)2(g0Bµ � gW 3

µ � gW 3µ) (1.31)

= @µh@µh�2µ2h2+h.o.t+

g2µ2

4�W+µW�

µ � g2µ

2p�hW+µW�

µ +g2µ2

8�cos✓2wZ0µZ0

µ�g2µ

4p�cos✓2w

hZ0µZ0µ+

g2

8cos✓2wh2Z0µZ0

µ

(1.32)

Here, the first term describes the free Higgs boson field, the �2µ2h2, g2µ2

4� W+µW�

µ and g2µ2

8�cos✓2w

Z0µZ0µ

terms describe the masses of the H0,W± and Z0 fields respectively. The higher order terms (h.o.t) predict 3and 4 point Higgs boson self-interactions and the remaining terms describe the interaction between the Higgsand weak bosons. Since there is no photon mass term in the Lagrangian this allows the photon to remainmassless while the weak bosons now have mass.


A consequence of the Higgs mechanism and the Higgs field is the manifestation of Higgs quanta, thisexcitation is known as the Higgs boson and is the final missing particle of standard model.

The Higgs mass is an unknown, it must be less than 1TeV due to measurements of the WW scatteringcross section. To cancel a mass of 1TeV the bare Higgs mass would have to be 1019GeV/c2, which is knownas the fine tuning problem. To solve this various SUSY theories have been derived in which each boson hasa corresponding fermion of equal mass and quantum numbers (except spin), but no such superpartners haveyet been found.

1.6 Higgs Production at the LHC

This project aims to analyze the Z! ⌧⌧ channel using 2011A CMS data looking for an excess of eventswhich could suggest the presence of a Higgs particle produced via Vector Boson Fusion VBF(qq!Hqq). Ascan be seen in the Feynmann diagram in figure 1.3 vector boson fusion is so called as vector bosons formfrom the partons of the protons in the LHC beam; these then fuse to form the Higgs. The remnants of thequarks hadronize into two jets in the forward part of the detector - these jets can be used as indicators thata VBF event has occurred. VBF production, despite having a cross section at least an order of magnitudelower than gluon fusion in the low Higgs mass range i.e. below mH = 2mw (see Figure 1.1), is a promisingchannel for Higgs discovery due the two outgoing jets which provide a characteristic signature for Higgsproduction. VBF jets are mainly in the forward direction with hadronic activity being heavily suppressed inthe central region due to the lack of colour exchange between the leading quark jets. Therefore, VBF canbe distinguished from background QCD by looking for a large rapidity gap between jets along with use of a‘central jet veto’.

Figure 1.1: Relative cross sections for Higgs productionas functions of Higgs mass [1]

Figure 1.2: Relative Branching Ratios of the Higgs asfunctions of Higgs mass [1]

This Higgs particle can only be detected at CMS by identifying its decay products, figure 1.2 shows therelative branching ratios for Higgs decays. In the low mass range, the decay width of any fermionic decayof the Higgs is proportional to the fermions mass squared; therefore, the heaviest fermions have the largestbranching fraction. The H !bb channel has the highest branching ratio in this range, however, this channelsu↵ers from large amounts of QCD background and therefore is not the best channel for Higgs discovery. TheH! ⌧⌧ along with the described VBF conditions will allow background from lepton+jet processes arisingfrom W/Z production via QCD to be removed, therefore allowing a relatively clean signature of the Higgs.

Figure 1.3: Feynmann Diagrams of main source of higgs production in the LHC a)gluon fusion b)VBF c)ttfusion d)W/Z associated production [1]

Chapter 2

The CMS Detector Design

2.1 The Large Hadron Collider ( LHC)

The Large Hadron Collider is a 27km circumference proton-proton collider based at CERN, the LHC is cur-rently running at

ps =7 TeV but will eventually run at

ps=14TeV making it the highest energy accelerator

on Earth. The Compact Muon Solenoid (CMS) is one of 2 general purpose detectors at the LHC and itsprimary aim is detection of the Standard Mode Higgs boson.

2.2 CMS Detector

The distinguishing feature of the CMS detector is a 3.8T superconducting solenoid, 6m in internal diameter.Within the volume of this field are a series of sub-detectors, starting nearest to the beam interaction point,these are: the silicon pixel tracker, the silicon strip tracker, the Electromagnetic Calorimeter(ECAL) andthe Hadronic Calorimeter(HCAL). Muon production is detected in gas-ionization detectors embedded in thesteel return yoke, these components will be described in detail later in the chapter.

CMS uses a right-handed co-ordinate system in which the origin is at the nominal interaction point. Thex axis points to the centre of the LHC while the y axis points perpendicular to the LHC plane and the zaxis points along the counterclockwise beam direction. The polar angle is measured from the positive z axisand the azimuthal angle is measured in the xy plane. Pseudo-rapidity is defined as: ⌘ = �ln[tan(✓/2)] and

pT =q(p2x + p2y) where |⌘| is used instead of theta as it is Lorentz invariant.[5]

Figure 2.1: An Overview of the CMS detector atCERN [1])

Figure 2.2: Di↵erent types of particles detected in dif-ferent parts [1]

2.2.1 The Tracker

Within a magnetic field of known strength (3.8T) the momentum of a charged particle may be reconstructedfrom measurements of the radius of its track through this field. The CMS tracking system makes use ofthis to achieve precise measurements of the trajectories and therefore the momentum of charged particles

7

Project Report The CMS Detector Design 8

allowing precise reconstruction of vertices hence the need for high granularity and fast response time. Theinner tracker measures charged particle tracks within the range |⌘| < 2.5.

The tracking system comprises of two trackers: the pixel detector and the silicon strip detector. Thepixel detector is the first detection layer surrounding the beam pipe and consists of 3 concentric cylindricallayers of silicon pixel sensors as well as a pixel end-cap disk placed on each end. A total of 66⇥106 pixels areused across the whole subsystem, this provides high 3D resolution that is ideal for identification of primaryvertices and track seeding. Surrounding this is the silicon strip detector made of silicon micro-strip sensorspositioned in 10 layers of cylindrical barrels and 12 layers in the endcap disks. The barrel modules havedi↵erent sizes and contain di↵erent numbers of strips but the separation is kept at 100 � 200µm to ensuregood hit position resolution. When a charged particle passes through the strip detector electron-hole pairsare created, the silicon is doped with impurities and a p-n diode junction is created which is held with areverse bias so as to e�ciently collect the charge liberated. The electron/hole pairs are read out from thestrip.

The CMS tracker consists of 1440 silicon pixel and 15148 silicon strip detector modules and providesan impact parameter resolution of approximately 15µm and a transverse momentum resolution of about1.5 % for 100 GeV particles [4]. The pixel detector is required close to beam pipe for higher resolution ashere it experiences a high particle flux, further out the occupancy drops meaning the micro-strip detector issu�cient. The performance of the combined system give >95 % reconstruction e�ciency as well as a radialvertex resolution of 20 µm and longitudinal vertex resolution of 100µm for particles of 10 < E < 100GeV[4].

Figure 2.3: Resolution of track parameters for single muons with transverse momenta of 1,10,100GeV: trans-verse momentum resolution (left) and global track reconstruction e�ciency (all tracks) (right) [4]

(right).

Figure 2.1 shows the reconstruction e�ciency as a function of ⌘, the e�ciency is about 99 % up to|⌘| = 1.6. This e�ciency drop is mainly due to the reduced coverage by the pixel forward disks. The trackerprovides coverage up to |⌘| = 2.5. Momentum resolution may be parameterized by:

�pT

pT= apT + 0.5% (2.1)

where a=15 for ⌘ <1.6 and 60 for ⌘ between 1.6 and 2.5. This change in a is due to change in the theradiation length(X0) of material inside the active volume of the tracker which increases from approx. 0.4X0at |⌘| = 0 to 1X0 at |⌘| = 1.6, before decreasing to⇡ 0.6X0 at |⌘| = 2.5 . At a transverse momentumof 100GeV multiple scattering in the tracker material accounts for 20-30 % of the transverse momentumresolution while at lower momentum it is dominated by multiple scattering [4].

2.2.2 The ECAL

Electromagnetic showers occur when there is an exponential increase in particles at high energies. Initially,a high energy photon undergoes pair production, producing an electron-positron pair which in turn radiatea high energy photon. This ‘chain’ will continue over a length scale of X0 which is defined above. Theelectromagnetic calorimeter detects such a shower by placing ionization detectors between sheets of densematerial (lead-tungstate) which will initiate this shower.

The electromagnetic calorimeter is crucial in the reconstruction of photons and electrons from ⌧ decay, inorder to do this accurately the ECAL is required to have both excellent energy resolution and high granularity.CMS has chosen Lead Tungstate as a scintillation material and the ECAL is constructed in two regions: thebarrel at |⌘| < 1.479 and the endcap at 1.479 < |⌘| < 3, there is however, a transition region between 1.444and 1.567. The barrel region comprises crystals of 25.8 X0 and a granularity of ��⇥�⌘= 0.00174⇥0.00174.The endcap region is instrumented with a lead-silicon preshower detector which consists 2 orthogonal stripdetectors with a strip pitch of 1.9mm. On the whole, the ECAL has an energy resolution of > 0.5 % for


unconverted photons of energy greater than 100GeV. The energy resolution is greater than 3 % for the rangeof electron used in this report.[4][5]

The Lead tungstate scintillation material has the required high density and small Moliere radius to providesmall lateral spread in the electromagnetic shower this is crucial in order to distinguish energy deposits fromdi↵erent sources and achieve high position resolution. On average, 90 % of the shower created from a singlephoton can be contained within one crystal. The amount of energy deposited in the ECAL is interpretedthrough scintillation of light which is detected via photo-detectors and read out from the back.

2.2.3 The HCAL

Hadronic showers produce much larger numbers of particles and therefore have a much larger lateral spreadso the hadronic calorimeter(HCAL) does not require the same level of granularity as the ECAL. Hadronicshowers take place over a characteristic length denoted by � (the absorption length) which is significantlylarger than the X0 meaning much more material is required to contain the hadronic shower.

The HCAL comprises of three regions: the hadronic barrel(HB), endcap (HE) and forward(HF) whichprovides coverage up to |⌘|=5.3, this gives a combined depth of 11 absorption lengths. The HB and HEconsist of brass absorber plates interleaved a plastic scintillator. The energy of the shower is measured viaCerenkov light emission from particle interactions with radiation-resistant quartz fibres which are insertedinto the brass plates.

The HCAL provides an energy resolution of 10 % for particles of energy greater than 100GeV [4].

2.2.4 The Muon System

The muon system is placed furthest from the beam as only muons and neutrinos travel to these distanceswithout depositing large amounts of energy. The muon barrel region is covered by drift tubes and the endcapregions by cathode strip chambers. In both regions resistive plate chambers provide additional coordinateand timing information, with a time resolution of 2ns allowing fast trigger decisions to be made. Muons canbe reconstructed in the range |⌘| <2.4, with a typical pT resolution, for the combined tracker and muonsystem, of 1 % for particles of E=100GeV as well as a detector e�ciency of >95%.[4]

2.2.5 Tau Triggers and Reconstruction

The aim of the trigger system is to reduce the data rate from 100TB/s to a more manageable 100-200MB/sby identifying events of interest; the trigger system, consists of the level-1 and High-level triggers, the formerreduces the event rate from 40MHz to 100kHz and the latter reduces this to 100Hz. The e�ciency of thetrigger is > 95%.

Taus have a lifetime of approx 10�13s and therefore are not detected directly in the detector. However,they decay either leptonically or hadronically to known decay products which may be detected. Electrons andmuons from tau decays are expected to be isolated in the detector; muons are reconstructed from informationin the tracker and muon system. On the other hand, electrons are reconstructed by a combination of tracksproduced by the Gaussian Sum Filter algorithm with ECAL clusters [5]. Specific requirements are enforcedto distinguish the electrons from pions which may produce ‘fake electrons’ as well as electrons from othersources such as photon conversions. Particle flow algorithims are used to reconstruct composite objects suchas jets and to measure missing energy.

Hadronic decays of tau leptons lead to hadronic jets, these may be either 1 or 3 prong decays and aretherefore relatively collimated when compared to background QCD, which may contain tens of chargedparticles. At high transverse momentum events the tau lepton is not massive enough to pull decay productsapart hence a relatively narrow shower forms in the HCAL this allows trigger decisions to be made. Also, Tau-jets are usually colour-isolated from the underlying event as a result of the secondary vertex been su�cientlydisplaced, this results in a more confined and therefore isolated jet.

Background may also appear due to electrons or muons ‘faking’ a tau signature. In such cases elec-trons/muons appear as the extreme case of a tau with a single charged hadron which can be reduced bylooking at the E/HCAL signatures in the electron case or HCAL and muon tracking signatures in the muoncase.

One way to search for Tau-jets uses 3x3 calorimeter regions in the L1, each of which has a 4x4 of combinedECAL+HCAL towers. Each region is equipped with a ‘tau-veto-bit’ which is turned ‘on’ if the region hastwo or more active ECAL or HCAL towers, if no bit is set ‘on’ in the nine regions within the window thenthe jet is considered to originate from a tau decay. This takes advantage of the fact that tau hadronic jetsare more collimated than QCD jets.

Tau-jet reconstruction at the HLT uses Particle Flow(PF) techniques. The PF techniques first identifieselectrons and muons and removes their tracks and calorimetric signatures. PF charged hadrons are then


Figure 2.4: A) ID of electrons and Photons and B) IDof Tau jets in L1 trigger [2] Figure 2.5: Reconstruction of tau-jet at HLT [1]

reconstructed by linking the remaining tracks to their corresponding HCAL deposits. First, a leading trackis found within a matching cone around the jet axis with pt > pTm, there must be 1 or 3 tracks whichoriginate from the same vertex and lie within a signal cone around this track. There should be no additionaltracks within an isolation cone around the jet axis.

2.3 Isolation

In order to eliminate leptons with significant numbers of charged hadrons along their track a relative isolationparameter is defined, this help discriminate against the already discussed QCD background. In the followinga analysis particle flow algorithms are used to reconstruct events. The relative isolation parameter may becalculated from the following equation:

Irel =⌃(P charged

T + E�T + Eneutral

T )

P lT

(2.2)

An extra factor of �� was introduced in the 2011A run to account for excess pile-up when compared toprevious runs.It is assumed that the ratio of charged to neutral particles is 2:1 and this is used to predict theneutral particle deposits based on PU particle deposits. The above expression now becomes:

Irel =⌃(P charged

T +max(E�T + Eneutral

T � 0.5EPUT , 0.0))

P lT

(2.3)

2.4 Current Limits and Previous Work

Prior to CMS and ATLAS work to find experimental proof for the existence of the Higgs had been undertakenby LEP as well as the two experiments at the Tevatron: DØ and CDF. LEP was an electron-positroncollider based at CERN in the 1990s; which produced aimed to produce Higgs bosons via quark-anti-quarkannihilation in association with a Z boson with a centre-of-mass energy of 205GeV. Higgs masses below114.5GeV/c2 were excluded by these experiments within a 95 % confidence level meaning that the StandardModel Higgs boson with that mass would yield more evidence than that observed in our data in at least95% of the a set of toy data models. Further information can be found from precision measurements of theW and Z masses which have excluded a mass region above 200GeV/c2. The Tevatron aimed to produceHiggs particles through gluon fusion as well as a smaller number by W,Z Bremsstrahlung (Section 1.6) andhas excluded a region around 150 � 160GeV/c2 at a 95 % confidence level. Figure 2.5 shows the latestcombined results from CMS for all channels under analysis as of 13/12/2011. As can be seen the Higgs hasbeen excluded from 127 to 600 GeV at 95 % confidence level, and 128 to 525 GeV at 99 % confidence level.However, SM Higgs bosons with a mass between 115 GeV and 127 GeV are still possible, this is within theregion been searched for the this particular analysis. There is an excess of events when compared to the SMprediction in this mass region this appears, quite consistently, in five independent channels. This is visible asa small peak over the 2 sigma band in the figure below. This excess is not enough, at this point, to warranta‘discovery’. This excess of events could be a statistical fluctuation in known background processes. Thelarger data samples to be collected in 2012 will reduce the statistical uncertainties, enabling CMS to make aclearer conclusion on the possibility of the existence of a standard model Higgs boson in this mass region. [7]


Figure 2.6: Combined Results from LEP, Tevatron andCMS (as of end of 2011)

Figure 2.7: Combined 2011 and 2010 results for lowmass region

Chapter 3

Software

Once the pre-selection of events and reduction of the data volume is carried out by the online trigger andData Acquisition System (TDAQ) events must be reconstructed and o✏ine analysis must take place. Belowis an outline of the computing techniques used to analyse the data in the following analysis. [8]

3.1 The ROOT Framework

The following analysis of the CMS 2011A data makes use of the data analysis framework ROOT. ROOTwas developed at CERN by Rene Brun and Fons Rademaker in the mid-1990’s to allow for the analysis ofthe huge amounts of data expected from experiments such as the NA49 and later the Large Hadron Colliderexperiments. ROOT is a C++ based object orientated analysis framework which is highly specialiesd for usein High Energy Physics. Thus, since its development ROOT has become an integral part of experimentalparticle physics and the physics community who have built in and added to the original software to createa specific, highly skilled and powerful analysis tool. The ROOT framework provides a set of common toolsfor all CMS analysis . The analysis given in the following chapter was undertaken using ready-collatedntuples but the analysis and plots where created by myself throughout the project using the ROOT libraries.Numbers extracted from ROOT plots will of course have some influence from counting/rounding errors,however, the main source of error will be statistical error in the number of estimated events and will beaccounted for using Poisson statistics. When numbers are used directly from ROOT the quoted error will bePoisson error.

3.2 RooFit

RooFit is a template fitting package used in the following analysis to extrapolate fit statistics and for back-ground analysis. In RooFit the errors provided are statistical only and do not take into account any systemicbias which may be present within the results. Roofit also does not take into account any statistical errorsalready present in the data and may therefore give a systemic under-estimate on a fit.[9]

3.3 LandS

For the final statistical analysis the LandS statistics package is used to extract a cross section the numbersoutput by the package are, of course, subject to statistical error, however, systemic error can be added intothe datacard and is parameterized as nusicence parameters in the underlying algorithms used to calculatethe cross-sectional limits. The final quoted error is a combination of LandS calculation of the statistical erroras well as that resulting from the specified systemic errors.

3.4 Event Generators

In order to provide simulation of possible background e↵ects in the data a number of Monte Carlo simulationswill be used to model: Z+jets, W+jets and tt̄ events*. These are studied under the same ROOT frameworkas the reconstructed CMS data events; such Monte Carlo is often referred to as ‘truth data’ as it avoidsany detector e↵ects and therefore allows e�ciencies etc. of the detector to be calculated. In this analysisMadGraph [10] was used to generate the background models, these were ready provided for the analysis.*These were provided by Mike Cutajar and are listed in Appendix 1.

12

Chapter 4

Results and Analysis

The following analysis begins by looking for the 3 di-lepton decays of the Z boson in the CMS 2011 A data.The reasoning behind this large emphasis on the Z boson decays is to put a very accurate estimate of finalevents resulting from Z ! ⌧⌧ , the predominant source of background in the Higgs di-tau decay channel. Thisestimate will eventually be derived from the Z! ee and µµ data, where lepton universality, and thereforeidentical coupling by each lepton to the gauge boson, results in equal numbers of decays to each of the 3leptons. As the data from all processes in the same CMS run (2011A) is subject to the same conditions it isfrom the data, and not an MC, that this ‘expected’ Z ! ⌧⌧ is taken for the final statistical analysis whichaims to put an upper limit at a 95 % confidence level on �(pp ! H ! ⌧⌧)/�SM .

4.1 Z ! µ+µ� analysis

The first part of the data analysis process is to identify the di-lepton decays of the Z boson, this is done byfinding two oppositely charged, same type leptons within the data and combining their Lorentz vectors; theinvariant mass of the resulting vector is then found and plotted against number of events.

4.1.1 Z Production, Initial and Final State Radiation

Z bosons in CMS are produced by Drell-Yan processes where a quark and anti-quark interact to producethe Z boson. The above method may run into di�culty due to initial and final state radiation. Initialstate radiation, in the form of photon or gluon emission, occurs in any process which involves either chargedor colored particles in the initial state, in the process shown in figure 4.1 this occurs when the incomingquark/anti-quark pair emit a photon/gluon before producing the Z boson. Final state radiation occurs whenthe resulting 2 oppositely charged muons emit radiation, this process will ‘remove’ energy from the sceneand will reduce the calculated Z reconstructed mass resulting in asymmetry in the observed resonance peak.The Feynman diagram in figure 4.1 shows both these processes occurring.

Figure 4.1: Feynmann Diagram of ISR and ISR for Z from quark interactions which decays into 2 muons

These two processes are quantum mechanically very di↵erent, and may be distinguished experimentally.ISR processes result in an invariant mass being found which is larger than the quoted Z mass whereas theFSR processes give a lower than expected invariant mass. The e↵ect of FSR is increased further in thedi-electron channel due to the its inverse dependence on mass, this is discussed in more detail in section 4.3.

4.1.2 Muon Quality Cuts

In order to exclude background processes such as QCD or meson decay a number of kinematic and isolationcuts must be applied to the data and MC, these are summarized in the table below:

13

Project Report Results and Analysis 14

Cut Value Cutflow % reduction

Before Any Cuts 1565188 N/APseudorapidity of muon <2.1 1465961 6.34 %

Transverse Muon Mommentum >20 GeV/c2 969508 31.72 %|dxy| < 0.045cm 932173 2.39 %|dz| < 0.2 cm 919417 0.81 %

Chi Squared < 10 867347 3.33%Muon Matched Stations > 1 780988 5.33%

Muon Hits > 0 0 0Muon Track Hits > 10 749039 2.04 %Muon Pixel Hits >0 724966 1.54 %

Muon Isolation Parameter <0.1 142373 9.12%ALL 582593 37.22% remains

Where |dxy| and |dz| refer to the impact parameters in the transverse and longitudinal directions respec-tively. When these cuts are all enforced the total number of muon events selected is reduced from 1565188events to 582593 events, the majority of the events removed are from the low mass region including resonancepeaks from other particles as well as background resulting from QCD processes and other Z+jets.

To suppress background from decays of other neutral particles muon detected at the outer muon systemshould have a matching track in the inner detector; this inner detector track should have created at least10 track hits because the short lifetime of the Z boson leads to a decay close to the primary vertex and theoutgoing tracks pass the entire track detector. The more the muon interacts with the inner tracker, as wellas the outer muon system, the more precise the track measurement will be. To reject poorly reconstructedcandidates every track should have at least 1 hit in the muon system and more than ten hits in the innertracker. These cuts can be seen to reduce particle number by 2.54 %.

As the track of a muon is determined from a fit to the hits in the inner tracking detector and the muonchambers, the Chi-squared of this fit can also be used to judge the reconstruction quality of the muon trackand should not exceed 10. Figure 4.2 shows how the mass reconstruction looks with this cut applied. Thereis no overall shape change, a small reduction in the 10 GeV/c2 peak is visible as well as an even smallerpercentage change in the 3GeV/c2 peak.

Figure 4.2: Overall shape of the di-muon data plotwhen only muons with Chi squared >10 are plotted

Figure 4.3: Overall shape of data when just Pseudo-rapidity of muon < 2.1 applied-little change in shapeseen

Muons with pseudorapidity >2.1 (tracker acceptance) are disregarded; this is because, as seen in figure2.2 the reconstruction e�ciency significantly decreases outside this range, this cut therefore ensures a goodquality Z peak can be seen. This cut reduces total number but there is little change to the overall shape ofthe distribution. A plot for this cut alone is shown in figure 4.3.

The muons are required to have a relative isolation (Section 2.3) < 0.1; this improves the reconstructionquality by decreasing QCD background and shows one of the greatest individual decrease in number ofparticles. Figure 4.4 shows the data when the isolation parameter alone in applied. It is clear that the largebump at low mass has almost disappeared, meaning, as expected, the majority of hits here came from QCDbackground.

The most important kinematic cut is the muon momentum cut, muons resulting from Z decay will haverelatively high energies and to reduce low energy muon background it is required that selected muons havetransverse momentum > 20GeV/c2. The results for this cut alone are shown in figure 4.5. It is clear thatthere is a large reduction in total particle number as well as overall shape. The smaller resonance peaks at


0-1.5, 3 and 10 GeV/c2 have been reduced significantly as well as the larger spread of background resultingfrom QCD processes. In total a reduction of around 32 % is observed by applying this momentum cut.

Figure 4.4: Overall shape of data when just Isolation<0.1 cut applied-QCD removed

Figure 4.5: Overall shape of the di-muon data plotwhen only muons with > 20GeV/c2 plotted

Figure 4.6 shows both the real and generated data with all kinematic cuts and isolation applied. Here anenergy shift of 0.16% has been applied to the MC, this alters the shape and ensures consistency.

A clear resonance peak is now observed with a mean of 90.839± 0.41GeV/c2 which is slightly lower thanthe PDG quoted value of 91.1876 ± 0.0021GeV/c2. This lowering may be a result of missing final stateradiation. The Z resonance peak may be parameterised by a Breit-Wigner function (Figure 4.7) defined by:

f(E) =k

(E2 �M2) +M2� 2(4.1)

where E=energy, M=mean mass value and �=decay width and k = 2p

2M��

⇡p

M2+�with � =

pM2(M2 + � 2

The reconstructed resonance peak has a relatively large width, quoted as 3.9 ± 0.008 GeV by ROOT.Both stable and unstable (including the Z resonance) particles can be characterized by their spin-parity andcentre-of-mass energy s. In the case of a stable particle this value is real,s =m2 � 0, in the case of quasi-stableparticles and resonances such as that for the Z boson s has complex values which may be parameterized bythe two real values “mass” ,m, (the mean of the resonance peak) and “width”� (the width of the resonancepeak), these may be combined in the form s = (m� i�

2 )2 among other ways. [12]A ratio of these resonance characterization parameters can be defined as (�/m), this spans a wide range

of values for di↵erent decaying particles, for the experimental data above this parameter is found to be0.0430± 0.0001. from the Breit-Wigner fit below, this is relatively large compared with much smaller valuesfor other electroweakly decaying particles e.g. (�/m)⇡0 ⇠ 10�7, (�/m)⇡± ⇠ 10�15 and (�/m)K0 ⇠ 10�14

[12].

Figure 4.6: Inclusive events in the Z to di-muon decaychannel along with Monte Carlo generated events

Figure 4.7: Breit-Wigner fit to the final data fordi-muon mass. Mean:90.839+/-0.004 Sigma:3.908+/-0.008

4.1.3 Background and Other Particles

It is clear from figure 4.2-4.5 that as well as having large amounts of QCD background there are 3 otherregions which show significant resonance peaks, although much lower in amplitude than the main Z peak,


it is believed that these are other particles and must be removed from the final sample. The smaller peakat 9.450 ± 0.002GeV/c2 makes up around 0.53 % of the background (i.e. that removed by above cuts) andcorresponds to the di-muon decay of the Upsilon Meson, the bound state of a bottom/anti-bottom quark,which has a quoted mass of 9.46GeV/c2. This particular meson decay has been previously analyzed at theCMS detector and is made up of three resonance peaks for the 1s, 2s, and 3s states, the first being thestrongest and resembling that shown in figure 4.8, much smaller peaks should be observed for the 2s and 3sstates but in the data these are clouded by other background e↵ects and are therefore not visible.

Figure 4.8: Upsilon particle reconstructed from datawith mean around 9.448+/-0.002 (RooFit)

Figure 4.9: J/psi particle reconstructed from data withmean around 3.0890 +/-0.0006 (RooFit)

The J/Psi meson, with quoted mass of 3.096GeV/c2, is responsible for the strong resonance centered on3.090± 0.0006GeV/c2 which spans 3.02 -3.15GeV/c2; this is shown in figure 4.9 and makes up 3.63 % of theremoved background.

The 3rd region, at relatively low mass, is due to 3 specific di-muon decays namely that from the: ⇢ meson(rest mass 0.775GeV/c22), ! meson (rest mass 0.782GeV/c2) and � meson (rest mass 1.018GeV/c2). Thefirst two can be seen by the distribution in figure 4.10 with a mean of 0.7795± 0.002GeV/c2 and the latterin figure 4.11 where the data peaks at 1.023± 0.003GeV/c2.

Figure 4.10: rho/omega particles reconstructed fromdata with mean around 0.7795 ± 0.002 (RooFit)

Figure 4.11: phi particle reconstructed from data withmean around 1.023 ±0.003 (RooFit)

In total only 4.86 % of the background in the di-muon channel is believed to come from other particles.The majority of these particles are removed by the transverse momentum cut but a small fraction will remainwithin the allowed parameters and remain, helping lower the experimental mean of the final data.

4.2 Jets

As described in the introduction, the aim of this analysis is to search for a VBF Higgs. In order to do thisthe number of VBF events in each channel must be found. VBF processes have the characteristics of havingtwo outgoing jets at high rapidity gap and without a central jet. This will be used in the following analysisto find the number of dimuon, dielectron and di-tau VBF events within the data.

4.2.1 Jets Selection and VBF Criteria

In order to suppress background from ‘fake-jet’ candidates which may result from other processes withinthe detector a number of cuts are placed on the jet candidates within all three di-lepton channels, these are


summarized below. Such ‘fake-jets’ may originate, primarily, from the promotion of low ET jets, comingfrom hard parton interactions, to higher energy or through the close impact of either a particle or low ET

jet from pileup interactions. Fake jets can also be formed in the calorimeter when particles from di↵erentinteractions impact in close proximity. Electron can also form fake jets [14]. There is no generic solution foridentifying whether a jet is fake or not, but usually fake jets have low transverse momentum, are found nearthe HE/HF boundary and have a broader transverse profile than expected.

Cut Value

mµµ > 50GeV/c2

Pseudo-rapidity of jet <4.5Transverse Jet Momentum >30 GeV/c2

Jet Beta -JetMuDeltaR(� R1 and 2) >0.5Mass of Dijet >400Delta|⌘| jj >4Opposite Hemispheres TrueCentral Jet Veto True

The Beta cut is ignored here to allow us to see both forward and backward jets. The central jet vetorequirement ensures there is no jets between the two selected jets. The last four cuts here help identify VBFjets and will be discussed later.

Two overlap parameters �R1 and �R2 are created, these are defined as the square root of the sum of thesquares of the di↵erences in muon and jet pseudo-rapidity and �; it is required that �R 1 and 2 >0.5. Onlyjets which have transverse momentum > 30 GeV/c2 are selected, this is essential for pile-up suppression andthe removal of electronic noise as well as other sources of fake jets. This momentum cut is very e↵ective atremoving low momentum ‘fake-jets’ reducing the number of selected jets by 39%. In addition, jets must have|⌘| < 4.5 as well as |⌘| > 2.4, corresponding to HCAL coverage . It is also necessary to ensure the jets arenot co-linear with the muons.

Figure 4.12: Di↵erence in pseudorapidity of the twooutgoing jets pre-VBF

Figure 4.13: Dijet Invariant Mass in Muon Channelpre-VBf selection

Figure 4.13 shows the distribution of reconstructed dijet mass for jets in the muon channel prior toVBF selection, it is clear that the mass of the jets reaches much higher than the Z mass ranging as far as1500GeV/c2 but with maximum number of jets around 95GeV/c2. Figures 4.12 and 4.13 show the spread ofjets in terms of mass and �⌘, in both cases good agreement with MC is seen. It is visible that the majorityof jets occur at low mass and separation-these are tagged as fakes and are removed.

4.2.2 VBF cutflow

As with the muon discussion it is helpful to look at each cut separately to see how the VBF selection criteriaa↵ect the momentum and rapidity distributions of the reconstructed Z boson. First we apply mµµ >50 with2 jets of pt > 30, figures 4.14 and 4.18 are produced in this case. Next we add the VBF criteria that theseparation �⌘jj > 4 this gives figures 4.15 and 4.19, the central jet veto cut is then added producing figures4.16 and 4.20. Finally the condition that mjj > 400GeV/c2 is added producing figures 4.17 and 4.21. Ascan be see the shape of the momentum and rapidity distribution gets more and more disrupted as more andmore events are cut out. In the first instance the MC and data are reasonably well aligned,however, in thefinal VBF selection these appear much less correlated. However, in the majority of cases the data is withinerrors of the MC. This di↵erence in shape is due to di↵erences in number of events. The MC has been scaled


by a numerical factor of 0.1855 which is equivalent to the data luminosity/luminosity of the MC. The MCtherefore has the scaled down shape which would be produced if there where 5 x more events than in thedata. As the data has so few events statistical uncertainties result in the types of fluctuations seen in thefinal VBF plots for the data. As the luminosity of the LHC increases the shape of the data should matchthat of the MC much better but for now this matching in errors is su�cient.

Figure 4.14: Pt of the reconstructed Z particle whenmµµ >50 and 2 jet cuts are applied.

Figure 4.15: Pt of reconstructed Z particle whenmµµ >50, 2 jets and delta eta >4 cuts are enforced

Figure 4.16: Pt of the reconstructed Z particle whenmµµ >50, 2 jet, delta eta and central jet veto cutsenforced

Figure 4.17: Pt of the reconstructed Z particle whenmµµ >50, 2 jet, delta eta, central jet veto and jet masscuts enforced

Figure 4.18: Eta of the reconstructed Z particle whenmµµ >50 and 2 jet cuts are applied.

Figure 4.19: Eta of reconstructed Z particle whenmµµ >50, 2 jets and delta eta >4 cuts are enforced

After all cuts are applied only 382 ± 19.5 (stat.) ± 11.5 (sys.) ±15.3 (lumi) data events remain and431.44 ± 21 (stat) ± 0.69 (momentum shift) ± 12.9 (sys.) ± 17 (lumi) MC events. The statistical error iscalculated from Poisson statistics and the systemic errors are a combination of errors in separation of pile up(0.5%) , trigger errors (2 %) and background e↵ects (0.5%) . Systemic and luminosity (4 %) uncertaintiesaccount for a total systemic uncertainty of 7 % these are discussed in sections 4.3.1 and 4.3.2 . The quotedmomentum shift accounts for 0.16 % and is applied as a correction to the MC to account for a bias whichwas placed on the MC. This ensures that the shapes of the data and MC align. A 3% trigger shift is alsoapplied to the MC and is discussed in Section 4.3.1.


Figure 4.20: Eta of the reconstructed Z particle whenmµµ >50, 2 jet, delta eta and central jet veto cutsenforced

Figure 4.21: Eta of the reconstructed Z particle whenmµµ >50, 2 jet, delta eta, central jet veto and jet masscuts enforced

The table below gives a break-down of the number of events remaining after each VBF cut.

Cut Data Events remaining (stat.)(sys)(lumi) MC Events remaining (stat)(sys)(mom)(lumi)

Muon Selection 582593 ± 800 ± 17468 ± 23424 563293 ± 751 ±16898± 901 ± 22532Jet Selection 22200 ± 150 ±666 ± 888 22910.7± 15.1 ± 687 ± 36.7±916Delta Eta>4 796 ± 28 ± 424 ± 32 750±25.6 ±22.5 ±1.2 ±30

CJV 689 ± 30 ± 21 ± 28 722.812±26.9 ± 21.7 ± 1.16±28.9mjj > 400GeV 385 ± 19.5± 11.5 ±15 .3 431.44± 21 ± 12.9 ± 0.69 ±17

Figure 4.22: VBF events in the Z to di-muon decay channel along with Monte Carlo generated events

4.3 Z ! e+e� analysis

Similar analysis may be done for the Z! ee decay, this occurs in a similar way to that for the di-muon decayand results in the distribution of invariant masses as shown in figure 4.23. This is with isolation or kinematiccuts enforced on the data as given in the table below but without VBF cuts.

Cut Value

Transverse Momentum > 20Pseudorapidity < 2.1

|dxy| <0.045cm|dz| < 0.2cm

Isolation (barrel) iso < 0.1Isolation (endcap) iso < 0.3

Nhits <1Delta R <0.1

Not in ECAL gap |⌘| <1.46 and |⌘| >1.558

Electrons are reconstructed by combining tracks produced by the Gaussian Sum Filter algorithm withECAL superclusters. It is necessary to apply cuts to distinguish prompt electrons from charged pions faking


electrons and electrons produced by photon conversions. The main parameters used to reduce the fakeelectron rate are:

• The angular di↵erence (di↵erence in acoplanarity) between the track and the supercluster (��)

• The ratio of hadronic calorimeter (HCAL) to ECAL energy associated with the supercluster (H/E),this must be small as electron would deposit much more energy in the ECAL

• The ECAL shower shape described by the RMS of the energy in the direction within the supercluster(�i⌘i⌘),

In this analysis W985 electron selection is used which splits electrons found in barrel and endcap:

Barrel/Endcap Cut

Barrel H/E <0.04�� <0.06�⌘ < 0.004�i⌘i⌘ < 0.01

Endcap H/E <0.025�� <0.03�⌘ < 0.006�i⌘i⌘ < 0.03

In both regions it is required that ‘Conv’<0.5 this rejects electrons from photon conversion.The resonance peak is fitted with a Breit-Wigner and has a mean of 90. 575 ± 0.006 and sigma 5.25 ±

0.013, this is larger than the quoted di-muon sigma of 3.89 ±0.01, this may be as a result of Bremsstrahlungor increased FSR. Bremsstrahlung radiation is produced when a high energy charged electron deceleratesand is deflected by the electric field from the charged atomic nucleus, this is represented in figure 4.26. Asin the discussion of FSR, this means that the electrons lose energy, as this is then used for determining theinvariant mass of the decaying Z it may result in a slightly lower mass being calculated this will result in abroadened peak in the direction of lower mass. This has greater e↵ect in the electron channel due to a 1

m4

dependence.

Figure 4.23: Inclusive events in the Z to di-electron de-cay channel along with Monte Carlo generated events

Figure 4.24: VBF events in the Z to di-electron decaychannel along with Monte Carlo generated events

In total 462723 ± 680(stat.) ± 27763 (sys) ± 18509 (lumi) inclusive data events and 450120 ± 671 (stat)± 27007 (sys) ± 18005 (lumi) MC inclusive events are observed. These numbers appear to suggest that thedi-electron data is consistant, within errors, with expectation (MC).

The final number of VBF Z ! ee events is found to be 307 ± 17.5(stat.) ± 18.4(sys) ± 12.3 (lumi). Forthe MC the value is found to be 367 ± 19.2 (stat) ± 22 (sys.) ± 0.59 (mom. shift) ±14.7 (lumi.) . Thesystemic calculations are discussed in the following two sections they include pile up e↵ects (1.5 %), triggere↵ects (4%), background e↵ects (0.5 %) and luminosity uncertainties (4 %). These two values are consistentwithin errors and the final VBF distribution, shown in figure 4.24 shows reasonable shape consistency withthe discrepancies being due to the systemic uncertainties (error bars are purely stat.).

4.3.1 Correction Factors

In order to compare the selected events from both MC and data a number of correction factors where applied:


Figure 4.25: Di-electron results fitted to a Breit-Wigner function with mean 90. 575 ± 0.006

Figure 4.26: Diagram representation of bremstrahlungradiation [15]

• Momentum Shift-Applied to muon MC to correct a bias which introduced calibration problems in therelative MC and data shapes. This was accounted for within the code for the inclusive result and isquoted as an error for the VBF case. The shift is small and is estimated to be - 0.16 %

• PU corrections-As the Monte Carlo samples contain a flat PU distribution an additional weight is ap-plied to fit the distribution observed in data [16]. This re-weighting is done by producing a distributionof the number of reconstructed vertices for both the data and MC. Both histograms are then normalizedto unity and an event weight is found to be the ratio of data/MC for each bin.

• Trigger Shift-In the above section the MC is scaled by 3% relative to the data to account di↵erencesin the trigger e�ciencies which were measured for leptons that are spatially matched to the triggerobjects. However, in the data used the leptons were accepted even if they are in a di↵erent part of thedetector to the lepton reconstructed at trigger level.

4.3.2 Calculation of E�ciency and Acceptances for the di-electron and di-muoncases

The data detection will not be 100 % e�cient at identifying, isolating, reconstructing and even triggeringand therefore all the data in the above discussion is open to systemic error from such sources. Appendix A.3lists the e�ciencies and correction factors used for ID and trigger. A selection e�ciency can be calculated

by finding the ratio: NMC

selected

NMC

Total

. An acceptance may also be calculated by finding the the fraction of Z events

falling within the pt and eta cuts, this gives a total e�ciency( acceptance x sel. e↵.) of 0.187 in the di-electroncase and 0.263 for the di- muon case. These are used in the following cross-section calculations.

4.3.3 Observed di-electron and di-muon Cross-sections

The cross-section is found by dividing the number of observed events (factoring in the e�ciency and ac-ceptance) by the integrated luminosity which is quoted as 2094 pb�1. For the di-muon case an inclusivecross-section of 1055 ± 32 (stat) ± 32 (sys.) ± 42 (lumi) pb and for the di-electron case an inclusive cross-section of 1022 ± 32 (stat.) ± 61 (sys.) ± 41 (lumi.)is found. These are found to be within 1� of each otheri.e. they are consistent within their respective errors as expected by lepton universality. In the VBF case307 ± 17.5(stat.) ± 18.4(sys) ± 12.3 (lumi) di-electron and 382 ± 19.5 (stat.) ± 11.5 (sys.) ±15.3 (lumi)di-muon events are found. These are numerically consistent when there respective e�ciencies are taken intoaccount, again as to be expected. The errors quoted here are Poisson statistical error and systemic errorwhich results from luminosity (4%) as well as trigger (2% for di muon case and 4% in the di-electron case),pile-up e↵ects (0.5% in di-muon case and 1.5% in the electron case) these are all justified in [17]. In addition,an uncertainty due background contributions is calculated to be 0.5% in both cases. This results in a totalsystemic uncertainty in the di-muon case of 7% and in the di-electron case 10%.

4.4 Z ! ⌧+⌧� analysis

The case for Z ! ⌧+⌧� is much more complicated as due to the short lifetime of the ⌧ only the decayproducts are visible in the detector. Therefore, before finding the invariant mass of the Z boson the individual⌧ decays must be reconstructed. The tau lepton decays both leptonically i.e. to e or µ particles and there


corresponding neutrinos or hadronically i.e. to mesons which appear as jets of quarks and gluons; the tablebelow summarizes these decays:

Decay Mode Branching Fraction (%) Leptonic, Hadronic or Semi?

⌧� ! µ�⌫µ⌫̄⌧ 17.4 Purely Leptonic⌧� ! e�⌫̄e⌫⌧ 17.9 Purely Leptonic⌧� ! ⇡�⌫⌧ 10.9 Hadronic (1-prong)⌧� ! ⇡�⌫⌧⇡

0 25.5 Hadronic (1- prong)⌧� ! ⇡�⌫⌧⇡

0⇡0 9.3 Hadronic (1-prong)⌧� ! ⇡�⌫⌧⇡

0⇡0⇡0 1.1 Hadronic (1-prong)⌧� ! K�⌫⌧ 0.7 Hadronic (1-prong)⌧� ! K�⇡0⌫⌧ 0.5 Hadronic (1-prong)⌧� ! ⇡�⇡+⇡�⌫⌧ 9.3 Hadronic (3-prong)⌧� ! ⇡�⇡+⇡�⌫⌧⇡

0 4.8 Hadronic (3-prong)other 1.4 -

With corresponding expressions for ⌧+. This results in decays of the Z ! ⌧+⌧� ! ⌧hadµ, ⌧hade, ⌧had⌧had ,ee,µµ or eµ, with neutrinos left out. The overall branching fraction to hadronic events is ⇡ 65% (3times that to leptons) due to there being 3 colours of each quark. Hadronic decays may be 1 prong or3 prong, both create very collimated jets in comparison to background QCD jets. This helps the triggersystem make accurate conclusions over which jets come from hadronic tau decays. The following analysisconcentrates on the use of the semi-leptonic decays namely: ⌧hadµ and ⌧hade as despite having the largestindividual branching fraction the hadronic decay has large QCD background and su↵ers twice as much fromine�ciencies in separating this from the tau signal.

Figure 4.27: Feynmann Diagrams for e⌧had and µ⌧had decays [6]

4.4.1 Kinematic Selection and Hadronic Tau Ideintification

The µ⌧had and e⌧had channels will have similar kinematic selection criteria. The basic kinematic requirementis that an event contains only one lepton with pT > 15 GeV which is, in the electron case, located in theECAL or in the muon case, in the muon system. In addition, each event must have one PF tau candidatewith pT > 20GeV, |⌘| < 2.3 and |dz| < 0.2cm. It is also required that the taus do not fall in the ECAL gapdefined as 1.442 < |⌘| < 1.566. Electron must also pass the WP80 as well as ID and conversion rejection cuts(Section 4.3), such cuts are not enforced on the muons as global and track quality cuts have already beenpassed. All the cuts documented in sections (Section 4.1.2) and (Section 4.3) still apply. [6]

For Tau identification it is required that a valid decay mode is found by the particle flow algorithm anddiscrimination is performed against muons and electrons as discussed in Section 2.2.5 (this is done priorto the analysis). In addition lepton-rejection is enhanced by ensuring that E+H

plead

> 0.2 which rejects both

electrons and muons faking a tau signal. Di-candidates are made with a minimum overlap (� R) of 0.2.Further muon and electron rejection ensures that no muons and electrons are included within the isolationcone.

Loose Tau Isolation ensures that no neutral hadrons or photons of ET >1GeV or charged hadrons withET > 1.5GeV are present:

ITauPFrel =

⌃pT

>1GeVh0 + ⌃p

T

>1GeV� + ⌃pT>1.5GeV

h±

pleptonT

< 0.5 (4.2)

Further QCD discrimination is performed by ensuring that pleading >5GeV, this is done prior to theanalysis.


The remaining fraction of events will still have large amounts of Z ! ll background. To reduce this a“loose” lepton criteria is created which requires a candidate to have pT > 10GeV and |⌘| < 2.4 and in theelectron case passing WP95 ID . Events containing two oppositely signed ‘loose’ leptons are rejected.

All oppositely charged lepton-tau pairs passing these criteria are then constructed. To discriminate againstbackground from W decays it is required that MT (l, E

missingT ) < 40GeV/c2 and P⇣ = Pmis

⇣ -1.5P vis⇣ > �20,

these are discussed in detail below.

4.4.2 ⌧had + µ Event Reconstruction and Background analysis

Figure 4.30 shows the invariant mass for reconstructed ⌧µ for both real data and generated data for back-ground processes namely:QCD, Wjets (W ! l⌫l, W! ⌧⌫⌧+jets) and tt̄ events. The table below documentsthe cut-flow as each kinematic and isolation cuts is applied to the data and MC backgrounds.

Cut Data W+jets tt̄jets

Kinematic Cuts (as given above) 85612 15705 1750Relative Isolation < 0.1 46610 27387 1767

� R(mu, tau)<0.2 46580 27344 1784Oppositely charged 35429 20948 1476

Pzeta - 1.5*Pzetavis > �20 22356 3395 678Transverse Mass (mu,MET) < 40GeV/c2 17994 2679 170

VBF cuts (as given above) 23 4.11 1.88

The relative isolation cut is used to reduce the QCD background, this will be discussed in more detail

later. The transverse mass is calculated asq

E2t (mu,MET )� (P 2

x (mu,MET ) + P 2y (mu,MET )) where

MET describes missing transverse energy i.e. that taken by the neutrinos. This cut, as will be shown inthe control plots below, is used to remove large amounts of W+jet background, but as the table suggests,not all of it. As can be seen in figure 4.28 in real tau decays the outgoing neutrinos tend to be collinear tooutgoing tau products, this is not the case in tt̄ and W+jet processes. In the case of the µ⌧had channel W+jetbackground, W ! l⌫l, can fake the Z decay where the isolated muon reconstructed in the event originatesfrom a genuine muon produced in the decay of the W boson, the tau jet on the other hand is termed a‘fake-jet’ and is due to either a quark or gluon jet faking the signature of a hadronic tau decay.

The P⇣ variable was introduced by CDF where the ⇣ axis defines a bisector between the two decayproducts, a P visible

⇣ factor is first found as the projection of the muon and tau-jet momenta onto this axis.

A second variable Pmissing⇣ is defined as the projection of the MET momenta onto this axis. If the products

are from a real decay then these will be collinear whereas in W+jet they will not be. The factor P⇣ in thetable above is the total momenta (MET, mu,tau) projected on this axis. Ensuring that Pmis

⇣ -1.5P vis⇣ > �20

ensures that the these two vectors are in a similar direction and will therefore reduce the number of W+Jetfakes in the final sample.

Figure 4.28: Relative directions of MET and tau variables for real and W+jets processes [18]

This analysis aims to calculate background contributions to the data from reducible background processesspecifically QCD, W+jet and tt̄. These will have relatively big cross sections at the LHC and will thereforegive significant background in the data. The following control plots (figures 4.29-4.32) can be used to look ataccurate ways to extrapolate the relative numbers of these background process, these are unstacked to allowspecific shape analysis.

The signal (i.e. the actual Z decay) is only present in the opposite sign region and therefore the samesign region is purely background events. The background in the SS region is mainly W+jets and QCD, anestimate of which will be discussed in the following section. The opposite sign region has several contributionsfrom QCD, Z ! µµ and W ! µ⌫ as well as the signal. It is clear that at this point there are many moreevents in the data than is expected for pure Z ! ⌧⌧ in both OS and SS regions. From figure 4.30 we cansee that in the opposite sign case, below a transverse mass of 40 GeV/c2 the data follows a similar shapedfall of to the Z+Jets MC but is broadened due to increasing W+Jet contributions as well as QCD e↵ects.After MT=40 the data begins to become more consistent with the MC for W+Jet. A side-band region may


Figure 4.29: Transverse Mass distribution in theµ⌧hadchannel Figure 4.30: PZeta Distribution in µ⌧had channel

Figure 4.31: Transverse Mass distribution in the µ⌧hadchannel for same sign region

Figure 4.32: Invariant Mass plot in W+Jet control re-gion for SS:OS (3:1)(from data)

be defined as MT > 80GeV/c2 where it is assumed that W+Jet background dominates. A similar conclusioncan be made from figure 4.31, before P⇣ < �20 the data has reasonable consistency with the Z! ⌧⌧ MC,with slight di↵erences due to the described backgrounds. After this point the data becomes consistent withthe W+Jet MC and it can be assumed by P⇣ < �40 that anything remaining is W+Jet background. Thisregion is defined as the W+jet control region. One can also define a Z ! ll control region in the 80-110 GeVmass window. This will be estimated numerically for the µ⌧ case and has much smaller e↵ect.

4.4.3 Method of Background Estimation

For all of the stated backgrounds the background is not taken directly from the MC but is extrapolatedfrom the data using defind control regions to calculate an e�ciency factor (✏ = NselectedMC/N controlMC)and using Ndata = ✏Ndatacontrol to get an estimate of background contribution to data. Background is nottaken directly from MC as although these are good first order approximations they are unsatisfactory dueto uncertainties in the PDF as well as radiation simulation and detector response.[6]

4.4.4 W+jets background in µ⌧had Channel

As described in the above section, it is expected that a large majority of W+jet events will be removed bythe requirement that transverse mass < 40GeV/c2 along with the P⇣ cut, however, not all are removed. Inorder for W + jets events to pass the transverse mass cut either the transverse momentum of the tau-jetcandidate, the missing transverse momentum or the angle between the missing momentum and muon mustbe small. In the latter scenario, the angle between the tau-jet and muon must be large.

Using a template derived from the Monte Carlo for the transverse mass distribution of W events thenumber of W events in the data region can be predicted by counting the number of data events in thesideband, the region dominated by W events. This method is described in [19]. From the previous discussionit is clear that the majority of the W+jets occur at high values of transverse mass i.e.MT > 40GeV/c2 andafter MT > 80GeV/c2 there is little contribution from any other background process. An e�ciency factor fcan be defined:


f =

R 400 PW (MT ) dMTR1

80 PW (MT ) dMT, Ndata

MT<40 = (NdataMT>80 �N tt̄

MT>80)f (4.3)

where Pw describes a PDF,which is chosen to be a log-normal function, fitted to the Monte Carlo for theW+jet when no cut is applied. This ratio is found to be 0.7 ± 0.037 where the error is found by varying theplot by its respective errors and recalculating the integral. In addition error is induced due to the fact thefit in figure 4.33 is not exact specifically, an underestimate in the < 40 range is clearly visible. Errors due toRooFit in this region are found to change ±174 events out of at total of 2679 events. An error of ± 200 inthe region > 80 is estimated by varying fit by horizontal error bars for mass between 80-85. The quoted errorin f is calculated through propagation of errors from the described sources. Further error may be induced inthe calculation from RooFit which does not take into account the statistical uncertainties on the templatehistograms. This means that shapes with larger statistical fluctuations get penalized by the fit resulting inan underestimate; this is systemic. [9]

Figure 4.33: Fit template to the transverse mass forW+jet Monte Carlo. Vertical error bars: Poissonstatistics and horizontal: bin width

Figure 4.34: Invariant mass plots for data regions B,Cand D. C and D are considered 100 % pure and C isconsidered 82 % pure

The number of W+jets expected within the data is extrapolated by multiplying the above e�ciency bythe number of data events in the sideband region (after subtracting the expected tt̄ contribution). The valueis found to be 2580±220 for opposite sign events. The errors in these values are due to propagation of Poissonstatistical errors in the values of N as well as that in the factor defined above. The numbers quoted aboveare for inclusive searches, for VBF the number of W+jet events expected in the data is just 4.11 ± 2.03. Inaddition, 741 ± 76 W+Jets are found in the inclusive SS region, a ratio of OS:SS of 3.5:1 as expected.

4.4.5 QCD Background in the µ⌧had Channel

QCD multi-jet processes contain real muon and electrons as well as a ‘fake’ hadronic jet, this has a lowe�ciency but will contribute due to its large cross-section (1000 x Z ! ⌧⌧). QCD will have a considerablecontribution and may be numerically estimated using the ABCD technique described in detail in [20]. Inthis technique the data events are split into 4 regions: A,opposite sign isolated events (those which remainin signal), B, opposite sign non-isolated region, C, same-sign isolated events and D, same sign non-isolatedregion; where the relative isolation is required to be less than 0.1 meaning that B and D are assumed to bepure QCD regions. It is assumed that the ratio of isolated to non-isolated events in opposite and same signregions are equivalent meaning number of QCD events in the final data selection may be calculated from:

n(A) =n(C)n(B)

n(D).f(C) (4.4)

where f(C) describes the purity of region C as is found to be 0.82:

f(C) =N(C)SS

iso �N(W + jets)SSiso �N(otherbackground)SS

iso

N(C)SSiso

(4.5)

Where N(W + jets)SS is taken as 741 and the other backgrounds is mainly tt̄ in the µ⌧had case (80events) but will include �+ jets in the e⌧had case. This gives 3580± 324 QCD events in the signal region.

A similar analysis can be done for the VBF case which has much fewer data events, 5.32 ± 3.3 (stat)events are found in that case out of 23 ± 4.8(stat) total data events.

In figures 4.35 and 4.36 the QCD distribution is modelled on the SS data shape but has been normalisedto have the number of events as calculated here.


4.4.6 t¯t, Di-boson and Z ! l+l� background in the µ⌧had channel

There will also be contributions from other sources such as tt̄ which can fake tau-jets in both the µ⌧had ande⌧had channels but this background is very small in the µ⌧had channel making up around 1 % of the data inboth the OS, where 140 events are found, and SS regions,where 80 events are found. This small contributionis expected as the cross-section is limited by the large top quark mass. This is extrapolated from fits to theMC for this process. In the VBF analysis only 1.88 ± 1.37 OS tt̄ events and 0 SS events are found. Di-bosonbackgrounds (WW and ZZ decays) are very small (expected 33 from MC in OS and SS pre-vbf and 0 in vbfselection) and are combined with the W+Jet MC in the final figures.

There may also be background from other Z+jets processes this provides background from two sources:

• A second Drell-Yan muon faking a hadronic tau, these are OS .

• A recoiling jet faking a tau-jet

This is estimated using the control region around the Z resonance peak (80-110 GeV/c2) when any second-lepton veto is ignored and the number of events in this region is multiplied by a selection e�ciency calculatedfrom ee and µµ data. 1618 events are found in this region of the data, multiplying this by the averagedi-lepton selection e�ciency, 0.225, calculated in section 4.3.2 gives 364 events. This is seen to make up just2 % of the total number of post-selection events.

Non-VBF(stat.) VBF (stat.)

Diboson 33±5.7 0tt̄ 140 ± 12 1.88 ±1.37

Z (other jets/dileptons) 364 ± 19 0W+Jets 2580 ± 220 4.11 ± 2.03QCD 3580 ± 324 5.32 ±3.3

Z ! ⌧⌧ 11025 ± 105 12.99 ±3.60Total Backgrounds 6964 ±392 11.3 ± 4.12

Total MC 17991 ± 406 24.30 ±5.46Data 17994 ± 134 23 ±4.80

Expected S/B 61.3 % 53.5%Expected S/

pB 132 3.86

The errors quoted in the above table are statistical and in most cases are from Poisson statistics, however,in the case of QCD and W+jets statistical errors from various discussed sources are added in quadrature.This is also the case in the background and MC summation rows. The signal to background ratio given heredescribes the ratio between the expected Z ! ⌧⌧ yield and the number of MC events. In the inclusive case 61% of selected events are expected to be signal whereas in the VBF case this is reduced to 53% of events. Thisreduction is not large and the yield of total data and expected S+B events is very close. The final Z ! ⌧⌧inclusive and vbf signals are shown in figures 4.35 and 4.36. It is clear that both shape-wise and numerically(within errors) the MC, when all backgrounds are accounted for, and data are reasonably consistent thissuggests that there is no huge excess indicating other particles are present and the background estimation isaccurate, however, statistical analysis is still needed to put a limit on this conclusion. For the VBF results thetotal number of events is much smaller (23) but the shape remains similar, with the characteristic maximumaround 60. Statistical fluctuations are relatively large due to the small number of events now present. Thereis still a very large fraction of QCD events remaining in this sample, this large fraction can now only bereduced by improving the e�ciency of the tau-jet trigger.

4.4.7 ⌧had+e Event Reconstruction and Background analysis

The W+jet and QCD background in e⌧had channel are estimated as described above and are found to be1254 ± 35.41 and 2438 ± 234 respectively where the errors are derived in a similar way as those for the µ⌧hadcase. In the QCD B and D are defined as having isolation >0.3 which is the isolation required for electronsin the endcap where A and C are still defined as having isolation <0.1 as required for electrons in the barrel.As well as the above described cuts a di-electron veto was added this helped reduce the background fromZ ! ee; there is a larger contribution from this process which is clearly visible around the Z resonance regionin both the data and MC. This is a result of the fact that electrons which have lost some energy due toBremsstrahlung/FSR can fake a tau signature (Section 4.3). As a result shape analysis is used to estimatethe number of Z ! l+l� events may by fitting the peak in the data which is visible around 90GeV/c2 withthe characteristic Breit-Wigner as seen in figure 4.40.


Figure 4.35: MC for Z ! ⌧⌧ along with other back-ground, these are numerically consistent with small de-viations in shape

Figure 4.36: MC for Z+Jet and W+jet and data whichwill include background sources for µ⌧ VBF events

Figure 4.37: pre-VBF invarient mass plot-clear devia-tion from MC -due to large amounts of background

Figure 4.38: VBF invarient mass plot for both dataand MC for Z+jets and other backgrounds

Figure 4.39: Signal for Z ! ⌧⌧ is parameterized as lognormal with statistical errors

Figure 4.40: Fit template to the Z resonance parame-terized by Breit-Wigner with statistical errors

The number of events in the complete Breit-Wigner is found to be 2880 ± 265 by integrating the fit . Thecharacteristic tau-decay is then fitted to a log-normal function using RooFit, this is modeled on the µ⌧hadcase where it was shown that there was little shape contribution from other di-leptons, the number of eventsin the Z resonance region when the log-normal shape is found by integrating the fit in this region. This gives1320 ± 134 events. The di↵erence BW-LogN is the found to be 1560 ±297; this suggests a total of 1560 ±134 Z events which are faking that e+tau signature.

A prominent resonance is clearly visible in the MC too; the number of Z ! ll events there is found inthe same way to be 1382 ± 176 and 354 ±78 QCD events are found in this region.

4.4.8 � +jets Background in the e⌧had Channel

This background contributes to the e⌧had channel only is a result of a photon faking a Z signature. Anestimate of its contribution can be found by defining a control region in which the di↵erence in � betweenthe electron and tau is > 2.5 and where any di-electron cuts are ignored. The control region for this process


must also have |cot(✓e � ✓track)| < 0.05.

Figure 4.41: �� for data and MC backgrounds (� con-trol region)

Figure 4.42: Invarient Mass in the � + jets controlregion

The number of estimated photon+jet events is then:

NSignal = Ncontrol✏ (4.6)

where ✏ described an MC -measured e�ciency for the OS region. This is found to be the ratio of MC +QCD background events in signal region to MC+ QCD background events in control region. ✏OS is found tobe 0.17 ± 0.012 and ✏SS is found to be 0.44 ±0.01, where the error is statistical and found by propagatingstatistical errors. Which results in 3690 ± 262 expected � + jet events expected in the opposite sign dataand 775 ± 128 same sign data events. These are added to the QCD plot in figure 4.37.

The table below summarizes the numbers of events in the e⌧had channel for both VBF and non-VBFprocesses.

Non-VBF (stat.) VBF (stat.)

Di-boson 28±5.29 0tt̄ 79 ± 8.89 0

Z (other jets/dileptons) 1560 ±134 0� + jets 3065 ± 262 0W+Jets 1254 ±35.41 1.42 ±1QCD 2438± 234 4.08 ± 2.02

Z ! ⌧⌧ + Z resonance peak 8216 ± 90.64 -Expected ! ⌧⌧ 6834 ± 198 5.22 ± 2.28

Total Backgrounds 8396 ± 378 5.5 ±2.51Total MC 15258 ± 426 10.72±3.38

Data 15125 ±123 10 ±3.16

Expected S/B 45% 48%Expected S/

pB 55.3 1.59

There is a slight excess in the MC, this is possibly due to an over-estimate in the background calculations,however, numerically the data and MC are consistent within errors when all backgrounds are considered. Inthese results S/B’s of 45-48 % are found, this means that this percentage of total events originate from thetarget Z decay, the cuts enforced on the selected events act to maximize this fraction but, o↵ course, muchbetter background exclusion is needed to get a pure signal. Figures 4.37 and 4.38 show the relative shapes ofthe backgrounds and data for both inclusive and vbf results. In both cases the data is relatively consistentwith the sum of the MC processes suggesting no huge excess resulting from incorrect background analysis orunaccounted for processes. Bin for bin there are some deviations, this could be a result of QCD and �+ jetsestimate where the histogram is modeled on the same-sign data (region C) and scaled. In order to get abetter estimate of shape an MC of the opposite sign QCD and �+ jets regions should be used. There is alsoa larger tail in the VBF case which extends much further for MC than the observed data. This is probablya result of the low luminosity of these reuslts and the fact that such small numbers ( < 1) are expected inthese regions for this luminosity. At increased luminosity the shape should match that of the inclusive resultswith slight alterations due to reduced contributions from QCD.


4.4.9 Systemic, Statistical and Theoretical Uncertainty

All the errors quoted above are statistical and were either obtained from assuming Poisson statistics or viaROOT, however, this does not take into account possible systemic errors which a↵ect the system as a whole.Below is a list of systemic uncertainties:

• Trigger e�ciencies:-The trigger and ID used to correct the MC are listed in appendix 3 and wereobtained from “tag-and-probe” [21]they have small dependence on transverse momentum and rapiditycorresponding to various detectors in CMS.

• Lepton ID e�ciencies:-Ine�ciencies in detection of electron and muon are small (<1%). These arefound using tag-and-probe techniques [29].

• Hadronic tau ID e�ciencies:- These are taken from [21] where data samples are selected using onlythe kinematic cuts as described in the present analysis and background is suppressed. The e�ciency istaken to be a ratio between the number of events that pass the tau ID requirement and the number ofpreselected events. The uncertainty here is 23 %, in terms of number of events this introduces ±5.29into the final µ⌧had VBF data and ±2.3 into the e⌧had final VBF data.

• Lepton Energy Scaling Uncertainties:-The e↵ect of energy scaling uncertainties on the acceptance wascalculated in [21] to be around 1 % based on ECAL resolution in the case of electrons and muon systemresolution in the case of muons.[6]

• Tau energy Scaling Uncertainties:- Found to be 3.2% [21] by taking into account the energies of thereconstructed taus and varying these within their respective uncertainty. After each independent shift,the missing transverse energy is recalculated and the event selection is repeated. The event yield iscompared to the nominal value and the relative di↵erence is quoted as the systematic uncertainty. Thisaccounts for a di↵erence of ±0.81 events in the µ⌧had VBF data and ± 0.35 in the e⌧had VBF data.

• Luminosity Uncertainty:- quoted as 4 % throughout the 2011A run giving di↵erences of ± 0.92 in theµ⌧had VBF data and ± 0.4 in the e⌧had VBF data.

• Theoretical Uncertainty:- induced from the use of MC for background simulations and for Higgs decaysimulations as well as uncertainties due to the inaccuracy of the reconstruction methods used. Thisarises from the uncertainty in the theoretical calculations of cross-sections and simulation of the physics.It is estimated that the error in the VBF Higgs MC will be just 2 % [1] with similar results expectedfor the SM MCs, in the ggH case this becomes 12%. These errors where found by comparing resultsfrom di↵erent generators.

Uncertainty e⌧ µ⌧

Trigger 1 % 0.2%Electron ID 1.3% -Muon ID - 0.9 %Tau ID 23% 23%

Electron Energy Scale 1.1% -Muon Energy Scale - 1.1%Tau Energy Scale 3.2% 3.2%

Luminosity 4% 4%

All the above uncertainties are taken into account within the LandS routine that is used to gain the finalcross-section value in the following analysis and are modeled as either log-normal or gamma functions.

4.4.10 Signal Events and Z ! ⌧⌧ cross section

The number of signal events is found by subtracting background from data.The cross section may be extracted from the data by the following equation:

�(pp ! Z ! ⌧⌧) =N

✏ABrL (4.7)

where N is the number of signal events extracted, A is the acceptance, ✏ is the selection e�ciency, Bris the decay branching ratio (0.224 for µ⌧had and 0.23 for e⌧had) and L is the integrated luminosity of the2011A run which is quoted as 2.094fb�1. These are summarized in the table below for both µ⌧had and e⌧had.


µ⌧had e⌧had

Br 0.224 0.23A 0.128 0.116✏ 0.35 0.22

A Tau-ID e�ciency of 0.474 is also assumed [21] and applied to the MC.Using the inclusive data and MC the following cross-sections for �(pp ! Z ! ⌧⌧) can be derived:

Data Observed Inclusive Cross Section (stats) (sys) (lumi) (Tau-ID)/pb

µ⌧had 1125 ±(33)(38)(45) (259)e⌧had 1155±(71)(40)(46)(266)MC Generated Cross Section (stats) (Sys) (lumi) (Tau-ID)/pbµ⌧had 1125± (11)(38)(45)(259)e⌧had 1052 ± (34)(37)(42)(242)

The quoted statistical uncertainty is found by adding the statistical errors on the numbers of events inquadrature before dividing by the e�ciencies, the systemic is found taking 5.5 % from above discussion, theluminosity uncertainty is taken to be 4 % from the above discussion and Tau-ID uncertainty is taken to be23% .

From the MC the cross sections are found to be consistent (within errors ) to the NNLO quoted valueof 972 ± 49[22] as well as previous experimental results from CMS [23]. The cross section found fromthe data (when other backgrounds subtracted) is also consistent with the MC for Z ! ⌧⌧ . A combinedcross-sections can be found to be 1140 ± 78(stat.)40(sys)46(lumi)26(tau-id)pb from the data and 1088±36(stat)33(sys)44(lumi)25(tau-id)pb these are consistent within errors. For the following counting anal-ysis the number of expected di-tau events will be found using the cross-sections calculated from the di-muonand di-electron channels as this is real data and therefore will be subject to the same conditions as the di-taudecays.

4.5 Statistical Analysis: Is there a Higgs Decay in the Data?

In the next section a statistical model is produced which will allow the probability of there being anotherparticle X of a given mass decaying via a di-tau channel.

4.5.1 Universality

As previously stated it is expected that all three Z ! ll decays have equal branching fraction, this comes fromthe fact that all 3 leptons have identical coupling to the standard model gauge bosons, this was originallyconfirmed by LEP and subsequently by CMS in various 2010 analysis papers. In the next section, the ideaof universality will be used to infer conclusions about the accuracy of the above results by comparing theobserved cross-sections for the 3 di-lepton decays of the Z boson.

4.5.2 Are ee and µµ data samples consistent with ⌧⌧?

In order to confirm universality the 3 channels are expected to have the same cross-sections (within errors).As can be seen in figure 4.43 all the experimentally derived inclusive cross-sections, as well as those derivedfrom MC for the tau channels are consistent with each other and the NNLO expected value of 972 ±49 pbi.e. within 1 �. Thus universality is confirmed and the 3 channels are said to be consistent.

From the VBF analysis of the di-electron and di-muon an acceptance of 0.0666% and 0.0672 % for selectionof a VBF event is found, this is the ratio of VBF/inclusive events; the average of these being 0.0669±0.0003%.It can be assumed that this e�ciency applies to the Z ! ⌧⌧ and therefore a predicted number of di-tauevents can be found:

NZ!⌧⌧ = NMCZ!⌧⌧AV BFBr (4.8)

where A is the average acceptance and Br is the branching ratio of each tau decay channel. This predicts7.57 µ⌧ and 5.6 e⌧ VBF events. In the following analysis these value will be used as the expected backgroundfrom Z ! ⌧⌧ .


Figure 4.43: Observed Z ! ll cross sections and the NNLO quoted value of 972 ± 49 pb. All values arewithin errors of this value.

4.5.3 Probability of there being a Higgs

The signature of the Higgs di-tau decay is very similar to that from Z di-tau decay and therefore the sameevent selection cuts may be used for the following analysis where six values of possible Higgs masses areconsidered, 115 � 140GeV/c2. Due to the very small number of VBF events the easiest way to extract thecross section limit is to carry out a counting experiment using LandS, a statistical analysis package specializedto work on LHC Higgs searches, rather than a more complicated shape analysis (Section 4.5.7). In such acounting experiment the shape of the observables is ignored and only the integral i.e. the number of eventsis used to get a upper limit on the ratio �

�SM

at a 95 % confidence level. Hybrid statistics will be used in thefollowing discussion. First LandS calculates a test statistic which is defined as:

R =L(S +B)|µ = 1

L(B)|µ = 0(4.9)

where L describes the maximized likelihood multiplied by a pdf of nuissance parameters. The ‘signal’ (S)here refers to the Higgs signal and ‘background’ (B) includes all the above derived backgrounds. L(S+B)describes the likelihood that the data is consistent with there being signal+background, whereas, L(B)describes the likelihood of what is observed being a result of the listed backgrounds. These likelihoods allbegin as Poisson distributions with either Nb orN(S+B) events expected:

Li(K,�) =�Ke��

K!(4.10)

where K describes the number of occurrences. For more than one channel this becomes:

LTotal =j=nchannelY

j=0

Lj (4.11)

LandS accounts for systemic uncertainties in the data by parameterizing them as nuisance parametersand fitted according to either a log-normal or gamma distributions, the former being used in case of luminos-ity,uncertainty in e�ciencies and cross-section corrections and the latter being used to account for statisticaluncertainties in background estimation.

In order to quantify the agreement between data and signal plus background hypothesis or background-only hypothesis expected probability distributions of the test statistic in the two hypotheses must be created.This is done by building 10000 toyMCs. The agreement between data and S+B hypothesis is given by CLs+b,probability to get a result which is less compatible with a signal when the signal hypothesis is true, and withthe B hypothesis by CLb. The probability to get a result less compatible with the background only hypothesisthan the observed one is then found and a ratio CLs =CLs+b/CLb computed. The 95 % CL upper limit on�/�SM is found using the result whenCLs=0.05 [24]. If a mass value gives a cross-section less than 1 x SMthat mass value is said to be excluded at a 95 % confidence level.

The expected limits in each case is found using LandS by generating large amounts of background onlyhypotheses data sets and calculating CLs for each one. The 1 and 2 sigma bands are found by computingcumulative probability density distributions, the median is defined as the point when the distribution crossesthe quantile of 50%, the ±1� bands are found when the distribution crosses at 16 % and 84 % quantilesand the ±2� bands are found from crossings of the 2.5 % and 97.5 % quantiles. This takes large amountsof CPU time and the generation of the following expected limits took several hours. Below is at table for


the observed and expected for the combined results form both channels where the expected number of higgssignal events are derived from MC and are listed in appendix 4. Figure 4.53 shows plots for the expectedHiggs signals for a the ranges of possible masses used.

4.5.4 Predicting Z ! ⌧⌧ from MC

mH/GeV Obs.(µ⌧) -2 � -1 � Median (Exp.) +1 � +2 �

115 5.42 ±0.036 2.97 3.79 5.29 7.67 10.8120 5.79 ±0.042 3.02 4.06 5.62 7.83 11.43125 5.481 ±0.026 2.93 3.83 5.33 7.77 11.05130 5.84±0.019 3.15 4.08 5.67 8.02 11.39135 6.37±0.236 3.58 4.62 6.26 8.84 12.87140 5.91±0.023 3,21 4.18 5.81 8.41 11.78

Figure 4.44: Plot of 95 % CL limit on Higgs cross section for both expected and observed from the e⌧ andµ⌧ channel

Results show little deviation from the expected but may not accurately portray what occurs in the detectortherefore conclusions must be based on the following analysis based on the data driven estimated of the Zdi-tau background.

4.5.5 Predicting Z ! ⌧⌧ from Data

mH/GeV Obs.(µ⌧) -2 � -1 � Median (Exp.) +1 � +2 �

115 6.64 ±0.032 2.75 3.61 5.30 7.04 9.82120 6.97 ±0.085 2.86 3.82 5.63 7.45 10.51125 6.61±0.73 2.73 3.65 5.29 7.08 9.53130 7.09±0.091 2.77 3.78 6.54 7.32 10.11135 7.712±0.067 3.28 4.36 6.25 8.25 11.76140 7.27 ±0.045 2.86 3.87 5.73 7.50 10.38

For the breakdown of limits from each channel see Appendix 5. As can be seen the results observed resultslie firmly within the ±1� regions suggesting consistency with the expected ( background-only hypothesis) .Cross-sections �(pp ! H ! ⌧⌧) of greater than 6.64-7.27 x �SM have therefore been excluded at a 95 %confidence level. It is clear from figure 4.47 that it is the µ⌧ results which help contribute to the substantiallowering of the 95% CL upper limit from 17-19 x�SM in the e⌧ channel to 8.05-9.2x�SM in the µ⌧ channelacross a mass range of 115-140GeV/c2 .The ratio of cross-sections in the e⌧ case is double that of the µ⌧case. This could be a result of the relatively small number of results in the latter case, meaning errors dueto inaccuracies in background estimation have a lot more influence. To conclude that the Higgs boson isexcluded completely this ratio must fall below 1 which of course is not the case in the analyzed data set.However, this upper limit is low enough for these results to carry some significance in the search for the Higgsboson.

In both cases the deviations from expectation are small and are below 1� and are therefore not thoughtto be statistically significant, any deviations are therefore believed to be a result of background fluctuations


Figure 4.45: Plot of 95 % CL limit on Higgs crosssection for both expected and observed from the e⌧and µ⌧ channel

Figure 4.46: Observed 95 % CL limit of �(H ! ⌧⌧)for di↵erent channels and combined limit-µ⌧ gives bestlimit

and errors which have not yet been calculated. Results published by CMS on 18/02/12 ([25])put limits of3.30-5.45 �SM . This is of course an improvement on our estimate and results from having double the amountof data for the 2012A run when compared to the 2011A run, this results in a better exclusion by a factor ofp2 and of course the method employed here is much less sophisticated than that used at CERN which again

results in a higher upper limit.

4.5.6 Statistical Significance

From the above discussion it is expected that any deviation from the background only hypothesis (expectedline) is not significant. Statistical significance describes the likelihood of an event occurring by chance. Figure4.47 shows the distribution of the null p-value (1�CLb) derived from the data. As expected the significanceis low, a significance of > 5 � (where sigma here represents standard deviation) is needed for a ‘discovery’which corresponds to 1-CLb <1-5 x10�7[28].The significance of the e⌧ results is half that of the µ⌧ case butneither is outside the 1� level of significance (when 1-CLb = 1 � 0.683). This suggests that, as expected,the fluctuations away from expectation are a result of random fluctuation in backgrounds and not due to thepresence of any Higgs particles.

Figure 4.47: Null p-vlaue for combined results using data to get Z di-tau background

4.5.7 Shape Analysis

Of course LandS doesn’t take into account the true shape of the di↵erent background and signal processesand this may induce some error into the above calculation. In order to correct this a more rigourous shapeanalysis may be carried out as described in [26]. This involves comparing not just the total number of eventsbut the histograms (or fitted shapes) as well and should allow estimation of systemic uncertainties inducedinto the above calculation due to not taking into account the signal/background shapes.


‘Shape analysis’ requires the proposed Higgs signals as well as all major backgrounds to be fitted withparametric functions, this may be done using RooFit as done for the background analysis. The fit functionscan then be analyzed again using LandS and RooStats. In this case each template histogram is representedby a shape template, along with the variation due to statistical uncertainty which is found using the fittingtool RooFit. ToyMC are then generated using these smoothed functions, which may then be input intoLandS in the same way as described above. The Higgs signals, Z ! ⌧⌧ , W+Jet background and data are allparameterized by lognormal functions given by:

f(x, µ,�) =1

x�p2⇡

e�(lnx�µ)2

2�2 (4.12)

The QCD is fitted to a convolution of a Landau function of the form:

f(x, µ,�) =1

⇡

Z1

0e�lnt� x�µ

�

tsin(⇡t) (4.13)

and a Gaussian function.These are all shown in figures 4.48-4.51 for the µ⌧had data only this is pre-vbf selection. The Z ! ll would

be represented by a Breit-Wigner in the electron case but is not used in the µ⌧ case as it provides a verysmall contribution to the overall data. In general, the shape templates appear to parameterize the templatehistograms well and therefore little bias will be introduced compared to using the histograms themselves.[9] There will of course still be some error arising from statistical uncertainties on the template histogramsas well as biases of the shape templates. Smaller backgrounds are added as systemic uncertainties. TheVBF results contain much fewer events, to model the shape of this case the fits are normalized such thatthe analytical integral of the fit corresponds to the number of VBF events in each channel. The templatehistogram integrals as well as the above fits are then input into the LandS package and the cross-sectionlimits were numerically similar to those for the numerical analysis.

The deviation is < 5 % from the counting experiment in the mass range 115 � 140GeV/c2, with largerdi↵erences at higher masses. This deviation will be viewed as a systemic uncertainty on the final quotedupper limit.

Figure 4.48: Fit to the W+Jet MC- parameterized bya lognormal

Figure 4.49: Z ! ⌧⌧ MC parameterized as lognormalfunction

Figure 4.50: Fit to the data for the µ⌧had parameter-ized by a lognormal

Figure 4.51: QCD background parameterized by aLandau and Gaussian convolution


4.5.8 Inclusive Discussion

In the inclusive search SM Higgs bosons formed from ggH through a quark loop (Section 1.6) are alsoconsidered as well as bbH were the Higgs boson is produced directly by bb annihilation from the b partondensity in the beam protons processes are considered. This latter case is generally considered negligible inSM searches but has much larger contribution in MSSM searches. An inclusive search involves finding 3 (gg,bb and the above VBF) di↵erent Higgs signals before any jet selection is enforced. In the following analysisonly the e⌧ channel is used.

The following table shows how many events where expected pre-jet/b-jet selection from MC specializedfor each process for two masses, this is placed here simply to compare the relative numbers of Higgs eventsin each channel, in the final analysis 5 ggH and bbH MCs were also used spanning the range 115-140GeV/c2:

Mass ggH (stat.) (theo.) VBF(stat.)(theo.)

120 104 ± 10 ± 12.48 4.7 ± 2.17 ±0.094140 125 ± 11 ± 15 4.34 ±2.08 ±0.086

As expected the ggH process dominates by over a factor of 10.This is of course to be expected from therelative production cross sections.The above numerical results suggest a ratio of 22:1 between ggH and VBFHiggs expected events.

The bbH process makes up less than 1 % of the total SM Higgs signal after the described pre-selection,and VBF makes up only ⇡ 4.5 % after pre-selection. The upper limits on the combined inclusive Higgscross-section upper limit taken from numerical analysis only are given in the table below and plotted infigure 4.52 where both the observed and expected values are calculated using LandS:

mH/GeV Obs.(e⌧) Observed CLs -2 � -1 � Median (Exp.) +1 � +2 �

115 85.122± 1.04 0.964 ± 0.01 60.21 69.99 82.14 95.12 109.9120 82.90 ± 0.13 0.965 ±0.1 57.97 68.21 79.91 91.86 107.11125 80.31 ± 1.27 0.0.97 ± 0.015 54.89 65.12 77.72 90.23 105.12130 76.95 ± 1.194 0.968 ± 0.13 52.13 61.32 74.51 87.77 101.23135 73.38 ± 0.96 0.968 ± 0.01 50.02 57.05 71.04 85.13 100.04140 70.60 ± 1.23 0.968 ±0.014 45.61 54.97 68.33 80.01 95.34

Figure 4.52: The results for the 95 % CL on the ��SM

for the inclusive search

Figure 4.53: MC for Higgs bosons formed by VBF withmasses 120-140GeV/c2

As can be seen from the CLs values which are all in the to 0.965-0.97 the observed results are consistentwith the background-only hypothesis.

As can be seen in figure 4.52 the observed cross-section lies within the ±2� region throughout. Theobserved �

�SM

is excluded above values within the range 85-70 for Higgs masses 115-140 GeV. These valuesare very large compared to the values observed for only VBF Higgs this is a result of the smallness of theintegrated luminosity at this point, much greater numbers of events are needed to be able to observe/excludean inclusive Higgs. These results show little significance and further study is definitely needed to give abetter conclusions for the inclusive Higgs search. Further extensions may also include MSSM higgs bosonsin the search.

Chapter 5

Conclusions

To conclude, the work carried out in this report was based on real CMS data taken during the 2011A run.The aim of the project was to use ROOT and knowledge of the standard model to put an upper limit onthe cross-section of a standard model Higgs boson decaying to two ⌧ leptons within this data. The resultspresented in chapter 4 show this has been done for both the VBF and inclusive case, meaning the basic aimsof the project have been fulfilled. The project can therefore be classified as a success, the results appearconsistent with expectation and previous analysis for this data set [27]. All the work presented in chapter 4is my own and all calculations were carried out by myself except were specific reference has been given.

The first stage of the analysis was to extract a good estimate of the Z ! ⌧⌧ background, this wascarried out by calculating the cross-sections of the Z ! ee and µµ and assuming universality. The resultingcross-sections were:

• �(pp ! Z ! ee) =1022 ± 32(stat) ± 61 (sys) ± 41(lumi) pb

• �(pp ! Z ! µµ) = 1055 ± 32 (stat.)± 32 (sys.) ± 42 (lumi)pb

• �(pp ! Z ! ⌧⌧)combined=1140 ± 78(stat.)40(sys)46(lumi)26(tau-id)pb (data)

These are consistent, within respective errors, with each other and theory confirming universality. Thenumber of expected VBF di-tau decays of the Z could then be estimated from the average of the ee and µµresults and used to put a limit on the cross-section of a VBF Higgs di-tau decay in the data.

The analysis has excluded, at a 95 % CL, upper limits on the Higgs cross-section of >6.64-7.27 ± 5%(shape) �SM for the VBF H ! ⌧⌧ ! ⌧H + µ and VBF H ! ⌧⌧ ! ⌧H + e channels. An inclusive searchhas also been carried out, focusing on the e⌧ channel and excluded cross-section > 85-70 for masses 115-140GeV/c2. It has been shown that there is no significant excess in the results which could indicate presence ofany other particle, such as the Higgs, within the data.

Work continues at CMS to put even stricter upper limits on the cross-section of the standard modelHiggs, however, so far there has been no ’discovery’ ( a result of 5� significance). Work also continues tofind/eliminate various SUSY extensions which propose Higgs particles. Most notably MSSM, work into thishas managed to exclude/put limits on possible Higgs cross-sections as well as parameter space values.

36

Project Report Appendix 37

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Appendix A

Appendix

A.1 Monte Carlo Simulations

Figure A.1: SM Monte Carlo Samples used

Figure A.2: Higgs VBF Monte Carlo Samples used

A.2 Di-muon and di-jet Contol Plots

*plots produced by David Kirkpatrick

39


Figure A.3: Pre-VBF control plots for the di-muon channel

A.3 Triggers and E�ciency

Name of Trigger UseIsoEle17IsoEle8 ee

Ele8 eeDoubleMu7 µµMu13Mu8 µµ

IsoEle15 LIsoTau20 e⌧IsoEle15 TIsoTau20 e⌧IsoEle18 MIsoTau20 e⌧IsoMu12 LIsoTau10 µ⌧IsoMu15 LIsoTau15 µ⌧


Figure A.4: Post-VBF control plots for the di-muon channel

A.3.1 ee

Type Criteria E↵.Trigger |⌘| < 0.8, 1st electron 0.989Trigger |⌘| < 1.6, 1st electron 0.991Trigger 1st electron, else 0.990Trigger |⌘| < 0.8, 2nd electron 0.989Trigger |⌘| < 1.6, 2nd electron 0.991Trigger 2nd muon, else 0.990

ID Pt(any elec)< 25GeV/c and Pt(any elec)> 20GeV/c 0.982ID Pt<30 GeV/c, either elec. 0.976ID either electron, else 0.986

*All supplied by Mike Cutajar

A.3.2 µµ

Type Criteria E↵.Trigger |⌘| < 0.9, 1st muon 0.973Trigger |⌘| < 1.5, 1st muon 0.963Trigger 1st muon, else 0.952Trigger |⌘| < 0.9, 2nd muon 0.973Trigger |⌘| < 1.5, 2nd muon 0.962Trigger 2nd muon, else 0.947

ID Pt< 25GeV/c, 1st muon 0.996*0.956ID Pt<30 GeV/c, 1st muon 0.998*0.98ID 1st muon, else 0.996*0.99ID Pt< 25GeV/c, 2nd muon 0.996*0.956ID Pt<30 GeV/c, 2nd muon 0.998*0.98ID 2nd muon,else 0.996*0.99


A.3.3 e⌧

As well as the above described selection and tau-ID e↵. The following are also applied:


Type Criteria E↵.Combined ID and Trigger Barrel electron with Pt<24GeV/c 0.891Combined ID and Trigger Barrel electron with Pt< 30.0GeV/c 0.917Combined ID and Trigger Barrel electron with Pt< 35.0GeV/c 0.931Combined ID and Trigger Barrel electron with Pt< 40.0GeV/c 0.936Combined ID and Trigger Barrel else 0.938Combined ID and Trigger Endcap electron with Pt<22GeV/c 0.842Combined ID and Trigger Endcap electron with Pt<24GeV/c 0.891Combined ID and Trigger Endcap electron with PT<30GeV/c 0.91Combined ID and Trigger Endcap electron else 0.93

Trigger Tau with Pt<22GeV/c 0.622Trigger Tau with Pt<24 GeV/c 0.768Trigger Tau with Pt<28GeV/c 0.801Trigger Tau with Pt<30GeV/c 0.819Trigger Tau with Pt<40GeV/c 0.841Trigger Tau else 0.861


A.3.4 µ⌧

Above tau e�ciencies are the same and the muon e�ciency is based on that of the 1st muon case in the µµcase

A.4 Higgs Expected Numbers

µ⌧

mass/GeV exp. Events115 2.17120 2.033125 2.15130 2.062135 1.79140 1.98

e⌧

mass/GeV exp. Events115 0.514120 0.496125 0.527130 0.412135 0.515140 0.475

These values have been multiplied by e�ciencies described above as well as the tau-ID and divided by2.093 fb�1 the luminosity of the present run

A.5 Higgs Exclusion For individual channels

1) e-⌧ channel exclusion limits

mH/GeV Obs.(µ⌧) -2 � -1 � Median (Exp.) +1 � +2 �115 17.79 10.87 14.77 19.49 28.39 38.82120 18.37 10.82 14.82 20.04 28.37 40.69125 17.03 11.89 14.02 18.89 27.35 38.56130 22.53 13.23 17.98 24.57 35.61 48.9135 17.81 10.71 14.39 19.70 28.34 39.15140 19.57 12.25 15.64 20.55 30.69 42.11


Figure A.5: Observed 95% CL upper limit �(pp ! H ! ⌧⌧)/�SM for e⌧ channel

2) µ⌧ exclusion limits

mH/GeV Obs.(µ⌧) -2 � -1 � Median (Exp.) +1 � +2 �115 7.95 3.28 4.11 6.07 7.98 11.06120 8.52 3.49 4.34 6.50 8.64 11.73125 8.05 2.95 4.00 6.16 8.18 11.12130 8.37 3.633 4.32 6.44 8.41 11.48135 8.76 3.87 5.10 7.34 9.23 13.44140 8.75 3.42 4.41 6.69 8.89 11.79

Figure A.6: Observed 95% CL upper limit �(pp ! H ! ⌧⌧)/�SM for µ⌧ channel

* page limit: 30 pages ± 10 %=33. Number of pages with text on =35. (this does not include anycontents/appendices/bibliography)

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