universita degli studi di bari aldo moro most, i would like to thank my ph.d. advisors prof. giorgio...

UNIVERSITA DEGLI STUDI DI BARIAldo Moro

Dipartimento Interateneo di Fisica M. Merlin

Scuola di Dottorato di Ricerca in Fisica

Ciclo XXV

Settore Scientifico Disciplinare: FIS/01

SEARCH FOR THE STANDARD MODEL HIGGS BOSON

IN THE DECAY CHANNEL H→ ZZ→l+l−τ+τ− WITH

THE CMS EXPERIMENT AT√

s =7 AND 8 TeV

Dottorando: Coordinatore:Dott. Simranjit Singh Chhibra Chiar.mo Prof. Salvatore Vitale Nuzzo

Supervisore:Chiar.mo Prof. Giorgio Pietro Maggi Dr. Nicola De Filippis

Esame Finale 2013

Dedicated to my revered teachers

&

lovable parents

“I am among those who think that science has great beauty.A scientist in his laboratory is not only a technician:

he is also a child placed before natural phenomenawhich impress him like a fairy tale.”

-Marie Curie

Acknowledgements

As I stand at the threshold of earning my doctorate, I am overwhelmed whenI recall all the people who have helped me to get this far. First and the fore-most, I would like to thank my Ph.D. advisors Prof. Giorgio Pietro Maggiand Dr. Nicola De Filippis for their constant support, judicious guidanceand invaluable inspiration.

Prof. Giorgio Pietro Maggi has always been readily available for help andsupport. I acknowledge him for his generosity and approachability in everystep of my research.

Dr. Nicola De Filippis is remarkable in his continual patience, kind in-sight, and helpful suggestions in tackling problems in my research. His enthu-siasm, curiosity and suggestions in high energy research is truly inspirational.

I sincerely thank the Director, Dipartimento Interateneo di Fisica “M.Merlin”, Universita degli Studi di Bari “Aldo Moro”, Bari for providing theadequate facilities to work in the department. I also thank the Director, Isti-tuto Nazionale di Fisica Nucleare (INFN), Bari for all their help and supportin completing my Ph.D. The financial support by INFN is duly acknowledged.

I would like to thank all the members of the CMS Collaboration, specially,of HZZ and 2l2tau sub-groups for providing valuable inputs and suggestionsin my research. I sincerely thank Dr. Alexander Savin for his valuable sug-gestions and his availability despite of his busy schedule. He never let mestuck with my questions and problems.

I duly acknowledge all the members of Bari CMS Group for their support.My special thanks to Dr. Marcello Maggi for his help and support through-out. I acknowledge his help in the software activities and appreciate his wayof dealing with problems.

I sincerely thank the referees of my thesis, Prof. Domenico Di Bari andProf. Aleandro Nisati for their valuable suggestions and comments concern-ing my thesis.

I wish to thank Dr. Ashok Kumar for his readily available support, and Iappreciate his way of encouraging the young students.

I also thank Mrs. Anna Massarelli for her help in administrative jobspertaining to my Ph.D. I specially thank Mr. Giacinto Donvito for his helpin grid related problems.

I would like to express my gratitude to my father Mr. Dalveer Singh, mymother Mrs. Jaswinder Kaur, elder brother Mr. Onkar Singh and his familyfor their love, support and encouragement throughout my life. I would like tothank all my relatives, specially to my lovable aunt Mrs. Surindra Kumari,for encouraging me to continue in science since my schooling.

I wish to thank my childhood friends Saurab and Gurvinder to provide mean environment full of true love and friendship in which I have grown up. Iwould like to thank my friends Gurpreet, Mahinder and Gurpreet (Pandori)for their fruitful company during my stay in Italy, far from my parents andmy home.

A spacial thank to my friends in Bari, Nicola, Liliana, Giorgia, Piet,Mario, Francesco, Cesare, Rosma and Massimo to make this journey moreenjoyable, exciting and motivational. I also thank to Adish for his supportand enjoyable company during my CERN visits.

Last but not the least, My deepest and sincere gratitude to the almighty‘God’ for inspiring and guiding this humble being. I could not have done thiswithout his blessings.

February 11, 2013 Simranjit Singh Chhibra

Contents

Introduction 1

1 The Standard Model and the Higgs Boson 51.1 The Standard Model of Elementary Particles . . . . . . . . . . 61.2 Spontaneous Symmetry Breaking and the Higgs Mechanism . 7

1.2.1 The Higgs Mechanism . . . . . . . . . . . . . . . . . . 91.3 Glashow-Weinberg-Salam Model . . . . . . . . . . . . . . . . . 101.4 The Higgs Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.4.1 Theoretical Constraints . . . . . . . . . . . . . . . . . . 151.4.2 Experimental Constraints . . . . . . . . . . . . . . . . 16

1.5 The Higgs Search at LHC . . . . . . . . . . . . . . . . . . . . 171.5.1 The Higgs Production . . . . . . . . . . . . . . . . . . 181.5.2 The Higgs Decay . . . . . . . . . . . . . . . . . . . . . 201.5.3 The Higgs Total Decay Width . . . . . . . . . . . . . . 22

2 Large Hadron Collider and the CMS Experiment 242.1 Large Hadron Collider at CERN . . . . . . . . . . . . . . . . . 24

2.1.1 Performance Goals . . . . . . . . . . . . . . . . . . . . 272.1.2 Number of Events at LHC . . . . . . . . . . . . . . . . 28

2.2 The Compact Muon Solenoid Experiment . . . . . . . . . . . 302.2.1 The Coordinate System . . . . . . . . . . . . . . . . . 302.2.2 The Magnet System . . . . . . . . . . . . . . . . . . . 312.2.3 The Inner Tracking System . . . . . . . . . . . . . . . 322.2.4 The Calorimeter . . . . . . . . . . . . . . . . . . . . . 352.2.5 The Muon System . . . . . . . . . . . . . . . . . . . . 392.2.6 Forward Detectors . . . . . . . . . . . . . . . . . . . . 432.2.7 Trigger and Data Acquisition . . . . . . . . . . . . . . 44

3 Event Simulation and Reconstruction 483.1 Event Generation . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.1.1 Parton Distribution Functions . . . . . . . . . . . . . . 52

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3.1.2 Hard Subprocesses . . . . . . . . . . . . . . . . . . . . 523.1.3 Parton Shower . . . . . . . . . . . . . . . . . . . . . . 533.1.4 Hadronization . . . . . . . . . . . . . . . . . . . . . . . 533.1.5 Underlying Event . . . . . . . . . . . . . . . . . . . . . 543.1.6 Hadron and τ Decays . . . . . . . . . . . . . . . . . . . 543.1.7 Validation and Tuning . . . . . . . . . . . . . . . . . . 553.1.8 Event Generators . . . . . . . . . . . . . . . . . . . . . 553.1.9 K-factors . . . . . . . . . . . . . . . . . . . . . . . . . . 563.1.10 Detector Simulation . . . . . . . . . . . . . . . . . . . 56

3.2 Reconstruction of Physics Objects . . . . . . . . . . . . . . . . 573.2.1 Track Reconstruction . . . . . . . . . . . . . . . . . . . 573.2.2 Vertex Reconstruction . . . . . . . . . . . . . . . . . . 583.2.3 Muon Reconstruction . . . . . . . . . . . . . . . . . . . 593.2.4 Electron Reconstruction . . . . . . . . . . . . . . . . . 613.2.5 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . 623.2.6 Missing ET Reconstruction . . . . . . . . . . . . . . . . 633.2.7 Hadronic Tau Reconstruction . . . . . . . . . . . . . . 64

3.3 Monte Carlo Samples . . . . . . . . . . . . . . . . . . . . . . . 663.4 Monte Carlo Generator Studies . . . . . . . . . . . . . . . . . 69

4 Search for The SM Higgs Boson in H→ ZZ→ l+l−τ+τ− FinalStates 774.1 Experimental Data Samples . . . . . . . . . . . . . . . . . . . 774.2 Lepton Identification . . . . . . . . . . . . . . . . . . . . . . . 78

4.2.1 Muon Identification . . . . . . . . . . . . . . . . . . . . 784.2.2 Electron Identification . . . . . . . . . . . . . . . . . . 80

4.3 Lepton Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . 824.4 Hadronic Tau Identification and Isolation . . . . . . . . . . . . 844.5 Establishing the Signal Selection Criteria . . . . . . . . . . . . 874.6 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.6.1 Leading Z Boson Selection . . . . . . . . . . . . . . . . 944.6.2 Sub-leading Z Boson Selection . . . . . . . . . . . . . . 954.6.3 Removal of Overlap with 4l (l = e, µ) Analysis . . . . . 99

4.7 Background Estimation . . . . . . . . . . . . . . . . . . . . . . 1134.7.1 Irreducible ZZ Background Estimation . . . . . . . . . 1134.7.2 Reducible Background Estimation . . . . . . . . . . . . 113

4.8 Line-shape Re-weighting for High Higgs Masses . . . . . . . . 1284.9 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . 132

4.9.1 Theoretical Uncertainties . . . . . . . . . . . . . . . . . 1324.9.2 Experimental Uncertainties . . . . . . . . . . . . . . . 132

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5 Final Results and the Statistical Interpretation 1345.1 l+l−τ+τ− Invariant Mass Distributions . . . . . . . . . . . . . 1395.2 Exclusion Limits . . . . . . . . . . . . . . . . . . . . . . . . . 1395.3 Combination with H→ ZZ(∗) → 4l (l = e, µ) Analysis . . . . . 141

Conclusions 147

A Statistical tools 149A.1 CLs Statistical Method . . . . . . . . . . . . . . . . . . . . . . 149

A.1.1 Case of Discovery . . . . . . . . . . . . . . . . . . . . . 150A.1.2 Case of Exclusion . . . . . . . . . . . . . . . . . . . . . 150

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List of Figures

1.1 Summary of the interactions between the constituents of theSM @wikipedia. . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 The potential V (φ) for a complex scalar field, for m2 < 0 andλ > 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.3 The upper and the lower bounds on the Higgs mass as a func-tion of the cut-off energy scale Λ[15]. . . . . . . . . . . . . . . 16

1.4 ∆χ2 of the fit to the electroweak precision measurements ofLEP, SLC, Tevatron and LHC as a function of the Higgs mass(March 2012). The solid line represents the result of the fit andthe blue shaded band is the theoretical error from unknownhigher order corrections. The yellow area represents the regionexcluded by direct search. . . . . . . . . . . . . . . . . . . . . 17

1.5 The SM Higgs production modes at LHC: (a) gluon-gluon fu-sion; (b) vector boson fusion; (c) W and Z associated produc-tion (or Higgsstrahlung); (d) tt associated production. . . . . . 18

1.6 The SM Higgs boson production cross-sections at√s = 7 TeV

(upper) and 8 TeV (lower)[18, 19, 20]. . . . . . . . . . . . . . . 191.7 The branching ratios for the different Higgs decay channels as

a function of mH[19, 20]. . . . . . . . . . . . . . . . . . . . . . 211.8 The SM Higgs boson total decay width as a function of mH[20]. 23

2.1 The LHC accelerator complex. . . . . . . . . . . . . . . . . . . 252.2 Schematic layout of LHC with clockwise-beam (red) and anti

clockwise-beam (blue). . . . . . . . . . . . . . . . . . . . . . . 262.3 Integrated luminosity recorded by the CMS experiment (left)

and the instantaneous luminosity (right) at√s = 7 TeV in

year 2011 (upper) and√s = 8 TeV in year 2012 (lower). . . . 28

2.4 Expected cross-section vs energy at proton-antiproton andproton-proton colliders. . . . . . . . . . . . . . . . . . . . . . . 29

2.5 A perspective view of the CMS detector. . . . . . . . . . . . . 302.6 The CMS coordinate system. . . . . . . . . . . . . . . . . . . 312.7 The CMS magnet system. . . . . . . . . . . . . . . . . . . . . 32

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2.8 Schematic of the CMS inner tracking system in the r−z plane.The η ranges of the different sub-systems are also shown. . . . 34

2.9 Silicon pixel detector layout. . . . . . . . . . . . . . . . . . . . 342.10 Longitudinal view of a part of CMS electromagnetic calorime-

ter showing the ECAL barrel and an ECAL endcap with thepreshower in front. . . . . . . . . . . . . . . . . . . . . . . . . 37

2.11 Different contributions to the energy resolution of the PbWO4

calorimeter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.12 Longitudinal view of the CMS detector: the locations of the

hadron barrel (HB), the endcap (HE), the outer (HO) and theforward (HF) calorimeters. . . . . . . . . . . . . . . . . . . . . 39

2.13 Longitudinal view of the muon detectors: DT, RPC and CSC. 402.14 The cross-section of a CMS drift tube with the anode wire,

which is spanned in the middle of the tube, and Field lines ofdrift Field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.15 Layout and the woking principle of CSCs: a pattern of wiregroup hits left behind by a muon passing through a chamber(Left), a pattern of induced charges on strips and half-striphits left behind by a muon (Right). . . . . . . . . . . . . . . . 42

2.16 Layout of the RPCs. . . . . . . . . . . . . . . . . . . . . . . . 432.17 The CASTOR calorimeter detector. . . . . . . . . . . . . . . . 442.18 The Zero Degree Calorimeter. . . . . . . . . . . . . . . . . . . 452.19 Schematic representation of the CMS L1 trigger system. . . . 462.20 The principal components of the DAQ system of the CMS

detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.1 Scheme of a proton-proton collision. Two partons of the in-coming proton interact in the hard interaction (red), while theproton remnants (magenta) provide the underlying event. Thepartons created in the hard interaction hadronization (lightgreen) and unstable hadrons decay further to stable particles(dark green). . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2 Track reconstruction efficiency[36, 37] for simulated single, iso-lated muons (left) and for pions (right) as a function of pT . . . 59

3.3 Reconstruction of muon objects at the CMS experiment. Trackertrack (red box), stand-alone track (green box) and global muon(blue box) are shown. . . . . . . . . . . . . . . . . . . . . . . . 60

3.4 Reconstruction of electron objects at the CMS experiment. . . 62

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3.5 Reconstructed jet energy fractions as a function of pseudo-rapidity (a) in the data correcponding to L = 6.2 nb−1 (b) andin the simulation. From bottom to top in the central region:charged hadrons (red), photons (blue), electrons (light blue),and neutral hadrons (green). In the forward regions: hadronicdeposits (pink) and electromagnetic deposits (purple). . . . . . 64

3.6 Invariant llττ mass distribution for Higgs masses mH = 200GeV (left) and mH = 600 GeV (right). A comparison is givenof generated Higgs mass (green) and visible llτhτh (red), llτlτh(blue) and llτlτl (pink) masses. . . . . . . . . . . . . . . . . . . 69

3.7 Invariant ll mass distribution of leptons coming from leadingZ decay for Higgs masses mH = 200 GeV (left) and mH = 600GeV (right). A comparison is given of generated leading Zmass (green) and visible ll mass (red). . . . . . . . . . . . . . 70

3.8 Invariant ττ mass distribution of taus coming from sub-leadingZ boson decay for Higgs masses mH = 200 GeV (left) andmH = 600 GeV (right). A comparison is given of generatedsub-leading Z mass (green) and visible τhτh (red), τlτh (blue)and τlτl masses (pink). . . . . . . . . . . . . . . . . . . . . . . 71

3.9 pT distribution of leptons and taus coming from leading Z andsub-leading Z bosons decay, respectively, for Higgs mass mH =200 GeV. Green and red distributions represents first highestand second highest pT of leptons. Blue and pink distributionsrepresents first highest and second highest pT of taus (upperleft: sub-leading Z → τhτh), pT of lepton and hadronic tau(upper right: sub-leading Z → τlτh), and first highest andsecond highest pT of leptons (lower: sub-leading Z→ τlτl). . . 72

3.10 pT distribution of leptons and taus coming from leading Z andsub-leading Z bosons decay, respectively, for Higgs mass mH =600 GeV. Green and red distributions represents first highestand second highest pT of leptons. Blue and pink distributionsrepresents first highest and second highest pT of taus (upperleft: sub-leading Z → τhτh), pT of lepton and hadronic tau(upper right: sub-leading Z → τlτh), and first highest andsecond highest pT of leptons (lower: sub-leading Z→ τlτl). . . 73

3.11 Azimuthal angle φ separation between Z bosons for Higgsmasses mH = 200 GeV (left) and mH = 600 GeV (right). . . . 74

3.12 Azimuthal angle φ separation between leptons coming fromleading Z boson decay for Higgs masses mH = 200 GeV (left)and mH = 600 GeV (right). . . . . . . . . . . . . . . . . . . . 74

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3.13 Azimuthal angle φ separation between taus coming from sub-leading Z boson decay for Higgs masses mH = 200 GeV (left)and mH = 600 GeV (right). . . . . . . . . . . . . . . . . . . . 75

3.14 η− φ space separation, in terms of ∆R, between Z bosons forHiggs masses mH = 200 GeV (left) and mH = 600 GeV (right). 75

3.15 η−φ space separation, in terms of ∆R, between leptons comingfrom leading Z boson decay for Higgs masses mH = 200 GeV(left) and mH = 600 GeV (right). . . . . . . . . . . . . . . . . 76

3.16 η − φ space separation, in terms of ∆R, between taus comingfrom sub-leading Z boson decay for Higgs masses mH = 200GeV (left) and mH = 600 GeV (right). . . . . . . . . . . . . . 76

4.1 Efficiency (from simulation) for the ∆β-corrected combinedHPS tau isolations as a function of generated τ pT (left) andreconstructed vertices (right) for

√s = 8 TeV. . . . . . . . . . 87

4.2 pT distributions for four highest pT leptons (left) and twohighest pT hadronic taus (right) in the event, for Higgs massmH = 200 GeV at

√s = 8 TeV. Where the pT values de-

crease from pl1T to pl4T for leptons, and from pτh1T to pτh2

T for thehadronic taus. The black vertical lines show the chosen cutvalues, 10 GeV for all the four leptons and 20 GeV for boththe hadronic taus. . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.3 Comparison of the pT distributions of four highest pT leptonsin the event for the signal and the backgrounds: first highest(upper left), second highest (upper right), third highest (lowerleft) and forth highest (lower right). The black vertical linesshow the pT threshold value of 10 GeV. . . . . . . . . . . . . . 89

4.4 Isolation variable distributions for the four leptons (upper),for the three muons (lower left) and the three electrons (lowerright) in the event with minimum isolation values, for Higgsmass mH = 200 GeV at

√s = 8 TeV. The black vertical lines

show the chosen cut values, 0.25 for all the four leptons forllτlτl final state, and for two well isolated muons(electrons).The value for the isolated muon(electron) with third minimumvalue is required to be less than 0.1(0.25) for llτlτh final states. 91

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4.5 Comparison of the isolation variable distributions for the threemuons in the event with minimum isolation values, the bestisolation (upper), the second best isolation (lower left) andthe worst isolation (lower right). The black vertical lines showthe chosen cut values, 0.25 for the two well isolated muons.The value for the isolated muon with third minimum value isrequired to be less than 0.15 for llτµτh final states. . . . . . . . 92

4.6 Comparison of the isolation variable distributions for the threeelectrons in the event with minimum isolation values, the bestisolation (upper), the second best isolation (lower left) andthe worst isolation (lower right). The black vertical lines showthe chosen cut values, 0.25 for the two well isolated electrons.The value for the isolated electron with third minimum valueis required to be less than 0.1 for llτeτh final states. . . . . . . 93

4.7 Comparison of signal and background for the ∆R values be-tween the two leptons giving the reconstructed leading Z boson(left) and the two objects giving the reconstructed sub-leadingZ boson (right). . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.8 Reconstructed invariant mass distribution of muons (left) andelectrons (right) coming from leading Z decay, for data 2011and 2012 at

√s = 7 (upper) and 8 TeV (lower) respectively. . 96

4.9 Electron and muon (hadronic tau) pT : data to simulation com-parison for electrons and muons coming from leading Z decay(hadronic taus coming from sub-leading Z decay). upper left:for leading electron; upper right: for sub-leading electron; mid-dle left: for leading muon; middle right: for sub-leading muon;lower: for hadronic taus. . . . . . . . . . . . . . . . . . . . . . 102

4.10 Electron and muon (loose) isolation: data to simulation com-parison for electrons and muons coming from leading Z decay.upper left: for leading electron; upper right: for sub-leadingelectron; lower left: for leading muon; lower right: for sub-leading muon. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.11 Electron and muon (hadronic tau) η: data to simulation com-parison for electrons and muons coming from leading Z decay(hadronic taus coming from sub-leading Z decay). upper left:for electrons; upper right: for muons; lower: for hadronic taus. 104

4.12 Cut-flow data to MC comparisons for µµτhτh final state fordata 2011 and 2012 at

√s = 7 (left) and 8 TeV (right) respec-

tively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.13 Cut-flow data to MC comparisons for eeτhτh final state for data

2011 and 2012 at√s = 7 (left) and 8 TeV (right) respectively. 106

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4.14 Cut-flow data to MC comparisons for eeτeτh final state for data2011 and 2012 at

√s = 7 (left) and 8 TeV (right) respectively. 107

4.15 Cut-flow data to MC comparisons for µµτeτh final state fordata 2011 and 2012 at


tively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.16 Cut-flow data to MC comparisons for µµτµτh final state for

data 2011 and 2012 at√s = 7 (left) and 8 TeV (right) respec-

tively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.17 Cut-flow data to MC comparisons for eeτµτh final state for

data 2011 and 2012 at√s = 7 (left) and 8 TeV (right) respec-

tively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.18 Cut-flow data to MC comparisons for eeτeτµ final state for data

2011 and 2012 at√s = 7 (left) and 8 TeV (right) respectively. 111

4.19 Cut-flow data to MC comparisons for µµτeτµ final state fordata 2011 and 2012 at


tively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124.20 Data to simulation comparison for the background estimation

control regions for µµττ with selection: same sign and noisolation requirements for both the τ ′s (top), same sign andisolation for the highest pT τ (middle and lower left), same signand isolation on the second highest pT τ (middle and lowerright) for 2011 data and simulation. Middle (lower) plots areobtained with Medium (Tight) isolation working point for tau. 116

4.21 Data to simulation comparison for the background estimationcontrol regions for µµττ with selection: same sign and noisolation requirements for both the τ ′s (top), same sign andisolation for the highest pT τ (middle and lower left), same signand isolation on the second highest pT τ (middle and lowerright) for 2012 data and simulation. Middle (lower) plots areobtained with Medium (Tight) isolation working point for tau. 117

4.22 Data to simulation comparison for the background estimationcontrol regions for eeττ with selection: same sign and no iso-lation requirements for both the τ ′s (top), same sign and iso-lation for the highest pT τ (middle and lower left), same signand isolation on the second highest pT τ (middle and lowerright) for 2011 data and simulation. Middle (lower) plots areobtained with Medium (Tight) isolation working point for tau. 118

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4.23 Data to simulation comparison for the background estimationcontrol regions for eeττ with selection: same sign and no iso-lation requirements for both the τ ′s (top), same sign and iso-lation for the highest pT τ (middle and lower left), same signand isolation on the second highest pT τ (middle and lowerright) for 2012 data and simulation. Middle (lower) plots areobtained with Medium (Tight) isolation working point for tau. 119

4.24 Data to MC comparison for the τ fake rates as a function of τpT for the Medium (left) and Tight (right) isolation workingpoints with the resulting fit overlaid, for 2011 (upper) and2012(lower). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

4.25 Control region for the µµτµτh(left) and eeτµτh(right) for jet tomuon fake rate measurements when no isolation is applied onτµ, for data 2011 (upper) and 2012 (lower). . . . . . . . . . . . 123

4.26 Control region for the eeτeτh(left) and µµτeτh(right) for jet toelectron fake rate measurements when no isolation is appliedon τe, for data 2011 (upper) and 2012 (lower). . . . . . . . . . 124

4.27 Jet to electron fake rates as a function of electron pT for theLoose (upper) and Tight (lower) isolation working points, fordata 2011 (left) and 2012 (right). . . . . . . . . . . . . . . . . 125

4.28 Jet to muon fake rates as a function of muon pT for the Loose(upper) and Tight (lower) isolation working points, for data2011 (left) and 2012 (right). . . . . . . . . . . . . . . . . . . . 126

4.29 Invariant mass distribution for generated Higgs boson for Higgsmass of 600 GeV (left) and 1000 GeV (right). The line-shapesbefore (red) and after (blue) the CPS re-weighting are shown. 130

4.30 Invariant mass distribution for generated Higgs boson after(blue) the CPS re-weighting for Higgs mass of 600 GeV (left)and 1000 GeV (right). The alternative shapes to describe theline-shape uncertainties are also shown. . . . . . . . . . . . . . 131

4.31 Reconstructed llττ invariant mass distribution after (blue) theCPS plus interference re-weighting for Higgs mass of 600 GeV(left) and 1000 GeV (right). The alternative shapes to describethe line-shape uncertainties are also shown. . . . . . . . . . . . 131

5.1 Events display for a eeτeτh candidate events in 2012 data. . . . 1355.2 Events display for a eeτeτµ candidate events in 2012 data. . . . 1355.3 Visible l+l−τ+τ− invariant mass derived by using the 2011

only, the 2012 only statistics and combining combining the2011 and 2012 data and the MC selection. . . . . . . . . . . . 140

x

5.4 Distribution of the observed events in 2011 and 2022 data inthe plane (mZ1 ,mZ2). . . . . . . . . . . . . . . . . . . . . . . . 141

5.5 CLs limits on σ(95%)/σSM from combined τ final states with2011 data at

√s =7 TeV and 2012 data at

√s =8 TeV. . . . . 142

5.6 CLs limits on σ(95%)/σSM as a function of mH from the fourleptons final states: (upper) leptons being electrons and muonsonly, (lower) leptons being electrons, muons and taus collec-tively, with 2011 data at


√s =8

TeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1455.7 Significance of the local excess with respect to the SM back-

ground expectation as a function of mH with 2011 data at√s =7 TeV and 2012 data at

√s =8 TeV, for four leptons

final states: (upper) leptons being electrons and muons only,(lower) leptons being electrons, muons and taus collectively. . 146

xi

List of Tables

1.1 The fundamental fermions. . . . . . . . . . . . . . . . . . . . . 61.2 The boson mediators. . . . . . . . . . . . . . . . . . . . . . . . 7

2.1 List of the nominal LHC parameters, for proton-proton colli-sions, relevant for the detectors. . . . . . . . . . . . . . . . . . 27

3.1 The cross-section and the branching ratios for the SM Higgsboson decaying to 4l′ final states (l′ = e, µ, τ), for Higgsmasses 150, 200, 250 and 350 GeV at

√s = 8 TeV[19]. . . . . 49

3.2 The Cross-section and the branching ratios for the SM Higgsboson decaying to llττ and 4l (l = e, µ) final states, for Higgsmass 200 GeV at

√s = 8 TeV[19]. . . . . . . . . . . . . . . . . 49

3.3 Tau decay modes and branching ratios (h denotes a pion or akaon)[49]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.4 Monte Carlo simulation samples used for the signal and back-ground processes. The cross-section values for signal samples(gg → H and V V → H) are taken from Reference [19]. . . . . 68

4.1 Datasets corresponding to data collected by the CMS experi-ment in years 2011 and 2012. . . . . . . . . . . . . . . . . . . 78

4.2 HLT paths used to select the final sample of 2011 and 2012data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.3 Thresholds for the BDT discriminator to identify electrons[51]. 824.4 Cut-flow data to MC comparisons for µµτhτh final state, for

data 2011 and 2012 at√s = 7 (upper) and 8 TeV (lower)

respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1054.5 Cut-flow data to MC comparisons for eeτhτh final state, for


respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.6 Cut-flow data to MC comparisons for eeτeτh final state, for


respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

xii

4.7 Cut-flow data to MC comparisons for µµτeτh final state, fordata 2011 and 2012 at

√s = 7 (upper) and 8 TeV (lower)

respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.8 Cut-flow data to MC comparisons for µµτµτh final state, for


respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.9 Cut-flow data to MC comparisons for eeτµτh final state, for


respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.10 Cut-flow data to MC comparisons for eeτeτµ final state, for


respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1114.11 Cut-flow data to MC comparisons for µµτeτµ final state, for


respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124.12 Estimated ZZ backgrounds for all the eight final states. The

errors quoted here are only statistical. . . . . . . . . . . . . . . 1144.13 Estimate of reducible background in different categories and

the final estimate using 2011 and 2012 data. The numbers inthe parenthesis are number of events in each category. . . . . . 129

5.1 The estimated ZZ, reducible backgrounds and events observedin data at

√7 and 8 TeV, The number of signal events expected

for the SM Higgs boson with a mass of mH = 200 GeV is alsogiven. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.2 Expected Standard Model Higgs event yields for 5.1 and 12.2fb−1, taken from simulation in 2011 and 2012 respectively.Errors quoted are statistical only. . . . . . . . . . . . . . . . . 137

5.3 List of observed l+l−τ+τ− candidates and their properties in2011 and 2012 data. . . . . . . . . . . . . . . . . . . . . . . . 138

5.4 The expected and the observed upper limit on σ(95%CL)/σSM.143

xiii

Introduction

The curiosity to study the ultimate constituents of matter and the natureof interactions between them evolved with the evolution of universe formankind. Many of the theoretical and experimental insightful aspects ofnuclear and particle physics have accomplished during the twentieth centuryand the period is considered as the ‘golden period’ for these ancestor physicsto the High Energy Physics (HEP). It all started with ‘J.J. Thomson’ who,in 1897, identified electron as a particle. People knew that atoms existed (orat least they conjectured that they did, as chemists had made quite clear)and were considered as the smallest and indivisible constituent of matter butthey were surprised to find out that they were divisible. Thomson showedthat electron was about 2,000 times lighter than hydrogen ion, which wasthe lightest thing around. In 1911, the amazing results of the existence ofatomic nucleus came up from the α-particle scattering experimental set upby ‘Ernest Rutherford’. Then, in 1913, ‘Niels Bohr’ came up with his atomicmodel, where electrons move about the nucleus in circular orbits, separatedfrom each other like rungs in a ladder.

As the experiments became more sophisticated and probed matter athigher and higher energies, all sorts of elementary particles started to showup. A remarkable trade off between energy and matter was at play, the ex-pression of Einstein’s famous E = mc2 formula: if particles are acceleratedto very high energies, making the head on collisions, the energy of their mo-tion can transform and result into production of new particles which do notexist in nature in ordinary conditions. The rules that control these mattertransmutations are the most basic laws of nature, in the sense that totalamount of conserved quantity remains the same before and after the colli-sion: conservation of energy, conservation of electric charge, and a bunchof other conserved quantities. In a sense, these laws constitute the beingof modern physics, while the myriad material transmutations constitute thebecoming. By the 1970s, a model capturing all that was known in particlephysics emerged, known as the ‘Standard Model (SM)’.

1

The SM describes the fact that all the hundreds of particles discoveredduring the twentieth century are made of only twelve fundamental particles,six quarks (that make up protons, neutrons and hadrons) and six leptons(electron, muon, tau and their respective neutrinos), and the interactionsbetween those particles are mediated by the gauge bosons. The SM predic-tions are verified experimentally at particle accelerators with ever-increasingaccuracy. However, there is still a part of the puzzle missing. The SM is es-sentially a massless theory and it does not explain the mass of the particles.In 1964, the Belgian physicists ‘Robert Brout’ and ‘Francois Englert’, andthe Scotsman ‘Peter Higgs’ proposed a mechanism in which particles of theSM gain mass by interaction with so-called the Higgs field[1, 2]. The Higgsboson, quantum of the Higgs field, is not yet discovered and its observationis one of the main goals of Large Hadron Collider (LHC), built by EuropeanCentre for Nuclear Research (CERN), in Geneva.

Direct searches for the SM Higgs boson have been already performed atLarge Electron-Positron (LEP) collider and at the Tevatron proton-antiprotoncollider. A lower bound of Higgs mass, mH ≥ 114.4 GeV/c2 at 95% Confi-dence Level (CL), has been found at LEP[3], while the experiments DØ andCDF at Tevatron have excluded the mass range 100 ≤ mH ≤ 103 GeV/c2

and 147 ≤ mH ≤ 180 GeV/c2 at 95% CL[4].

The LHC recorded the first proton-proton collisions at centre of massenergy of

√s = 7 TeV on March 30th, 2010. Two general purpose experi-

ments were built at the point of proton-proton interaction, A Toroidal LHCApparatus (ATLAS) and Compact Muon Solenoid (CMS), to record and re-construct collisions with very high precision. These two experiments havebeen designed to cover a large spectrum of signatures in the LHC environ-ment and the search for the Higgs boson is the major guider criterion followedto define the requirements and performances of detectors. Both the Higgs-hunting experiments have observed an excess in their data, with a level ofcertainty worth a ‘discovery’. On July 4th, 2012, CERN announced the dis-covery of new boson of mass 125 GeV/c2 decaying to two Z bosons, andtwo photons and hence with spin different from one, and therefore called aHiggs-like particle[5, 6]. The most recent results of direct searches for theSM Higgs boson at the CMS experiment have been excluded the mass range100 ≤ mH ≤ 700 GeV/c2 with a small gap at low mass between 121 and 128GeV/c2[7], where a new boson has been discovered. The new boson withmass near to 125 GeV/c2 corresponds to a significance of 6.9σ with respectto the predictions for the backgrounds.

2

The content of this thesis is based on a physics analysis that has beenperformed to search for the SM Higgs boson which decays into two Z bosonswith the further decay of one Z boson into a pair of leptons (leptons beingelectrons or muons) and second Z boson into a pair of taus. It complementsthe H → ZZ(∗) → 4l (l = e, µ) analysis[8] above the kinematical thresh-old for the ZZ production. The data collected by the CMS experiment inyears 2011 and 2012 at center-of-mass energy of

√s = 7 and 8 TeV has been

used for this analysis. In the CMS environment, the Higgs search with lep-tons and taus in the final states is one of the promising searches because ofreasonable cross-sections and branching ratios, and dynamic performance ofelectromagnetic and hadron calorimeters that provides efficient leptons andtau reconstructions. Eight final states have been considered for this analysisby taking into account the hadronic (65%) and leptonic (35%) decays of taus.

The thesis is outlined as follows: the first chapter presents the brief in-troductory ideas about the theoretical basis of the SM and the spontaneoussymmetry breaking mechanism leading to the generation of Higgs boson. Thesecond chapter provides the overview of LHC and the CMS experiment. Inaddition, the SM Higgs boson production and decay modes are discussed.The third chapter provides the details about Monte Carlo (MC) event gen-eration, and reconstruction of physics objects used in this analysis (e, µ andτ). The analysis performed at the level of generator is also presented inthis chapter. In the fourth chapter, the analysis performed at the level ofreconstruction is presented which includes the event selection, estimation ofbackgrounds contributing in the signal phase space and the correspondingvalidation studies etc. The fifth chapter consists of the results obtained, interms of the final llττ invariant mass distributions and the exclusion up-per limits, and finally the conclusions. Moreover, the combined results ofH→ ZZ(∗) → 4l (l = e, µ, τ) decay channel are presented.

The material of the text has been compounded from advanced texts,review articles, and particularly from original papers. A short bibliographyis given at the end of the thesis for better understandings.

3

Chapter 1

The Standard Model and theHiggs Boson

The Standard Model (SM), formulated in 1970s, accounts all the experimen-tal data from high energy experiments. It was first described by SheldonGlashow, in 1960, to unify the electromagnetic and weak interactions[9],postulating SU(2)× U(1) symmetry on basis of the accepted theory of elec-troweak interaction1. For this discovery, Glashow was awarded with theNobel Prize in Physics, in 1979, along with Steven Weinberg and AbdusSalam who formulated the same theory independently in 1967 and 1968respectively[10, 11]. This chapter provides a brief introduction starting withelementary particles and the interaction between them followed by Glashow-Weinberg-Salam (GWS) model of electroweak interactions. Some useful theo-retical informations are given for better understanding of GWS model: spon-taneous symmetry breaking and the Higgs mechanism. Last part of the chap-ter is focused on the Higgs physics at hadron colliders.

All the treatise presented in the following sections is sourced from [12],[13] and [14]. It is important to note that the natural units, i.e. c = h = 1,are used, unless otherwise specified.

1The SM, in actual, is a non-abelian gauge theory with the symmetry group U(1) ×SU(2) × SU(3) and has a total of twelve gauge bosons: photon, three weak bosons andeight gluons. Where U(1), SU(2) and SU(3) describes electromagnetic, weak and stronginteractions respectively. In this chapter, SU(2) × U(1) symmetry is described whichexplains the Higgs boson hypothesis.

5

1.1. The Standard Model of Elementary Particles 6

1.1 The Standard Model of Elementary Par-

ticles

The SM states that all matter is built from a small number of fundamen-tal spin 1

2particles, or fermions: six quarks and six leptons. For each of

the various fundamental constituents, its symbol and the ratio of its electriccharge Q to the elementary charge e of the electron are given in Table 1.1.The leptons, e for ‘electron’, µ for ‘muon’ and τ for ‘tau’, carry unit negativecharge and the mass increases as we move from left to right in the table. Theneutral leptons are called neutrinos, denoted by ν and the different flavourof neutrinos is paired with different flavour of charged lepton, as indicatedby the subscript. The neutrinos were postulated by Pauli, in 1930, in orderto describe the energy measurements of nuclear β-decay. On the other hand,the up (u), down (d), strange (s), charm (c), bottom (b) and top (t) quarkscarry the fractional charges, of ±2

3e and ±1

3e, and exist only in the composite

states such as proton (uud) and neutron (ddu).

Table 1.1: The fundamental fermions.

Particle Flavour Q/|e|

leptonse µ τ –1νe νµ ντ 0

quarksu c t +2/3d s b –1/3

The SM is a quantum field theory which treats the interactions betweenthe fermion constituents in terms of an exchange of vector bosons whichare integral-spin particles, listed in Table 1.2 (the gravitational interactionis not taken into account as it is not relevant at the scales of mass anddistance typical of the particle physics). The electromagnetic interactions aremediated by massless particles called photon, denoted by γ. The masslessgluons, denoted by g, are responsible for the strong interactions. The weakinteractions occur due to exchange of two massive vector bosons: W± and Zhaving mass ∼ 80 and ∼ 90 GeV respectively. Figure 1.1 illustrates all theseinteractions along with the Higgs boson, denoted by H, which endows massto the weak interaction mediators, which we will later see in Section 1.3.

1.2. Spontaneous Symmetry Breaking and the Higgs Mechanism 7

Table 1.2: The boson mediators.

Interaction Mediators Spinparity

strong gluon, g 1−

electromagnetic photon, γ 1−

weak W±, Z0 1−, 1+

Figure 1.1: Summary of the interactions between the constituents of the SM@wikipedia.

1.2 Spontaneous Symmetry Breaking and the

Higgs Mechanism

The generation of the masses of electroweak gauge bosons is called the elec-troweak symmetry breaking (EWSB) and understanding this EWSB mech-anism is one of the primary goals of the Large Hadron Collider (LHC). Inthe SM, the electroweak symmetry breaking is achieved via the Higgs mecha-nism, based on the idea of spontaneous symmetry breaking. In this section, abrief detail of the spontaneous symmetry breaking and the Higgs mechanismis presented.

Let us start by taking a most general Lagrangian, L, for a complex scalarfield φ = (φ1 + iφ2)/

√2 with mass m, given by

L = T − V = (∂µφ)∗(∂µφ)−m2φ∗φ− λ(φ∗φ)2 (1.1)

where λ is a dimensionless constant which is representing the coupling


of four-particle vertex. This Lagrangian is invariant under the global U(1)symmetry: φ→ eiθφ.

For m2 < 0 and λ > 0, the potential V (φ) = m2φ∗φ + λ (φ∗φ)2 gives the

minimum at |φ(x, t)| =√−m2

2λfor all space x, and time t. For m2 > 0, the

potential gives a minimum at 0, if the self-coupling λ is positive. The shapeof the potential for m2 < 0 looks like a wine bottle or Mexican hat as shownin Figure 1.2.

Figure 1.2: The potential V (φ) for a complex scalar field, for m2 < 0 andλ > 0.

It is important to note that there is a continuous circle of minima inφ1, φ2 plane. Physically, this means that the ground state of our system hasinfinite degeneracy. And of course, we have the right to arbitrarily choose oneof them as our ground state, say Re(φ) = φ1 = µ√

2λand Im(φ) = φ2 = 0,

by considering µ2 = −m2. Hence we have the ground state (the vacuumexpectation value) of the field φ, given by

〈φ〉0 =µ√2λ≡ v√

2(1.2)

by taking v = µ/√λ. Furthermore in the weak interactions, we are

concerned with the small evaluation of perturbation about energy minimum,


and therefore introducing the variation around the ground state, we write

φ =1√2

(η + v)eiξ/v (1.3)

where η(x, t) and ξ(x, t) are the fluctuation fields, with 〈η〉0 = 0 and〈ξ〉0 = 0.

Thus the Lagrangian given by equation 1.1 becomes

L =1

2(∂µη∂

µη + ∂µξ∂µξ) +

1

v2(η2 + 2ηv)∂µξ∂

µξ

− λv2η2 − 1

4λ(η4 + 4η3v) +

1

4λv4 (1.4)

The third term has the form of a mass term (−12m2ηη

2) for the η-field.

We can find that the mass for the η-field is mη =√

2λv2 (=√−2m2), and

the mass for the ξ-field is mξ = 0. Hence we get a massless particle whichcorresponds to the Goldstone boson described by the Goldstone theorem2.Furthermore, the appearance of mass term for the η-field is spoiling thegauge-invariance property of the global U(1) symmetry because gauge sym-metry prohibits the generation of mass for the vector field. This behavior iscalled spontaneous symmetry breaking.

1.2.1 The Higgs Mechanism

Since the Goldstone boson is massless, but almost all the particles in thenature are massive except the photons and the neutrinos. Hence the obviousquestion would be that what is the goodness for the Goldstone boson? Theanswer is that it endows the mass to the gauge bosons by the Higgs mecha-nism.

In order to demonstrate, we need to study spontaneous symmetry break-ing of a local gauge U(1) symmetry. The Lagrangian for a complex scalarfield which is invariant under the local U(1) transformation φ → eiθ(x)φ, isgiven by

L = (Dµφ)∗(Dµφ) + µ2φ∗φ− λ (φ∗φ)2 (1.5)

where Dµ = ∂µ − ieAµ is the covariant derivative with gauge field, Aµ,

2The Goldstone theorem related to the symmetry breaking states that every brokengenerator of a symmetry group has a corresponding massless (spin-0) Goldstone boson.

1.3. Glashow-Weinberg-Salam Model 10

which transforms as

Aµ → Aµ +1

e∂µθ (1.6)

Since the chosen minimum point of the potential is at 〈φ〉0 = v√2, we can

again write

φ =1√2

(η + v)eiξ/v (1.7)

where ξ = ξ(x) is the Goldstone field. Let θ(x) = ξ(x)v

, the kinetic termin Lagrangian becomes

(Dµφ)∗(Dµφ) =1

2(∂µ + ieAµ)(η + v)(∂µ − ieAµ)(η + v)

=1

2∂µη∂

µη +1

2e2v2AµA

µ +1

2e2(η2 + 2ηv)AµA

µ

(1.8)

Therefore we have eliminated the Goldstone field ξ by talking the advan-tage of gauge invariance. In other words, the Goldstone boson is eaten bygauge field and does not appear in the theory. It implies that we have

φ =1√2

(η + v)eiξ/v → 1√2

(η + v) (1.9)

Moreover from equation 1.8, we can see that the gauge field (photon) hasacquired a mass mA = ev. Indeed, ξ-field has come back as the helicity zerocomponent of the massive photon:

Aµ → Aµ +1

ev∂µξ since θ =

ξ

v(1.10)

Therefore our Lagrangian describes two interactive massive particles: avector gauge boson Aµ and a massive scalar η. The later is called the Higgsparticle. This mechanism, by which the spontaneous symmetry breakinggenerates a mass for a gauge boson, was explored and generalized to thenon-abelian case by Higgs, Kibble, Guralnik, Hagen, Brout and Englert, andis known as the Higgs mechanism.

1.3 Glashow-Weinberg-Salam Model

In 1960, Glashow worked out the case for the SU(2)×U(1) gauge theory[9],but he did not get the mass for W and Z bosons. In 1967, 68, Weinberg andSalam applied the Higgs mechanism to the SU(2)×U(1) gauge theory[10, 11].


They claimed the unification of weak and electromagnetic interactions.

The Lagrangian for GWS model is

L = (Dµφ)†Dµφ+ µ2φ†φ− λ(φ†φ)2

(1.11)

where Dµφ = (∂µ + igT aAaµ + ig′ Y

2Bµ)φ. T a (with a = 1, 2, 3) and Y

are the generators of SU(2) (corresponds to weak isospin interactions withcoupling constants g) and U(1) (corresponds to weak hypercharge interac-tions with coupling constants g′) symmetry groups respectively. Aaµ (witha = 1, 2, 3) and Bµ are the gauge fields corresponding to SU(2) and U(1)symmetry groups respectively.

Furthermore, to keep the Lagrangian invariant, the four real fields φi(corresponding to W±, Z and photon) must belong to SU(2)×U(1) multiplet.In 1967, Weinberg made a choice to arrange them in an isospin doublet withweak hypercharge Y = 1:

φ =

(φ+

φ0

)=

1√2

(φ1 + iφ2

φ3 + iφ4

)(1.12)

Moreover due of the infinite degeneracy of appropriate ground state, wecan arbitrarily choose

〈φ〉0 =

(0

v/√

2

)(1.13)

Next step is to look for the broken generators. The SU(2) group genera-tors for spin 1

2particle can be expressed as Pauli matrices: T a = 1

2σa. Then

we have

1

2σ1 〈φ〉0 =

(0 1/2

1/2 0

)(0

v/√

2

)=

(v/2√

20

)6= 0

1

2σ2 〈φ〉0 =

(0 −i/2i/2 0

)(0

v/√

2

)=

(−iv/2

√2

0

)6= 0

1

2σ3 〈φ〉0 =

(1/2 00 −1/2

)(0

v/√

2

)=

(0

−v/2√

2

)6= 0

I 〈φ〉0 =

(1 00 1

)(0

v/√

2

)=

(0

v/√

2

)6= 0 (1.14)

Hence all the generators are broken in GWS model. But since 〈φ〉0 isneutral, the electroweak U(1) symmetry with generator Q remains unbroken,


i.e.

Q = T 3 +Y

2=

(1

2σ3 +

1

2I

)(0

v/√

2

)= 0 (1.15)

The vacuum is thus invariant under U(1)em transformations and the pho-ton remains massless. Now there are three broken generators:

T 1 =1

2σ1; T 2 =

1

2σ2; T 3 − Y

2=

1

2σ3 − 1

2I (1.16)

And hence there are three Goldstone bosons in GWS model which gen-erates massive gauge bosons.

Introducing the variation around the ground state, we can rewrite thefield as

φ =1√2

(H + v)e[iT 1ξ1+iT 2ξ2+i(T 3−Y2

)ξ3]

(01

)(1.17)

Then we can take advantage of the gauge invariance and eliminate thethree Goldstone bosons ξ1, ξ2 and ξ3, i.e.

φ→ 1√2

(H + v)

(01

)(1.18)

Taking the relevant term of the original Lagrangian and using equation1.18, we obtain

L =1

8[(−gA3

µ + g′Bµ)2 + g2(A1

µA1µ + A2

µA2µ)](H + v)2 (1.19)

So the fields A1µ and A2

µ have acquired a mass, given by

m2A1 = m2

A2 =1

4g2v2 ≡ m2

W (1.20)

This gives the mass for the W bosons, which is generated by the gaugefields W±

µ , given by

W±µ =

1√2

(A1µ ∓ iA2

µ) (1.21)

We can also find that the field −gA3µ+g

′Bµ has also acquired a mass. To

find the mass of this field, we first need to normalize the field:

Zµ =1√

(g2 + g′2)(gA3

µ − g′Bµ) (1.22)


where the normalization factor comes from 〈Zµ |Zv〉 = δµv. Then theLagrangian can be written in terms of Zµ field,

L =1

8[(g2 + g

′2)ZµZµ + g2(A1

µA1µ + A2

µA2µ)](H + v)2 (1.23)

This implies that the field Zµ acquires a mass

m2Z =

1

4(g2 + g

′2)v2 > m2W (1.24)

However, the orthogonal combination field Aµ = 1√(g2+g′2)

(g′A3µ + gBµ),

it has no mass term and corresponds the photon in GWS model!

Therefore we illustrate the details about how the massive particles emergethough the spontaneous symmetry breaking in the GWS model. The gaugefield A1

µ, A2µ and Zµ have eaten the Goldstone bosons ξ1, ξ2 and ξ3 to acquire

the mass of W± and Z bosons. And one Goldstone boson still remains mass-less interpreted as photon.

We can also see that both photon and Z boson are linear combination ofA3µ and Bµ fields. Thus we can write this in matrix form:(

ZµAµ

)=

(cos θw − sin θwsin θw cos θw

)(A3µ

Bµ

)(1.25)

where cos θw = g√(g2+g′2)

and sin θw = g′√(g2+g′2)

. θw is called weak mixing

angle, also known as the Weinberg angle.

Using equations 1.21 and 1.24, we can relate the mass of W boson andthe mass of Z boson by the weak mixing angle, i.e.

mW = mZ cos θw (1.26)

Furthermore using equations 1.19 and 1.23, the couplings of vector bosonsto the Higgs field, can be given by

gHW =1

2vg2 =

2

vm2

W (1.27)

gHZ =1

2v(g2 + g

′2) =2

vm2

Z (1.28)


and hence the ratio of decay of H→WW to H→ ZZ would be

BR(H→W+W−)

BR(H→ ZZ)=

(gHW

1/2gHZ

)2

= 4

(m2

W

m2Z

)2

∼ 2.4 (1.29)

Moreover, through spontaneous symmetry breaking, also the fermionsacquire a mass proportional to the vacuum expectation value of the Higgsfield. We can get the fermion masses and coupling with the Higgs field byconsidering the Yukawa interactions, given by

mf =GHf√

2v (1.30)

gHf =GHf√

2=mf

v(1.31)

where GHf is a free parameter. Hence the mass of the fermions cannotbe predicted by the theory.

Equations 1.21 and 1.24 relate the W and Z boson masses to some basicparameters: g, g

′, −µ2 and λ of the theory. Remarkably, these relations

allow the masses of W boson and the Z boson to be determined in term ofthree experimentally well known quantities:1) Fine structure constant: α = e2/4π = 1/137.042) Fermi coupling constant: GF = 1.66× 10−5 GeV−2

3) weak mixing angle: θw.

The parameter v, the Higgs vacuum expectation value can be expressedin terms of GF as v = (GF

√2)−1/2 ' 246 GeV. And the parameters g and

g′

can be expressed in terms of electric charge and weak mixing angle asg sin θw = g

′cos θw = e. Therefore the mass of W and the Z bosons can be

interpreted as a function of the basis physical quantities:

mW =

(απ

GF

√2

)1/21

sin θw; mZ =

(απ

GF

√2

)1/22

sin 2θw(1.32)

Historically, these equations were used to predict the masses of the W±

and Z bosons using the value of θw obtained from the neutrino scatteringexperiment: νµ + e− → νµ + e−.

1.4. The Higgs Mass 15

1.4 The Higgs Mass

In the SM, the Higgs boson is the only particle which has not been discoveredso far and hence the Higgs mass is the undetermined one. It depends on v andhence on λ. The former has already been calculated in terms of the Fermicoupling constant but the later is characteristic of the φ-field and cannotbe determined other than measuring the Higgs mass itself. However, boththeoretical and experimental constraints exist, including those from directsearch at colliders, in particular at Large Electron-Positron (LEP) collider.

1.4.1 Theoretical Constraints

The theoretical constraints[15] to the Higgs mass have been set by impos-ing the cut-off energy scale Λ, in terms of the validity of the perturbationtheory and we expect non-standard physics after it breaks down. The upperand the lower bounds on the Higgs mass as a function of the Λ are givenin Figure 1.3. The lower bound originates from the requirement of runningquartic coupling λ to be positive. In other words the φ potential field shouldbe bounded even after the inclusion of radiative corrections, at least up toa certain value on Λ scale. The minimum of such a potential is an absoluteminimum (vacuum stability). Furthermore, the stability lower bound canbe released by allowing metastability of the ground state, instead of requir-ing its absolute stability, provided the life-time of the metastable vacuum islarger than the age of the universe, ∼ 1010 years. Instead the upper bound isfound by requiring that the running quartic coupling of the Higgs potentialλ remains finite up to certain value on Λ scale, i.e. µ < Λ (triviality), andafter that the λ leaves the perturbative regime. The triviality upper boundobtained imposing the conditions λ < 1 and λ < 10 are shown in Figure 1.3.

For a cut-off scale of the order of Planck energy scale (Λ ∼ 1019) GeV,the Higgs mass is required to be in the range 130 < mH < 190 GeV. If newphysics appears at lower mass scales, the bound becomes weaker, e.g. forΛ = 1 TeV, the Higgs mass is constrained to be in the range 50 < mH < 800GeV. On the basis of the present theoretical knowledge, the Higgs sector inthe SM remains largely unconstrained. While there is no direct predictionfor the mass of the Higgs boson, an upper limit of ∼ 1 TeV can be inferredfrom the unitarity arguments[16].

1.4. The Higgs Mass 16

Figure 1.3: The upper and the lower bounds on the Higgs mass as a functionof the cut-off energy scale Λ[15].

1.4.2 Experimental Constraints

Since the time of the SM theory has come up, several experimental effortshave been carried out, till now, to discover the Higgs boson and hence mea-sure its mass. The direct search at LEP has led to a lower bound on its massof 114.4 GeV at 95% Confidence Level (CL)[3]. Indirectly, high precisionelectroweak data constrains the mass of the Higgs boson via their sensitivityto the loop corrections. Assuming the overall validity of the SM, a globalfit[17] to all the precision electroweak measurements performed by the fourexperiments at LEP, and by SLD, CDF and DØ[4] (nowadays updated withthe LHC measurements) leads to the results, given in Figure 1.4. The solidcurve is the result of the fit, while the shaded band represents the theoreticaluncertainty due to unknown higher order corrections.

The preferred value for its mass corresponding to the minimum of thecurve, is mH = 94+29

−24 GeV (at 68% CL derived from ∆χ2 = 1 for the blackline, thus not taking the theoretical uncertainty shown as the blue band intoaccount). The precision electroweak measurements tell us that the mass ofthe Higgs boson is lower than about 152 GeV (one-sided 95% CL upper limitderived from ∆χ2 = 2.7 for the blue band, thus including both the exper-imental and the theoretical uncertainty). This limit increases to 171 GeVwhen including the LEP-2 direct search limit of 114 GeV shown in yellow.

The Tevatron experiments, CDF and DØ, also search for the Higgs boson

1.5. The Higgs Search at LHC 17

0

1

2

3

4

5

6

10040 200mH [GeV]

2

LEPexcluded

LHCexcluded

had =(5)

0.02750±0.000330.02749±0.00010incl. low Q2 data

Theory uncertaintyMarch 2012 mLimit = 152 GeV

Figure 1.4: ∆χ2 of the fit to the electroweak precision measurements of LEP,SLC, Tevatron and LHC as a function of the Higgs mass (March 2012). Thesolid line represents the result of the fit and the blue shaded band is thetheoretical error from unknown higher order corrections. The yellow arearepresents the region excluded by direct search.

and the most recent combined result excluds the mass range of 100 ≤ mH ≤103 GeV and 147 ≤ mH ≤ 180 GeV at 95% CL[4]. Moreover, the CMSexperiment at LHC have excluded a Higgs mass range of 100 ≤ mH ≤ 700GeV with a small gap at the low mass between 121 and 128 GeV [7].

1.5 The Higgs Search at LHC

The LHC, also designated as the Higgs discovery machine, is running for theHiggs hunting since the first collision on March 30th, 2010. A brief detailof LHC is given in next chapter. In this section, the Higgs production andthe decay processes in proton-proton collision at LHC are detailed. The pro-duction cross-sections and decay branching ratios at center-of-mass energy,√s = 7 TeV and 8 TeV associated with the uncertainties are also given. All

the information leads to the knowledge of the most promising channels atLHC for the discovery of the Higgs boson.


1.5.1 The Higgs Production

The main processes contributing to the Higgs production at a hadron colliderare represented by the Feynman diagrams, given in Figure 1.5. The cross-sections for the production modes parametrized in mH, are given in Figure1.6.

(a) (b)

(c) (d)

Figure 1.5: The SM Higgs production modes at LHC: (a) gluon-gluon fu-sion; (b) vector boson fusion; (c) W and Z associated production (or Hig-gsstrahlung); (d) tt associated production.

Gluon-Gluon Fusion

Among all the Higgs production mechanisms at LHC, the gluon-gluon fusionis dominant over the whole mass range due to the high luminosity of gluonsin proton-proton collisions. The process is shown in Figure 1.5a, which isperformed via a top quark triangular loop. Next-to-leading order (NLO)QCD corrections have been found to increase the cross-section for this processby a factor of ∼ 2. Next-to-next-to-leading order (NNLO) calculations arealso available and show a further increase of about 10–30%. There is about10–20% uncertainty on the cross-section of the Higgs boson from gluon-gluon


[GeV] HM100 200 300 400 500 1000

H+X

) [pb

]

(pp

-210

-110

1

10= 7 TeVs

LHC

HIG

GS

XS W

G 2

010

H (NNLO+NNLL QCD + NLO EW)

pp

qqH (NNLO QCD + NLO EW)

pp

WH (NNLO QCD + NLO EW)

pp ZH (NNLO QCD +NLO EW)

pp

ttH (NLO QCD)

pp

[GeV] HM80 100 200 300 400 1000

H+X

) [pb

]

(pp

-210

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1

10

210= 8 TeVs

LHC

HIG

GS

XS W

G 2

012

H (NNLO+NNLL QCD + NLO EW)

pp

qqH (NNLO QCD + NLO EW)

pp

WH (NNLO QCD + NLO EW)

pp ZH (NNLO QCD +NLO EW)

pp

ttH (NLO QCD)

pp

Figure 1.6: The SM Higgs boson production cross-sections at√s = 7 TeV

(upper) and 8 TeV (lower)[18, 19, 20].

fusion mostly due to the parton density function, and it is shown by the blueband in Figure 1.6.

Vector Boson Fusion

The vector boson fusion (VBF) is the second dominant process of the Higgsboson production (shown in Figure 1.5b) with its cross-section of about afactor of 10 smaller than the gluon-gluon fusion production mode in mostof the Higgs mass regions. The cross-sections of the two production modesbecome comparable only for very high Higgs masses (∼ 1 TeV). However,this channel is very interesting because of its clean experimental signaturedue to the presence of two forward jets in the large pseudo-rapidity regions


with high invariant mass. It has an advantage in terms of suppressing morebackgrounds and hence increasing the signal over background ratio, despiteof the low cross-section. Moreover, both leading order (LO) and NLO cross-sections for this production mode are known with the small uncertainties andthe higher order QCD corrections, ∼ 10%, shown in Figure 1.6 by the redband.

Associated Production

In the associated production mode, or the Higgsstrahlung process, shownin Figure 1.5c, the Higgs boson is produced in association with a W± or Zboson. The cross-section for this process is several orders of magnitude lowerthan the gluon-gluon and the VBF production modes. The QCD correctionsare quite large and the NLO cross-section result in the increase of the cross-section by a factor of 1.2–1.4 with respect to the LO cross-section. There isabout 20–25% uncertainty for this production mode.

The last production mode is illustrated in Figure 1.5d. It is the associatedproduction of a Higgs boson with a tt pair and the cross-section is about 100times less than the gluon-gluon fusion. But the presence of the tt pair inthe final state can provide a good experimental signature. The higher ordercorrections increase the cross-section by a factor of about 1.2.

1.5.2 The Higgs Decay

The branching ratios of the different Higgs decay channels are shown in Fig-ure 1.7 as a function of mH. Regarding the mass, the Higgs decay processesare divided into the complementary low, intermediate and the high mass re-gions. In the low mass region (up to ∼ 130 GeV), the Higgs boson decayinginto fermions is dominating process, in particular, the H→ bb channel, sincethe b quark is the heaviest fermion. In the intermediate region, the Higgsboson decays into vector boson pairs dominate. A peak in the H→W+W−

decay is visible around 160 GeV, where the production of two on mass-shellW bosons become possible and the production of a real ZZ pair is still notallowed. At high masses (∼ 350 GeV), also tt pairs can be produced. In-deed, the most promising decay channels for the Higgs discovery do not onlydepend on the corresponding branching ratios, but also on the capability ofexperimentally detecting the signal while rejecting the backgrounds. Suchchannels are illustrated in this section.


[GeV]HM100 200 300 400 500 1000

Higg

s BR

+ T

otal

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ert

-310

-210

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HIG

GS

XS W

G 2

011

bb

cc

ttgg

Z

WW

ZZ

Figure 1.7: The branching ratios for the different Higgs decay channels as afunction of mH[19, 20].

Low Mass Region

In the low mass range, mH < 130 GeV, there are two important decay pro-cesses:

• The Higgs decays into bb, it has the highest branching ratio but theQCD di-jet background makes it quite difficult to use this channelfor the Higgs discovery. The only feasible search for the Higgs bosonin this decay mode is the Higgs production in association with thevector boson, decaying leptonically. The final-state leptons allow todiscriminate signal events from QCD backgrounds with only two jets.

• The Higgs decays into two photons, it has a much lower branchingratio but the two high energy photons constitute a very clean signaturewith only very few backgrounds, mainly from qq → γγ and Z→ e+e−.Assuming that the Higgs boson exists in this region, the mass can bemeasured with high precision using this decay channel.

Intermediate Mass Region

In this mass range from 130–180 GeV, the decay of Higgs boson into a pair ofW, and Z bosons are the main processes. The branching ratio of H→WW(∗)

is always higher than H → ZZ(∗), particularly in the mass regions between2mW and 2mZ, where the Higgs boson can decay into two on mass-shell Wbosons (with BR ∼ 1) and can not decay to two on mass-shell Z bosons. Thefollowing are the two best channels in this mass region:


• H→WW(∗) → 2l2ν, it is the most promising channel because of verylow background. However, due to the presence of neutrinos in thefinal states, it is impossible to reconstruct the Higgs mass with highprecision.

• H → ZZ(∗) → 4l, it is also important in this region. Despite of itslower branching ratio, it is very important channel since it offers a veryclean experimental signature with a very high signal to backgroundseparation power. Furthermore, it allows to reconstruct the Higgs masswith high precision. Therefore this channel has always played a majorrole for the Higgs discovery in this mass range.

High Mass Region

This region corresponds to the Higgs mass values above the 2mZ threshold,mH > 180 GeV, where the Higgs boson can decay either into two real Z, andW bosons. Despite of the fact that the branching ratio of H → ZZ is lowerthan the H → WW but, in particular, H → ZZ → 4l is the most importantdecay channel in this region and considered as the ‘golden channel’ for theHiggs discovery since it provides a clean signature with low background. Inaddition, the 2l2q, 2l2ν and 2l2τ decay channels also become important inthis range.

1.5.3 The Higgs Total Decay Width

The total decay width of the Higgs boson which is given by the sum over allthe possible decay channels, is shown in Figure 1.8. The total decay widthis very narrow in the low mass range, ΓH < 10 MeV, but the width becomesrapidly wider for masses larger than 130 GeV, and reaches to about 1 GeVslightly above the ZZ threshold. The low mass range is therefore the mostchallenging region, because the total decay width is dominated by the exper-imental resolution.

In the high mass region, the total decay width comprises of the ZZ andthe WW partial widths, given as

Γ(H→W+W−) =g2

64π

m3H

m2W

√1− xW

(1− xW +

3

4x2

W

)(1.33)

Γ(H→ ZZ) =g2

128π

m3H

m2Z

√1− xZ

(1− xZ +

3

4x2

Z

)(1.34)


where

xW =4m2

W

m2H

; xZ =4m2

Z

m2H

(1.35)

For the higher Higgs masses, decay width is comparable to its mass sinceit is proportional to m3

H. For mH ∼ 1 TeV, one has a total decay width ofΓH ∼ 700 GeV that results in a very broad resonant structure.

Figure 1.8: The SM Higgs boson total decay width as a function of mH[20].

Chapter 2

Large Hadron Collider and theCMS Experiment

2.1 Large Hadron Collider at CERN

The Large Hadron Collider (LHC)[21, 22], the largest and highest energyparticle accelerator ever built, with its 27 km in circumference, runs underthe border between France and Switzerland, at the European Organizationfor Nuclear Research (CERN) laboratory. By colliding the hadrons, LHCrecreates the conditions hypothesized to have existed after the big bang.Worldwide scientists are working in this project and expect it to aid ourunderstanding of how the universe came into being and to show much aboutthe SM and the physics beyond it.

LHC is $7.7 billion project consists of a chain of several accelerators,which are needed to reach its final center-of-mass energy. Figure 2.1 showsa schematic view of the accelerator complex which provides protons for theLHC.

The acceleration of protons starts from a LINear ACcelerator 2 (LINAC2)which obtains the proton beams by stripping the electrons from hydrogenatoms, injects the protons traveling with one third of speed of light to theProton Synchrotron Booster (PSB). The PSB squeezes the proton bunch andthe energy reaches to 1.4 GeV and the velocity of beam reaches up to about91.6% of the speed of light. In the next step, in the Proton Synchrotron(PS), the protons circulate for 1.2 seconds and the energy reaches to 25 GeVand obtain their final bunch structure. The speed of the beam reaches about99.9% of the speed of light. At this point, the transition occurs and the

24

2.1. Large Hadron Collider at CERN 25

Figure 2.1: The LHC accelerator complex.

further increase in energy results in the increase in the mass of protons andthey become 25 times heavier than the rest mass. Before the bunches arelaunched into the orbit of the gigantic LHC ring, they are accelerated toacquire the energy of 450 GeV, in the Super Proton Synchrotron (SPS).

The LHC ring contains two vacuum pipes containing the proton beams,traveling in the opposite directions. Finally, the proton beams will be ac-celerated to a center-of-mass energy of 7 TeV (in the nominal case)1. Thevelocity at this stage is so near to the speed of light, resulting in a totalenergy of 362 MJ stored per beam. A high technology magnet system allowsthe beams to reach the nominal energy, consists of a total of about 9600 mag-nets. By means of ultra sophisticated kickers, the incoming proton bunchesare synchronized. 1232 super-conducting dipole magnets with a magneticfield of 8 T are used to keep the protons within the ring. Furthermore, 858quadrupole magnets are used as the magnetic lenses for focusing and correct-ing the beams. The counter rotating beams cross-over in the four detecter

1The operational energy for LHC during the years 2011 and 2012 was 7 TeV and 8 TeV(3.5 TeV and 4 TeV per beam) respectively for proton-proton collision.


caverns, where they could be made to collide: the four main experimentsATLAS, CMS, ALICE and LHCb, are located at the four interaction regionsin the LHC ring, shown in Figure 2.2. The energy of the collision is doublethan that of the individual opposing protons and the collisions are trackedin the detectors. Two general purpose detectors, CMS and ATLAS, are de-signed specifically for the Higgs boson search within the SM context, andfor physics beyond it. While LHCb and ALICE are designed to study theproperties of b-meson and the heavy ion collisions1, respectively.

Figure 2.2: Schematic layout of LHC with clockwise-beam (red) and anticlockwise-beam (blue).

1LHC also permits the collisions of heavy ions.


2.1.1 Performance Goals

The list of the nominal LHC parameters is given in Table 2.1. At the nomi-nal center-of-mass energy,

√s = 14 TeV, the designed luminosity is L = 1034

cm−2s−1 for the CMS and ATLAS experiments, and the goal is to collect thetotal integrated luminosity of 3000fb−1, in the total life of the experiments.

The machine luminosity, considering the gaussian beam distribution, isgiven by

L =γfkBN

2P

4πεnβ∗F (2.1)

where γ is the relativistic gamma (Lorentz) factor, f is the revolutionfrequency, kB the number of bunches per beam, Np is the number of pro-tons per bunch, εn is the normalized transverse beam emittance, β∗ is theβ-function at the collision point and F is the geometric luminosity reductionfactor due to the crossing angle at the interaction point.

Plots given in Figure 2.3 represents the total integrated luminosity deliv-ered by LHC and recorded by the CMS experiment in year 2011 (from 13thMarch to 30th October) while running at center-of-mass energy of 7 TeV, andyear 2012 (from 4th April to 13th October) while running at center-of-massenergy of 8 TeV (nominal energy is not yet achieved by LHC).

Table 2.1: List of the nominal LHC parameters, for proton-proton collisions,relevant for the detectors.

LHC Parameters Nominal ValuesCircumference 26.659 kmCenter-of-mass energy (

√s) 14 TeV

Nominal Luminosity (L) 1034 cm−2s−1

Luminosity life-time 15 hrs.Time between two bunch crossings 24.95 nsDistance between two bunches 7.48 mLongitudinal max. size of a bunch 7.55 cmNumber of bunches (nb) 2808Number of protons per bunch (Nb) 1.15× 1011

beta function at impact point (β?) 0.55 mTransverse RMS beam size at impact point (σ?) 16.7 µmDipole field at 7 TeV (B) 8.33 TDipole temperature (T) 1.9 K


Figure 2.3: Integrated luminosity recorded by the CMS experiment (left) andthe instantaneous luminosity (right) at

√s = 7 TeV in year 2011 (upper) and√

s = 8 TeV in year 2012 (lower).

2.1.2 Number of Events at LHC

The number of events per second of a given physics process is related to thecross-section of the corresponding process and the machine luminosity L, isgiven by

N = σ × L (2.2)

where σ is the the cross-section for the particular process. Figure 2.4shows the predictions for some important SM cross-sections at proton-antipr-oton and proton-proton colliders, calculated at NLO in perturbation theory.It also shows the cross-section for the Higgs boson production of mass 125GeV, via three possible production processes discussed in chapter 1: gloun-gluon fusion, vector boson fusion and associated production, at L = 1033

cm−2s−1. It is clear that the production of a Higgs boson is several or-


ders of magnitude less than the total inelastic cross-section which increasessignificantly with the increase in center-of-mass energy. One expects the pro-duction of Higgs boson of mass 125 GeV about every 10 seconds at nominalcenter-of-mass energy of LHC.

0.1 1 1010

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σσσσjet

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eve

nts

/ s

ec f

or L

= 1

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proton - (anti)proton cross sections

σσσσW

σσσσZ

σσσσt

σ

σ

σ

σ

(( ((nb

)) ))

√√√√s (TeV)

Figure 2.4: Expected cross-section vs energy at proton-antiproton andproton-proton colliders.

2.2. The Compact Muon Solenoid Experiment 30

2.2 The Compact Muon Solenoid Experiment

The Compact Muon Solenoid (CMS)[23] experiment is located approximatelyabout 330 feet underground in Cessy, France. The general purpose detectorhas been built to explore the new physics at TeV energy scale. Figure 2.5shows the schematic of the CMS detector, which has an overall length of 21.6m, a radius of 7.5 m and a total weight of 12,500 ton. It is composed by acentral barrel and two closing endcaps. It consists of several sub-detectors toidentify precisely the different particles produced in the collisions that leadsto the full event reconstruction. In this section, an overview of the CMSdetector components is presented which leads to the better understanding ofoperation of the detector.

Figure 2.5: A perspective view of the CMS detector.

2.2.1 The Coordinate System

CMS uses a right-handed coordinate system with the interaction point is cho-sen as the center of the coordinate system, the z-axis along the counterclockw-ise-beam axis, the y-axis is vertically upward and the x-axis is pointing to thecenter of the LHC ring, as illustrated in Figure 2.6. The azimuthal angle φ is


measured with respect to the x-axis in the xy-plane and the polar angle θ isdefined with respect to the z-axis. Suppose the four-momentum of a particlehas the coordinates (E, px, py, pz), then the longitudinal component is givenas pz and the transverse component is given by pT =

√p2x + p2

y. Hence therapidity is given by

y =1

2· lnE + pz

E − pz(2.3)

Figure 2.6: The CMS coordinate system.

If a particle is ultra-relativistic (p m), its rapidity can be approximatedby the pseudo-rapidity η, given by

η = −ln(

tanθ

2

)(2.4)

where we have η = 0 for the particles moving perpendicular to the z-axis and η = ±∞ in the ±z-direction. Both ∆η and ∆φ of two particlesare independent of Lorentz boosts along the z-axis, therefore the distancebetween two particle can be measured in a third Lorentz invariant variable:

∆R =√

∆η2 + ∆φ2 (2.5)

2.2.2 The Magnet System

The magnet system of the CMS detector is one of the most important detectorcomponent for precise charge and momentum measurements of the emergingparticles. It causes the bending of the charged particles in the transverse


direction to the beam axis for the signature in central part of the detector.The momentum p, of a charged particle carrying one unit of charge movingin a magnetic field B, is given by the relation

p[GeV] = 0.3B[T]r[m] (2.6)

where r is the radius of curvature of the particle track.

The super-conducting solenoidal magnet system of the CMS detector isabout 13 m long and has an inner diameter of 5.9 m, which produces astrong magnetic field of 3.8 T. The CMS magnet system is shown in Figure2.7. The current required for this strong magnetic field is 19,500 A, resultingin a stored energy of 2.7 GJ.

Figure 2.7: The CMS magnet system.

2.2.3 The Inner Tracking System

The CMS tracker is the innermost part of the detector and it is designedto reconstruct the tracks of the charged particles with high efficiency andmomentum resolution. It ensures the reconstruction of primary as well asthe secondary vertices1, making the detector highly hermetic. It covers apseudo-rapidity range of |η| < 2.5. Since the particle flux decreases as 1/r2

within the detector, the tracking system is required to be as close as possibleto the interaction point, depending on the radiation hardness of the material

1long-lived particles registers the secondary vertex in detector.


that is used to make it. The CMS inner tracker system is 5.8 m in length andof 2.5 m in diameter around the interaction point placed inside the magnetsystem. The tracker is further subdivided into two parts: the pixel trackingdetector and the strip tracking detector. Where the former is made highlysophisticated to have the high momentum resolution and extreme accuracyto track the paths of emerging particles. A highly sophisticated electronicsand powerful cooling are the obvious requirements for such operation. Figure2.8 gives the general layout of the tracker. Each line represents a detectormodule. The double lines indicate the back-to-back mounted modules tiltedby 100 mrad, and they deliver the stereo hits. The transverse momentumresolution of the inner tracker is given by

∆pTpT

= C1 · pT ⊗ C2 (2.7)

where the term C2 contains the multiple Coulomb scattering effects, whichare dominant for low energy particles. Whereas C1 depends on the detectorgeometry, in particular on the number of hits n used to reconstruct a track.It also depends on track length L and on the resolution on the single point(hit) measurement, σx, given as

C1 ∝σx√

n ·B · L2(2.8)

therefore C1 is minimal for tracks made of many hits and traveling a longpath within the tracker volume.

Pixel Detector

The pixel tracker is made of silicon material, so-called silicon pixel vertexdetector. It consists of three cylindrical layers pattern in the barrel region atthe radial distance of 4.4 cm, 7.3 cm, 10.2 cm, with a total length of 53.3 cm,and two disks in each endcap region, at |z| = 34.5 cm and 46.5 cm, with radiiranging from 6 to 15 cm, as shown in Figure 2.9. It consists of 65 million ofpixels in total with dimensions of 100× 150 µm2: 47923200 in the barrel and17971200 in the endcap region. Hits in the pixel detector provides the truespace points with considerable benefits for pattern recognition, and henceleads to the precise detection of primary vertex. The pixel detector deliversthe spacial resolution of about 10 µm along the r−φ coordinate and of about20 µm in the r − z plane for such true space points.


Figure 2.8: Schematic of the CMS inner tracking system in the r − z plane.The η ranges of the different sub-systems are also shown.

Figure 2.9: Silicon pixel detector layout.

Strip Detector

After the pixels and on their way out of the tracker, particles pass throughthe strip detectors which is reaching out to a radius of 130 cm. The strip de-tector is also made of silicon material and contains two collections of barrelmodules for a pseudo-rapidity range of |η| < 1.6: the Tracker Inner Bar-rel (TIB) and the Tracker Outer Barrel (TOB). In the endcaps, it containstwo collections of modules for a pseudo-rapidity range of 1.6 < |η| < 2.5:


the Tracker Inner Discs (TID) and the Tracker EndCaps (TEC). The siliconstrip detector layout is shown in Figure 2.8.

The silicon strip detector consists of 10 active silicon layers which contains9.3 million of strips, covering 198 m2 of area. The resolutions for the differentparts of the silicon detector are different which depend on their position withrespect to the interaction point: 23–35 µm for TIB/TID, 35–53 µm for TOBand 230–530 µm for TEC.

2.2.4 The Calorimeter

The CMS calorimeter is the sub-detector next to the inner tracking systemwithin the solenoidal field volume. It measures the energy of both neutraland charged particles with high energy resolution. It consists of two parts:the Electromagnetic CALorimeter (ECAL) which measures the energy de-posits by electrons and photons via electromagnetic interactions, and theHadron CALorimeter (HCAL) which instead measures the hadronic showersand the energy of jets and contributes to the precise determination of missingtransverse energy.

Electromagnetic Calorimeter

The experimentally difficult channel, H → γγ, has been used as the bench-mark for optimizing the ECAL design aiming for about 1% resolution on thedi-photon invariant mass. The ECAL is a high-resolution, high-granularitydetector composed of 75848 lead tungstate (PbWO4) crystals, provides thepseudo-rapidity coverage of |η| < 1.479 in the barrel which is called the ECALBarrel (EB), and of 1.479 < |η| < 3.0 in the endcap region named ECALEndap (EE). The ECAL mechanical design is given in Figure 2.10. Indeedthe precision energy measurement, involving photons and electrons, is car-ried out to |η| < 2.6. This limit has been determined by the considerationsof radiation dose, amount of pile-up energy2 and the geometric acceptancematches of the inner tracking system. The crystals are almost pointing tothe interaction point; their axes are tilted by 3 in the barrel and by 2−8

in the endcap regions with respect to the straight lines originating from theinteraction vertex. The scintillation light is detected by avalanche photodi-odes (APDs) in the barrel region and by vacuum phototriodes (VPTs) in theendcap region. The nominal operating temperature of ECAL is 18C.

2At LHC, one single bunch crossing may produce several separate events, so-calledpile-up events.


The properties of the ECAL lead tungstate crystals were optimized forthe use in the CMS experiment during a long R&D project in collaborationwith the Bogoroditsk Plant (BTCP) and the Shangai Institute of Ceram-ics (SIC). PbWO4 is a radiation hard, fast response scintillator which has ashort radiation length (X0 = 8.9 mm) and a small Moliere radius of 21.9 mmwhich allow a very compact system. Each crystal provides the transversegranularity of ∆η×∆φ = 0.0175× 0.0175 corresponding to a crystal frontalarea of approximately 22 × 22 mm2. The small Moliere radius reduces theeffect of pile-up contributions to the energy measurement by reducing thearea over which the energy is summed. In the endcap regions, the granular-ity increases progressively to a maximum value of ∆η × ∆φ ≈ 0.05 × 0.05,though the crystal front section does not change. Moreover, the scintilla-tion decay time of the crystals is very short which makes it possible for theelectronic read-out to collect ∼ 80% of the light within a time window of 25ns. A total thickness of about 26 rad lengths at |η| = 0 is required to limitthe longitudinal shower leakage of high energy electromagnetic showers to anacceptable level. This corresponds to a crystal length of 23 cm in the barrelregion.

In addition, a preshower detector is used to provide π0 − γ separationhaving strong photon identification ability, and for the vertex reconstructionfor photons. It is present in the endcap region in front of EE, consists of twolead radiators and of two planes of silicon strip detectors, for a total radiationlength of 3X0 and it allows the use of slightly shorter crystals of 22 cm inEE. It covers the a pseudo-rapidity range of 1.653 < |η| < 2.6.

For the energy range of about 25–500 GeV, which is appropriate for pho-tons from the H → γγ decay, the energy resolution can be parametrizedas[24] (σE

E

)2

=

(a√E

)2

+

(b

E

)2

+ c2 (2.9)

where a is the stochastic, b is the noise, and c is the constant term.The stochastic term includes fluctuations in the shower containment as wellas a contribution from photoelectrons. The noise term corresponds to theelectronic, pile-up and the digitization noises. Moreover, the constant termaccounts the non-uniformity of longitudinal light collection, inter-calibrationerrors and the leakage of energy from the back of the crystals. For the lin-ear response calorimeters such as ECAL at the CMS experiment, the signalobeys the rules of Poisson statistics and hence relative precision is equal toa/√E. On the other hand, the electronic, pile-up and the digitization noises


Figure 2.10: Longitudinal view of a part of CMS electromagnetic calorimetershowing the ECAL barrel and an ECAL endcap with the preshower in front.

are energy independent, defines the second term of energy resolution relation.

Figure 2.11 summarizes the different contributions expected for the en-ergy resolution. The curve labelled intrinsic includes the shower containmentand a constant term of 0.55%. The constant term must be kept down to thislevel in order to profit from the excellent stochastic term of PbWO4 in theenergy range relevant for the Higgs search. To achieve this goal, in situ3

calibration/monitoring using isolated high pT electrons is mandatory.

Hadron Calorimeter

The design purpose of HCAL detector is apparently the measurement of di-rection as well as the energy of jets and the missing transverse energy. It isinstalled between ECAL at the radius of r = 1.77 m, and the magnet withthe outer radius of r = 2.95 m as shown in Figure 2.12. The whole HCALconsists of four sub-systems: the Hadron Barrel (HB), Hadron Endcap (HE),Hadron Outer (HO) and Hadron Forward (HF) calorimeters, which providesthe required hermetic architecture. The barrel and the endcap regions havethe pseudo-rapidity coverage of |η| < 3 and beyond the HF placed at 11.2 mfrom the interaction point extends the coverage to |η| < 5.2.

3In experimental physics ‘in situ’ typically refers to a method of data collection ormanipulation of a sample without exposure to an external environment.


Figure 2.11: Different contributions to the energy resolution of the PbWO4

calorimeter.

HCAL is a sampling calorimeter with an alternate layer pattern of ab-sorber made of stainless steel or brass, and the fluorescent scintillator materialwhich acts as the active element and produces a rapid light pulse when theenergetic particle passes through it. The absorber material has been cho-sen because of its hadronic interaction length and of its property of beingnon-magnetic, and hence no destruction of magnetic field occurs. The activemedium uses the well known tile and wavelength shifting fibre concept tobring out the light and send into the readout boxes. The HCAL is consist of70,000 tiles in total. The energy of a particle is then measured as the sumof the light energies emitted by the scintillating tiles. The dynamic energyrange goes from 5 MeV to 3 TeV. The HCAL depth, expressed in terms ofinteraction lengths, ranges from 5.1 λI at η = 0 to 9.1 λI at η = 1.3, whereasit is 10.5 λI in the endcap regions.

Both HB and HE scintillators have a granularity of ∆η ×∆φ = 0.087×0.087, except in the very high η-regions where it matches the ECAL one.Moreover, HO which is located just behind the HB and outside of the solenoiduses iron as the absorber material, acts as tail catchers that effectively in-creases the thickness of the calorimeter in the central pseudo-rapidity re-gion and ensures that no energy leaks out at the back of the HB. The HFcalorimeters are useful to identify and reconstruct the very forward jets. Itis a Cerenkov light sub-detector which is made up of quartz fibers embedded


within a long steel absorber. The design energy resolutions for different partsof HCAL are

σEE

= 65%√E ⊗ 5% (HB) (2.10)

σEE

= 85%√E ⊗ 5% (HE) (2.11)

σEE

= 100%√E ⊗ 5% (HF ) (2.12)

HF

HE

HB

HO

Figure 2.12: Longitudinal view of the CMS detector: the locations of thehadron barrel (HB), the endcap (HE), the outer (HO) and the forward (HF)calorimeters.

2.2.5 The Muon System

The muon system of the CMS detector has been designed to provide anefficient muon trigger as well as a precise measurement of muon momentumand charge. It provides a powerful support for the discovery of new physicsand precision measurements of the SM physics. The topology of the finalstate of H → ZZ → 4µ analysis gives reasons for the construction of amuon system with a wide angular coverage and no acceptance gap. Theschematic of muon system is given in Figure 2.13. The muon system ofthe CMS detector is embedded in the iron return yokes (used to close the


magnetic flux) of the magnet. The whole system consists of three sub-systemsarranged in cylindrical barrel and planar endcap regions and covers a totalarea of 25,000 m2: Drift Tubes (DT) in the barrel, Cathode Strips Chambers(CSC) in the endcaps and Resistive Plate Chambers (RPC) in both barreland endcap regions.

Figure 2.13: Longitudinal view of the muon detectors: DT, RPC and CSC.

Drift Tube Chambers

Drift Tubes (DT) are used to reconstruct muon tracks as well as the trigger-ing devices in the barrel for a pseudo-rapidity range of |η| < 1.2. The totalof 250 chambers are distributed over five wheels (50 per wheel) along the zcoordinate, with 12 sectors per wheel (one per φ sector) and four stationsper sector. Each of the four DT stations: MB1, MB2, MB3 and MB4, aredefined from the innermost position up to the outermost as shown in Figure2.13, and contains 12 chambers each (MB4 station contains 14 chambers ex-ceptionally).


The basic constituent of a DT chamber is a cell with dimensions of 42×13mm2, as shown in Figure 2.14. The anodes are 50 µm stainless steel wireslocated in the centre of the cells, kept at a potential of 3.6 kV while thetwo parallel alluminium boundaries act as cathode at negative potential of1.2 kV. The chamber works with gas mixture of Ar and CO2 in the ratio of85:15 which guarantees the good quenching properties and the saturation ofthe drift velocity (∼ 5.4 cm/µs). This corresponds to a maximum drift timeof ∼ 390 ns, or 15 bunch crossings. The passage of muon or any chargedparticle through DT causes the ionization of the gas inside the cell and theelectrons and ions are accelerated to the anodes and cathodes, respectively.In addition, electrode strips at 1.8 kV are used to shape the electric field linesto enhance the linear variation of distance travelled by the electrons and ionswith time. This describes the spacial resolution of tracks of ∼ 180 µm. Eachchamber provides a resolution of ∼ 100 µm in the r − φ plane and of ∼ 1mrad along the φ coordinate.

Figure 2.14: The cross-section of a CMS drift tube with the anode wire,which is spanned in the middle of the tube, and Field lines of drift Field.

Cathode Strip Chambers

Cathode Strip Chambers (CSC) in the endcap regions cover the pseudo-rapidity range of 0.9 < |η| < 2.4, where the residual magnetic field betweenthe plates of the return yoke is intense and the particle rate is high. CSCs arethe multi-wire proportional chambers with a cathode strip readout. It con-sists of the arrays of positively-charged anode wires crossed with negatively-charged copper cathode planes/strips within a gas volume, as shown in Figure2.15. Each chamber consists of six layers with 9.5 mm thick gaps filled with agas mixture of Ar, CO2 and CF4 in the proportion 40:50:10. Anode wires are


placed in the middle of the gap and permit a fast response for bunch crossingidentification and the reconstruction of the radial coordinate. One of the twocathode planes is segmented into strips with a pitch varying from 8.4–16 mmthat reconstruct the bending coordinate φ, by measuring the centroid of thesignal induced on three adjacent strips with an accuracy ranging from 80–450µm. The whole system consists of 468 chambers which are distributed overfour stations (ME1 to ME4) per endcap with 1, 2 or 3 rings, according tothe disk position. Every ring consists of 18 or 36 chambers covering the fullazimuthal range.

Figure 2.15: Layout and the woking principle of CSCs: a pattern of wiregroup hits left behind by a muon passing through a chamber (Left), a patternof induced charges on strips and half-strip hits left behind by a muon (Right).

Resistive Plate Chambers

Resistive Plate Chambers (RPC) are used as dedicated trigger detectors bothin the barrel and the endcaps with the pseudo-rapidity coverage of |η| < 1.6.Their fast response of about 2ns and the readout segmentation make themideal for the triggering purposes. They also participate in the track recon-struction but due to the coarse segmentation their contribution to the preci-sion of the coordinate measurement is limited (∼ 1 cm).

The RPCs used in CMS are double gap chambers made of two par-allel plates of phenolic resin (bakelite), a high-resistivity plastic material(1010 − 1012 Ωcm), with a few mm thick gas in between and a conductivegraphite coat on the outer surface that makes HV and ground electrodesrespectively, as shown in Figure 2.16. It works in avalanche mode witha gas mixture of C2H2F4, Iso-C4H10 and SF6 with a ratio of 96.2:3.5:0.3.


Aluminium strips separated from the graphite layers by an insulating PET(polyethylene teraphtalate) film, read out the signals. Copper strips placedin the middle between the two gaps measure the bending coordinate φ. Atotal number of 480 chambers are distributed over five wheels, 12 sectors perwheel and six layers per sector in the barrel region. In the endcap regions,362 chambers are distributed over three disks per side with two rings perdisk and 36 chambers per ring.

Figure 2.16: Layout of the RPCs.

From the trigger point of view, the RPC system is segmented into 33towers covering the full pseudo-rapidity region. In each tower, coincidencesof RPC hits in the same bunch crossing and consistent with pre-defined hitpatterns are searched in order to find muon candidates. In the barrel, theRPC trigger requires a coincidence of at least four out of six layers in thepre-defined patterns for high momentum muons and a coincidence of threeof the innermost four layers for low momentum muons. In the endcaps, acoincidence of three out of three layers is required.

2.2.6 Forward Detectors

CASTOR

The Centauro And Strange Object Research (CASTOR) detector is instru-mented in a very forward region of the CMS detector with the purpose ofsearch for exotic events in central Pb-Pb collisions at LHC. It is a Cherenkoveffect based quartz (acting material) and tungsten (absorber material) calori-meter (45 degrees inclination with respect to the beam axis), placed at a dis-tance of 14.37 m from the interaction point and provides the pseudo-rapidity


coverage to the region 5.2 < η < 6.6. It is cylindrical in shape with inner andouter radii of 3.7 cm and 14 cm respectively, with depth of 10.5 λI in terms ifinteraction length. The light signal originated while the passage of chargedparticle is transmitted to photo multiplier tubes by means of air-core lightguides. The detector is composed of a 20.12 X0 thick electromagnetic sectionand of a 9.5 X0 thick hadronic section. The whole unit is azimuthally dividedin 16 sectors and longitudinally segmented in 12 reading units provides theenergy resolution of ∼ 1%. Figure 2.17 gives the schematic of the CASTORcalorimeter.

Figure 2.17: The CASTOR calorimeter detector.

The Zero Degree Calorimeter

The Zero Degree Calorimeter (ZDC) is designed to catch particles (neutronsand very forward photons) very close to the beam axis, in particular forheavy ion collisions. In addition, it works for beam tuning and luminositymonitoring. The design of the ZDC includes two independent calorimetersections: an electromagnetic section and a hadronic section. Cherenkov effectbased sampling calorimeters using tungsten and quartz fibers are chosen forthe energy measurements. It is installed 140 cm far from the interactionpoint on the both sides, ZDC+ and ZDC-, between the two LHC beam pipeswith the pseudo-rapidity coverage of |η| ≥ 8.5. The mechanical and opticaldesign is shown in Figure 2.18.

2.2.7 Trigger and Data Acquisition

At the nominal operational conditions of LHC, one expect the bunch crossingrate of 40 GHz corresponding to 25 ns of bunch crossings time at the CMS


Figure 2.18: The Zero Degree Calorimeter.

interaction point. Each bunch crossing give rise to about 20 proton-protoncollisions and hence we get 600 million collisions per second. One raw eventneeds ∼ 1 MB of memory to be recorded on the tape and therefore the fi-nal memory requirement is 40 TB per second. Since the Data AcQuisitionsystem (DAQ) of the CMS experiment can cope with 100 GB of data persecond, a drastic rate reduction is needed. In other words, a precise selectionof useful events by physics purpose is required. The CMS trigger systemhelps in this selection which takes decision in a short time of 25 ns as per therequirements. It consists of two independent levels: the Level-1 (L1) and theHigh Level Trigger (HLT).

The Level-1 Trigger

The L1 trigger is completely hardware based system capable of bringing downthe event rate from the initial 40 MHz to 100 kHz. The L1 schematic is givenin Figure 2.19. Since the latency between the bunch crossing and the L1 toaccept the signal is 3.2 µs, the L1 takes the decision on the basis of thecalorimeter and the muon system information. The tracker information donot participate because the track reconstruction time exceeds the time limitsof L1 decision. The accepted events are passed to the HLT.

The Calorimeter Trigger selects the four ‘best’ candidates of each of thefollowing categories: electrons and photons, central jets, forward jets and


Figure 2.19: Schematic representation of the CMS L1 trigger system.

jets identified on the basis of the shape of the deposited energy. These candi-dates are handed over to the Global Calorimeter Trigger (GCT) along withthe measured missing transverse energy.

The Muon Trigger is performed independently by DTs, CSCs and RPCs.The DT and CSC triggers carry out a local muon reconstruction by compar-ing the slopes of track segments built in subsequent detector layers. The RPCtrigger compares a given muon track with pre-defined hit patterns dependingon the track pT . The four best muon candidates are passed to the GlobalMuon Trigger system which discards the low-quality tracks after matchingthose from DTs and CSCs with those from RPCs. The L1 electronics isinstalled partly directly on the detectors, partly in the underground controlroom about 20 m far from the experimental cavern.

The High Level Trigger

The High Level Trigger (HLT) is a software system implemented in an EventFilter Farm which is single processing farm containing 1000 CPUs processesdata from ∼ 700 front-end electronics. It reduces the event rate down to thefinal output of ∼ 100 Hz that can be written on tape.

The HLT is divided in 2 ‘virtual’ trigger levels: Level-2 and Level-3 trig-


gers (L2 and L3). Since L1 trigger performs the reduction in rate thereforethe HLT can have access to the complete read-out data and capable to per-form complex calculations similar to those performed at the analysis level.At L2, the information from the muon system and the calorimeters is usedand more refined objects are reconstructed using the L1 tracks as seeds. Itdefines a region in the η − φ space in which a seed for L3 objects is found.The L3 trigger matches the L2 seeds with the tracker tracks which leads tothe availability of the full event information. Further selection is completelydependent on the physics analyses requirements.

The Data Acquisition System

The Data Acquisition (DAQ) perform the transportation of the data fromabout 650 front ends at the detector side to the ‘filter units’ for the processingof complete events. The central DAQ runs the online software on about3000 PCs used for intelligent buffering and processing of the event data.The principle components of the DAQ system of CMS are shown in Figure2.20. The detector front-ends are read out through a builder network with abandwidth of 100 GB per second. Complete events are fed to the event filtersystems at a rate of maximal 100 kHz. The large rate to the filter systemsstems from the design choice of CMS to build the full event already afterthe L1 trigger instead of building partial events as in traditional multi-leveltrigger systems.

Figure 2.20: The principal components of the DAQ system of the CMS de-tector.

Chapter 3

Event Simulation andReconstruction

The discovery of SM Higgs boson would shed light on the spontaneous elec-troweak symmetry breaking mechanism, as explained in chapter 1. In thischapter, the experimental motivations for the SM Higgs boson search inH → ZZ → l+l−τ+τ− (l = e, µ) decay channel with the CMS experiment,and the various steps involved in the search are described. This chapter ismainly focused on the generation of signal and background-like events, andreconstruction of the physics objects used in this analysis (e, µ and τ). As thefirst step of the analysis, the studies of the signal-like events are performedat the level of generator and are presented in the last part of this chapter.Such studies lead to the informations about the physics observables whichare used at the level of reconstruction to separate the signal-like events fromthe background-like events.

The SM Higgs boson search in H→ ZZ→ l+l−τ+τ− decay channel com-plements the SM Higgs boson search in the H → ZZ → 4l channel[8]. Thefinal states including taus have reasonable cross-section and branching ratios.Moreover, the presence of leptons, which record a clean signature in the CMSenvironment, provides a reasonable separation of signal and background-likeevents. Table 3.1 contains the cross-section values for SM Higgs boson de-caying to 4l′ (l′ = e, µ, τ) final states at

√s = 8 TeV, for four Higgs masses

150, 200, 250 and 300 GeV. Table 3.2 consists a comparison of cross-sectionvalues for SM Higgs boson decaying to 4l and llττ final states, for Higgs mass200 GeV at

√s = 8 TeV.

In H→ ZZ→ l+l−τ+τ− analysis, both the Z bosons are required to be onmass-shell, hence it is sensitive for the Higgs mass range of 190 < mH < 1000

48

49

GeV. One Z boson which is called ‘leading Z’, is required to decay eitherinto µ+µ− or e+e−, whereas the second Z boson, the ‘sub-leading Z’, decaysinto τ+τ− with four possible final states by taking the hadronic and leptonicdecay of tau into account: τhτh, τµτh, τeτh and τeτµ. Where τh representsthe hadronically decaying taus. Therefore the analysis consists of eight finalstates:

• Leading Z→ µµ: µµτhτh, µµτeτh, µµτµτh and µµτeτµ

• Leading Z→ ee: eeτhτh, eeτeτh, eeτµτh and eeτeτµ

The major backgrounds for this search come from the processes like SMZZ, the Z and WZ production in association with jets, and the tt. The finalstates where ττ → µµ, ee are not considered since these are accounted in theH→ ZZ→ 4l Higgs search.

Table 3.1: The cross-section and the branching ratios for the SM Higgs bosondecaying to 4l′ final states (l′ = e, µ, τ), for Higgs masses 150, 200, 250 and350 GeV at

√s = 8 TeV[19].

σ (pp→H) (pb) BR (H→ZZ(∗)) σ (pp→H→ZZ(∗)→ 4l′) (fb)

H150 15.56 8.25E-02 13.23H200 8.21 2.55E-01 21.26H250 5.48 2.97E-01 16.50H300 4.10 3.07E-01 12.75

Table 3.2: The Cross-section and the branching ratios for the SM Higgsboson decaying to llττ and 4l (l = e, µ) final states, for Higgs mass 200 GeVat√s = 8 TeV[19].

BR σ (fb)

llτhτh 4.88E-04 4.01llτlτh 5.25E-04 4.31llτlτl 1.53E-04 1.26µµµµ 2.88E-04 2.37eeµµ 5.75E-04 4.72eeee 2.88E-04 2.37

3.1. Event Generation 50

Moreover, the main steps involved in H → ZZ → llττ analysis can besummarized as following

• study of the signal-like events using Monte Carlo (MC) simulationsaiming for the understanding of physics observables to define the signal-like events separately from the background-like events;

• use of the information collected from the simulation studies to definethe selection criteria for the signal-like events with a strong reductionpower of background-like events;

• estimation of the backgrounds contributing in the signal phase space,where the signal phase space is defined as the region suppose to bepopulated with the signal-like events;

• measurement of the statistical and the systematic uncertainties in-volved in the analysis;

• finally the statistical interpretation of the results to establish the dis-covery or the exclusion of the possible signal, related to the existenceof the Higgs boson.

The first step of the analysis is presented in this chapter. Chapter 4 de-scribes the signal selection, the background estimations and the systematicsinvolved. The final results and the statistical interpretation of the results arepresented in the chapter 5.

3.1 Event Generation

Proton-proton (pp) collisions allow the search for SM Higgs boson as wellas the new physics due to large scales of momentum transfer involved. Butthe understanding of final states of high energy particle collisions such asthose at the LHC is an extremely challenging theoretical problem. There areseveral basic phases of the process that are needed to be simulated:

• a primary hard subprocess;

• the parton showers associated with the incoming and the outgoing col-ored participants in the subprocess;

• the non-perturbative interactions that convert the showers into outgo-ing hadrons, so-called hadronization, and connect them to the incomingbeam hadrons;


• the secondary interactions that give rise to the underlying event, andthe decays of unstable particles that do not escape from the detector.

Of course, not all these steps are relevant in all processes. In particular,the majority of events that make up the total hadron-hadron cross-sectionare of soft QCD type and rely more on phenomenological models. At theother extreme the simulation of events such as the SM Higgs production andthe SM backgrounds, rely essentially on all of the components. A typicalin-elastic pp collision at LHC is given in Figure 3.1.

Figure 3.1: Scheme of a proton-proton collision. Two partons of the incomingproton interact in the hard interaction (red), while the proton remnants(magenta) provide the underlying event. The partons created in the hardinteraction hadronization (light green) and unstable hadrons decay furtherto stable particles (dark green).

Over last thirty years, a crucial tool of factorization has been devel-oped which allows the separation of many processes of interest into differentregimes according to the scales of momentum transfer involved[25]. The hard


and soft scale regimes describe the hard subprocess and hadronization pro-cess respectively. The hard and soft regimes are distinct but connected byan evolutionary process that can be calculated in principle from perturbativeQCD. One consequence of this scale evolution is the production of many ad-ditional partons in the form of initial and final-state parton showers, whicheventually participate in the low-scale process of hadron formation. All theregimes are eminently suited to computer simulation using Monte Carlo tech-niques. Moreover, the important components involved in the event generationprocess can be described as following:

3.1.1 Parton Distribution Functions

The Parton Distribution Functions (PDFs) play an important role in eventgenerations[25, 26], for the simulation of hard processes, parton showers andunderlying events. They are defined as the momentum distribution functionsof the partons within the proton (when the spin direction of the partons isnot considered), since the protons accelerated to high energies can be con-sidered as a stream of partons, each carrying a fraction x of the longitudinalmomentum. In other words, they represent the probability densities to finda parton carrying a momentum fraction x at a squared energy scale1. Thus,the choice of PDF set influences both cross-sections and event shapes.

3.1.2 Hard Subprocesses

The simulation normally begins with a hard subprocess[25], in which con-stituents of the colliding protons interact at a high momentum scale to pro-duce a few outgoing fundamental objects: SM quarks, leptons and/or gaugeor Higgs bosons, or hypothetical particles of some new theories. The mo-menta of the colliding constituents are selected by sampling the PDFs of theproton at the energy scale of the subprocess. These distributions have beenmeasured at lower energies in other processes and are evolved to higher scalesusing the QCD evolution equations for parton densities2. Convolution withthe differential cross-section of the subprocess and integration over phasespace gives the relevant production cross-section.

1Squared energy scale is given as Q2 = −q2, where the transfer of modulus of fourmomentum q takes place at high energy collision.

2QCD evolution equations for parton densities are valid in the theory of the strongQCD interactions which determine the rate of change of parton densities when the energyscale chosen for their definition is varied.


Using the Monte Carlo method for the convolution and phase-space inte-grations mean that we obtain at a same time the momentum distributions ofthe primary produced objects, in the form of a set of representative phase-space points.

3.1.3 Parton Shower

The hard subprocess, by definition, involves large momentum transfers andtherefore the partons involved in it are violently accelerated. Just as acceler-ated electric charges emit QED radiation (photons), the accelerated coloredpartons emit QCD radiation in the form of gluons. Unlike the unchargedphotons, the gluons themselves carry colour charges and can therefore emitfurther radiation, leading to parton showers[25]. In principle, the showersrepresent the higher-order corrections to the hard subprocess. However, itis not feasible to calculate these corrections exactly, instead, an approxima-tion scheme is used, in which the dominant contributions are included ineach order of perturbation theory describing the hard subprocess. Thesedominant contributions are associated with collinear parton splitting or soft(low-energy) gluon emission.

Using the Monte Carlo method to generate the values of splitting pa-rameters for each splitting, a parton shower is developed from each coloredparton of the hard subprocess.

3.1.4 Hadronization

At some point, the evolution perturbation theory becomes invalid and thedynamics enter in a non-perturbative phase, which leads to the formation ofthe observed final-state hadrons. This hadronization process is not amenableto the currently available non-perturbative techniques for calculation, andtherefore event generators have to rely on models based on general featuresof QCD.

String Model

The string model for hadronization[25] is based on the observation from lat-tice simulations of QCD where at large distances, the potential energy of thecolor sources, such as a heavy quark-antiquark pair, increases linearly withtheir separation corresponding to a distance-independent force of attraction.This is thought to be due to the self-attraction of the gluonic field causing it


to collapse into a string or tube configuration with thickness of the order of1 fm when the separation of the sources becomes much larger than this.

Cluster Model

The cluster hadronization model[25] is based on the so-called pre-confinementproperty of QCD which describes that at the evolution scales much less thanthe hard subprocess scale, q Q, the partons in a shower are clustered incolourless groups with an invariant mass distribution that is independent ofthe nature and scale of the hard subprocess, depending only on q and thefundamental QCD scale Λ. It is then natural to identify these clusters atthe hadronization scale Q0 as proto-hadrons that decay into the observedfinal-state hadrons.

3.1.5 Underlying Event

In hadron collider events that contain a hard subprocess, there is extra hadronproduction that cannot be ascribed to showering from the coloured partonsparticipating in the subprocess. Furthermore this extra activity known asthe underlying event is greater than that in so-called minimum-bias events3.The underlying event[25] is believed to arise from collisions between thosepartons in the incoming hadrons that do not directly participate in the hardsubprocess.

3.1.6 Hadron and τ Decays

Many of so-called primary hadrons, originating directly from string breaksand/or cluster decays are unstable and undergo further decay until a set ofparticles is obtained that can be considered stable on time scales relevant tothe given measurement4[25]. In case of tau leptons, it undergo the furthersemi-leptonic decay to a tau neutrino and either hadron or lepton. The de-cay modeling can therefore have a significant impact on final particle yieldsand spectra, especially for the lowest-lying hadronic states, which receive thelargest relative contributions from decays.

3The collisions that do not yield an identifiable hard subprocess are called minimum-bias events.

4e.g. a typical hadron-collider definition of a “stable particle” is ct ≥ 10 mm, whichincludes the weakly-decaying strange hadrons (K,Λ,Σ±, Σ±,Ξ,Ω).


3.1.7 Validation and Tuning

Validation in the context of Monte Carlo generators means confronting amodel with all relevant data that it claims to be able to describe[25]. It isessential that the validation is global because the model should describe theunderlying physics and not just parameterize the data, otherwise it wouldnot have any predictive power. In this sense, validation is important fordeveloping models as well as for debugging both code and physics models.Tuning means adjusting the free parameters of the model within their allowedranges and as per the detector simulation to improve the description of therelevant data.

3.1.8 Event Generators

PYTHIA

The general-purpose event generator, PYTHIA[27], has probably been themost used generator for LHC during the last 20 years. The PYTHIA pro-gram is a standard tool for the generation of high-energy collisions includinga coherent set of physics models for the evolution from a few-body hard pro-cess to a complex multi-hadronic final state. PYTHIA treats an extensive listof hardcoded subprocesses, over 200, that can be switched on individually.These are mainly two-body to one body decay, two-body to two body decay,and some two-body to three body decay, but no multiplicities higher thanthat. Consecutive resonance decays may lead to more final-state particles aswell as the parton showers. The subprocess cross-sections have to be convo-luted with PDFs to obtain the event rates.

Another important package is TAULA[28] which is used to model thetau lepton decays by properly taking into account the tau polarization. Thedescription of the tau polarization is very important in view of the scalarnature of the Higgs boson and this needs to be described properly.

POWHEG

The other generators used at CMS is POWHEG[29]. The main idea of thePOWHEG method is that the hardest emission (the one with the highestpT ) is simulated according to the exact NLO cross-section. Then during theparton shower, the hardest emission is excluded and subsequent emissionsare vetoed if they are harder than the hardest emission. The POWHEGmethod compared with PYTHIA, provides a much better description of basic


processes such as vector boson and Higgs production, and used explicitly todescribe final states with low multiplicity such as inclusive W/Z production.

MadGraph

MadGraph generator[30] has the ability to identify the relevant sub-processesof a given process. It generates both the amplitudes and the mappingsneeded for an efficient integration over the phase space. Once the eventsare generated, MadGraph is interfaced to PYTHIA for the parton showerand hadronization procedures.

3.1.9 K-factors

Next-to-leading order (NLO) cross-section calculations are imperative forexperimental analyses at the LHC since some highly interested processesmay involve large logarithms that need to be resumed or extra partonicprocesses may contribute only when going beyond the leading-order (LO)approximation. Some of the information from a NLO calculation can beencapsulated in the K-factor given as the ratio of the NLO to LO cross-section for a given process, including the values of the renormalization andfactorization scales as well as the PDFs used at LO and NLO. For example,in case of the SM Higgs production in pp collision:

K =σHO(pp→ H +X)

σLO(pp→ H +X)(3.1)

where HO stands for the higher order cross-section.

The QCD corrections to the transverse momentum and rapidity distri-butions are also available in the case of vector-boson fusion and gluon-gluonfusion. In the latter case, that is the one of main interest for this work, there-summation of the large logarithms for the pT distribution has been per-formed at the next-to-next-to-leading-logarithm (NNLL) accuracy. In thegluon-gluon fusion mechanism the calculation of the cross-sections at next-to-next-to-leading order (NNLO) is also necessary[31].

3.1.10 Detector Simulation

The complexity of the CMS Detector requires very sophisticated simulationto properly reproduce the detector behavior in the presence of particles fromproton collisions. The CMS detector simulation is based on the Geant4

3.2. Reconstruction of Physics Objects 57

toolkit[32]. GEANT4 relies on the accurate detector description includingthe full geometry, the materials of the detecting devices and also taking intoaccounts the ‘sensitive’ parts (those furnished with a readout system) op-posed to ‘dead materials’, to simulate the particle response. It takes as inputthe particles from the event generator and then propagates them through thedetector taking into account the measured magnetic field map (for chargedparticles) and any interactions between particle and material such as bremm-stralung, multiple scattering and photon conversions. At the final stage,GEANT4 produces a set of simulated hits in the active material such as theenergy loss of a particle in the sensitive volume of a detector. Subsequently,there is the digitization step to model the response of the detector readoutelectronics: signal collection and electronic effects are computed, noise isadded and pile-up events are superimposed. The following step in the analy-sis is called reconstruction and can be applied independently from the originof input data (simulation or real data).

3.2 Reconstruction of Physics Objects

In the reconstruction phase, collected collision information from all sub-detectors of the CMS experiment, stored in ‘raw’ data format, is used toreconstruct the high-level objects such as jets, tracks, vertices and leptonsetc. It involves the primary step of building up the ‘RecHits’ collectionscorresponding to the different parts of the detector. RecHits objects containseveral useful information such as energy releases, 3D-position and collectedcharge of the particle which is interacting with the sub-detector matter. Re-cHits collections are further used by high level reconstruction algorithms toreconstruct the physics objects. The reconstruction of the physics objectsinvolved in this analysis is presented in this section.

3.2.1 Track Reconstruction

Tracks are the fundamental objects need to be reconstructed as precisely aspossible since the reconstruction of high-level objects is highly dependent onit. In addition, the Particle Flow (PF) algorithm[33] is strongly dependenton sophisticated track reconstruction, which is used to reconstruct taus, jetsand missing transverse energy, Emiss

T .

The track reconstruction at CMS is performed by the combinatorial trackfinder (CTF)[34]. The reconstruction[35] starts from the hit formation byclustering the silicon pixel and strip tracker information where the hit posi-


tion provides the seed to the track seed generators. Track seed generatorsare responsible for building up the initial track using the triplets or the pairsof hits. The constraint from the beam spot or a vertex is also taken intoaccount. Further propagation of the initial track takes place which resultsin the association of one additional compatible hit corresponding to eachsilicon strip. The propagation continues until either the limit of the trackeris reached or no more compatible hits can be found. Moreover, in multipleseeds per track or multiple tracks per seed situations (which results in morethan one reconstructed trajectories), the iterative reconstruction process isperformed which can introduce some ambiguities. To remove the ambigui-ties, the fraction of hits that are shared between two trajectories is calculatedusing the formula

fshared =Nshared

min(N1, N2)(3.2)

where Nshared, N1 and N2 give the number of shared hits, number of hitsof first and second track candidates, respectively. For fshared > 0.5, the trackwith least number of hits is rejected. The track with the highest χ2 is dis-carded for N1 = N2. In the final step, this collection of hits is fit to obtainthe best estimate of the track parameters.

The CMS tracking system is capable to reconstruct the tracks with pTas low as 0.7 GeV in the central region (η ∼ 0). This value varies with thedistance to the outermost tracker layer. The reconstruction of tracks withpT ∼ 1 TeV is possible at maximum, at the CMS experiment. Figure 3.2shows the track reconstruction efficiency measured from simulated samplesof muons and pions. Barrel, transition and endcap regions are defined by thepseudo-rapidity intervals [0–0.9], [0.9–1.4] and [1.4–2.5], respectively.

3.2.2 Vertex Reconstruction

The reconstruction of the vertices in the event starts from the tracks col-lection. Prompt tracks are selected based on the transverse impact param-eter along with uncertainty, number of hits, and the normalized track χ2.The selected tracks are then clustered, using Deterministic Annealing (DA)clustering[38] in z-direction and the cluster is fit with an adaptive vertexfit[39], where tracks in the vertex are assigned a weight between 0 and 1based on their compatibility with the common vertex. The sum of weightsroughly corresponds to the effective number of tracks accepted by the adap-tive vertex fitter. This sum is directly related to the number of degrees offreedom assigned to the vertex through Ndof = 2

∑wi − 2 for an uncon-


Figure 3.2: Track reconstruction efficiency[36, 37] for simulated single, iso-lated muons (left) and for pions (right) as a function of pT .

strained fit and Ndof = 2∑wi for a fit with beam constraint. Tracks are

then selected with Ndof > 4 which corresponds to at least 4 tracks assignedto the (unconstrained) vertex because the weight of every track is always(slightly) smaller than 1.

Multiple vertices are possible and the vertices in the output are sortedaccording to the sum of the square of the transverse momenta of the tracks inthe track cluster. The vertex corresponding to the highest sum is consideredas primary vertex (PV). Rest are related to multiple pile-up interactions.

3.2.3 Muon Reconstruction

Muons are reconstructed using the tracker and the muon detectors infor-mation. Tracks are first reconstructed independently in the inner tracker(tracker track) and in the muon system (standalone-muon track) of the CMSexperiment[40]. Based on these objects, two approaches are used for themuon reconstruction, given in figure 3.3.

Global Muon Reconstruction (outside-in)

For each standalone-muon track, a matching tracker track is found by com-paring parameters of the two tracks propagated onto a common surface.A global-muon track is fitted combining hits from the tracker track and


standalone-muon track, using the Kalman-filter technique[41]. At large trans-verse momenta, pT ≥ 200 GeV, the global-muon fit can improve the momen-tum resolution compared to the tracker-only fit[40, 42].

Figure 3.3: Reconstruction of muon objects at the CMS experiment. Trackertrack (red box), stand-alone track (green box) and global muon (blue box)are shown.

Tracker Muon Reconstruction (inside-out)

In this approach, all tracker tracks with pT > 0.5 GeV and total momentump > 2.5 GeV are considered as possible muon candidates and are extrapo-lated to the muon system taking into account the magnetic field, the averageexpected energy losses, and multiple Coulomb scattering in the detector ma-terial. If at least one muon segment (i.e. a short track stub made of DT orCSC hits) matches the extrapolated track, the corresponding tracker trackqualifies as a Tracker Muon. Track-to-segment matching is performed in alocal (chamber) coordinate system, where local x is the best-measured co-ordinate (in the r − φ plane) and local y is the coordinate orthogonal to it.The extrapolated track and the segment are considered to be matched if thedistance between them in local x is less than 3 cm or if the value of the pullfor local x is less than 4, where the pull is defined as the difference betweenthe position of the matched segment and the position of the extrapolatedtrack, divided by their combined uncertainties[40].

Tracker Muon reconstruction is more efficient than the Global Muon re-construction at low momenta, p ≤ 5 GeV, because it requires only a single


muon segment in the muon system, whereas Global Muon reconstruction isdesigned to have high efficiency for muons penetrating through more thanone muon station and typically requires segments in at least two muon sta-tions. About 99% of muons produced in pp collisions within the geometricalacceptance of the muon system and having sufficiently high momentum arereconstructed either as a Global Muon or a Tracker Muon, and very often asboth. Candidates found both by the Global Muon and the Tracker Muon ap-proaches that share the same tracker track are merged into a single candidate.

For a small fraction of the cases (∼ 1%) where both approaches fail, thetrack reconstructed at the muon chamber is considered as the muon can-didate, so-called ‘stand-alone muon’. If the standalone-muon tracks are notincluded in a Global Muon and share a muon segment with the tracker muon,they are merged with a Tracker Muon.

3.2.4 Electron Reconstruction

Two complementary approaches are used at CMS for electron reconstruction:‘Tracker driven’ and ‘ECAL driven’ seeding.

ECAL Driven Seeding

The ECAL driven algorithm starts from the reconstruction of ECAL ‘super-clusters’ [43] of transverse energy ET > 4 GeV that is optimized requirementfor isolated electrons in the pT range relevant for Z or W decays, down topT ' 5 GeV. Supercluster is a group of one or more associated clusters ofenergy deposits in the ECAL constructed using an algorithm which takesinto account their characteristic narrow width in the η coordinate and theircharacteristic spread in φ due to the bending in the magnetic field of electronsradiating in the tracker material. As a first filtering step, superclusters arematched to track seeds (pairs or triplets of hits) in the inner tracker layersand electron tracks are built from these track seeds. Trajectories are recon-structed using a dedicated modeling of the electron energy loss and fittedwith a Gaussian Sum Filter (GSF)[44].

Tracker Driven Seeding

In the case of electrons in jets, pollution of the supercluster energy by parti-cles produced near the electron degrades the energy measurement. Tracker


driven algorithm helps in this case. The algorithm starts from all recon-structed tracks and electromagnetic clusters. From the inner track position,the bremstrahlung hypothesis is tested at the point on the calorimeter sur-face calculated by extrapolating a straight line from the track position andmomentum vector at the corresponding detector layer, given in Figure 3.4.The process is repeated for all layers and a supercluster is defined by sum-ming all linked electromagnetic cluster deposits.

Figure 3.4: Reconstruction of electron objects at the CMS experiment.

Furthermore, a preselection is applied based on a multivariate analysisfor candidates found only by the tracker driven seeding algorithm[33]. Forcandidates found by the ECAL driven seeding algorithm, the preselectionis based on the matching between the GSF track and the supercluster inη and φ[45]. The few ECAL driven electron candidates (∼ 1% for isolatedelectrons) not accepted by these matching cuts but passing the multivariatepreselection are also kept.

3.2.5 Jet Reconstruction

Four types of jets (from which the quark and gluon energies and directionsare inferred) are reconstructed at CMS, which differently combine individ-ual contributions from sub-detectors to form the inputs to the jet clusteringalgorithm: calorimeter jets, Jet-Plus-Track (JPT) jets, Particle-Flow (PF)jets, and track jets. The calorimeter jets are completely based on calorimeterinformation and JPT jets are the improvements to the calorimeter jets thatimproves the measurement by exploiting the associated tracks. Track jets


are reconstructed using only the well measured tracks. At CMS, the mostlyused jets are the PF jets, which are reconstructed combining the informationfrom all the sub-detectors. PF jets are used to reconstruct as well as identifythe tau objects, and are of higher interest from the point of view of the the-sis work. The following text is describing the PF based reconstruction of jets.

The PF jet algorithm uses the PF event reconstruction[33], starts fromthe reconstructing and identifying all stable particles in the event such asphotons, charged and neutral hadrons etc. with a thorough combination ofall CMS sub-detectors towards an optimal determination of their direction,energy and type. Charged hadrons, in particular, are reconstructed from thetracks in the central tracker. Energy clusters in the ECAL and HCAL leadto the reconstruction of the photons and the neutral hadrons respectively.Clusters separated from the extrapolated position of tracks in the HCALconstitute a clear signature of these neutral particles. Furthermore, the pre-cise study of the excess in the calorimeter energy ensures the overlappingof neutral particle with charged particles. This study involves the compari-son of the energy deposited to the sum of the track momenta correspondingto the charged particles. These individual particles are then clustered intojets using the ‘anti-kT ’ algorithm with the size parameter R = 0.5 in η − φspace[46]. The PF algorithm gives better performance for momentum andspatial resolutions with respect to calorimeter jets, as it uses the trackingdetectors and of the excellent granularity of the ECAL. The PF algorithmtherefore allows to resolve and precisely measure the charged hadrons andphotons inside jets that constitute the ∼ 90% of the jet energy, given inFigure 3.5. While the lose of 10% corresponds to neutral hadrons that areaffected by the poor HCAL resolution, especially for low neutral hadron ET .

3.2.6 Missing ET Reconstruction

The missing transverse energy[47] used in this analysis has been computedusing PF algorithm[33]. It is estimated in terms of momentum imbalancein the plane perpendicular to the beam direction. The missing transversemomentum vector is computed as the opposite of the transverse momentumsum of all PF particles reconstructed in the event.

~EmissT = −

∑i

~P iT (3.3)

The magnitude of this vector is the missing transverse energy EmissT .


Figure 3.5: Reconstructed jet energy fractions as a function of pseudo-rapidity (a) in the data correcponding to L = 6.2 nb−1 (b) and in thesimulation. From bottom to top in the central region: charged hadrons(red), photons (blue), electrons (light blue), and neutral hadrons (green). Inthe forward regions: hadronic deposits (pink) and electromagnetic deposits(purple).

3.2.7 Hadronic Tau Reconstruction

Hadronic taus used in this analysis have been reconstructed using HadronPlus Strips (HPS) algorithm[48]. The HPS algorithm starts from a PF jetand reconstructs the possible tau decays inside the jet, given in Table 3.3.The key point of this algorithm is the robust π0 reconstruction which is thequite often final product from the tau decay. A spacial attention is paidto the π0 → γγ decay, where the further photon conversion in the CMStracker material leads to the broadening of calorimeter energy signature dueto bending of charged electrons and muons in magnetic field of 3.8T.

Reconstruction of π0 Sub-clusters

HPS algorithm accounts for the photon conversion by reconstructing photonsin ‘strips’. Starting from the highest electromagnetic PF candidate inside thejet, the photon (and/or PF electron) candidates are clustered in strips thatare narrow in η and are dynamically growing in φ to include the convertedphoton energy. The association distance for η is 0.05 and for φ is 0.2 radians.Strips satisfying a minimum transverse momentum requirement of pstripT > 1GeV are finally combined with the charged hadrons to reconstruct individual


Table 3.3: Tau decay modes and branching ratios (h denotes a pion or akaon)[49].

Decay Mode Branching Ratio (%)

τ− → h−ντ 11.6τ− → h−π0ντ 26.0τ− → h−π0π0ντ 10.8τ− → h−h+h−ντ 9.8τ− → h−h+h−π0ντ 4.8

Total 63

other hadronic decays 1.7

hadronic tau decay modes.

Charged Hadrons and Strips Combination

The decay modes that are reconstructed with the HPS algorithm are thefollowing

1. Single Hadron: this decay mode reconstructs one prong tau decays ordecays of type τ− → h−π0 when the π0 has very low energy to bereconstructed as strips.

2. Hadron Plus One Strip: this type is aiming to reconstruct one prongtaus that are produced in association with a π0 where the photons fromthe π0 decay are very near in the calorimeter surface. The strip takescare of the possibility that one or both of those photons have converted.

3. Hadron Plus Two Strips: this type is aiming to reconstruct one prongtaus that are produced in association with a π0 where the photons fromthe π0 decay are well separated in the calorimeter surface.

4. Three Hadrons: this type is aiming to reconstruct the three prongdecays of taus. Three Hadrons are required with a compatible charge(|q| = 1) coming from a common vertex estimated by the Kalmanvertex fit algorithm.

The tau decay modes of τ− → h−h+h−π0ντ and τ− → h−π0π0ντ havenot been introduced to the algorithm yet.

3.3. Monte Carlo Samples 66

Furthermore, a constraint is applied on the strip mass to match the π0

mass and the invariant mass of the hadron plus strip is calculated. Thisinvariant mass should be compatible with the mass of the ρ(770) resonance.For the hadron plus two strips decay mode, the photon mass constraint isapplied on each strip. Moreover, the invariant mass of the two strips shouldbe in a mass window constrained by the π0 mass. The three prong decaycan be well identified since it is free from conversion effects and energy lossand the reconstructed visible tau mass should be compatible with the a1 res-onance.

In addition, a preselection is applied to reject the backgrounds. It involvesa narrowness criteria for the cone of the hadronic tau, should be smaller thancone(∆R) ≤ 2.8/pτT . The pτT is computed by summing the four-vectors ofreconstructed charged hadron and the strips, and the cone is defined by themaximum distance of the associated constituents from the tau four-vector.The cone size should be less than 0.1 but more than 0.05 to account thematerial effects properly. In case of reconstructing more than one tau decaymodes for a specific PF jet, a selection criterion is applied to pick the bestone. In such a case of overlap, the most isolated candidate is selected whichis defined as the tau candidate with the lowest isolation ET sum using PFgamma and PF charged hadron candidates.

3.3 Monte Carlo Samples

The complete set of MC simulation samples used for the analysis are sum-marized in Table 3.4 along with the informations about cross-section valuesand the event generators. The Fall11 (7 TeV) and Summer12 (8 TeV) officialsamples have been used for this analysis.

Signal Samples

The signal samples, gluon-gluon fusion gg → H and vector-boson fusionqq → H, are generated by POWHEG at next-to-leading order (NLO). Forthe gluon-gluon fusion process a re-weighting process has been applied to thePOWHEG spectrum to match with the spectrum predicted by the next-to-next-to-leading order (NNLO) and next-to-next-to-leading-logarithm (NNLL).

Background Samples

Irreducible backgrounds: SM ZZ production through qq → ZZ and gg → ZZproduction modes. This is called indistinguishable background because of


same signature by real out-coming objects from the decay of Z bosons.POWHEG is used to generate the former process by taking into account thecomplete NLO simulation, interfaced to PYTHIA for showering, hadroniza-tion, decays and for the underlying event. On the other hand, the gg2ZZtool[50] has been chosen to generate gg → ZZ events at LO, whereas show-ering and hadronization are dealt with by PYTHIA.

Reducible backgrounds:

• Z + light jets production with Z → l+l− decays. This is one of theinstrumental backgrounds which contributes due to the limited effi-ciency of detector for object identification: one or two of the jets aremis-identified as leptons or τh.

• Zbb/Zcc associated production with Z→ l+l− decays. This backgroundis due to leptons, most probably µ′s, inside the b(b)/c(c) jets. Also thereis probability of b(b)/c(c) jets to be mis-identified as τh.

• WZ + jets production with Z → l+l− and W± → l± or τ± decays.One mis-identified jet along with three real objects comprises the back-ground.

• the production of top quark pairs in the decay mode tt → WbWb →l+l−ννbb. This background contributes due to the same reason as forZbb background.

MadGraph tool has been used for the Z + jets and WZ + jets event gen-eration. tt background events have been generated using POWHEG. Othercontributions to multiple jet production from QCD hard interactions are alsoneeded to be considered in early stages of the analysis, as well as other di-boson (WW), and single top backgrounds.

Moreover, for each event in a simulated sample an event weight is assignedgiven as

w =σ × ε× L

N(3.4)

where σ is the cross-section, ε is the efficiency of the generator levelrequirements, L is the integrated luminosity and N is the number of producedevents before any generator level requirements.


Table 3.4: Monte Carlo simulation samples used for the signal and background processes. Thecross-section values for signal samples (gg → H and V V → H) are taken from Reference [19].

Process MC σ(N)NLO Comments and sample namegenerator 7 TeV 8 TeV

Higgs boson H→ ZZ→ 4lgg → H POWHEG [0.02-6] fb [0.03-8] fb mH = 190–1000 GeVV V → H POWHEG [0.01-0.7] fb [0.02-0.9] fb mH = 190–1000 GeVZZ continuumqq → ZZ→ 4e(4µ, 4τ) POWHEG 15.34 fb 76.91 fb ZZTo4e(4mu,4tau)qq → ZZ→ 2e(2µ)2τ POWHEG 30.68 fb 176.7 fb ZZTo2e(2mu)2taugg → ZZ→ 2l2l′ gg2ZZ 9.74 fb 12.03 fb GluGluToZZTo2L2Lgg → ZZ→ 4l gg2ZZ 3.85 fb 4.80 fb GluGluToZZTo4LOther di-bosonsWZ→ 3lν MadGraph 0.868 pb 1.057 pb WZTo3LNutt and single ttt→ l+l−ννbb POWHEG 17.32 pb 23.64 pb TTTo2L2Nu2Bt (s-channel) POWHEG 3.19 pb 3.89 pb T TuneXX s-channelt (s-channel) POWHEG 1.44 pb 1.76 pb Tbar TuneXX s-channelt (t-channel) POWHEG 41.92 pb 55.53 pb T TuneXX t-channelt (t-channel) POWHEG 22.65 pb 30.00 pb Tbar TuneXX t-channelZ/W + jets (q = d, u, s, c, b)W + jets MadGraph 31314 pb 36257.2 pb WJetsToLNuZ + jets MadGraph 3048 pb 3503.7 pb DYJetsToLLQCD inclusive multi-jets, binned pmin

T

b, c→ e+X PYTHIA QCD Pt-XXtoYY BCtoEEM-enriched PYTHIA QCD Pt-XXtoYY EMEnrichedMU-enriched PYTHIA QCD Pt-XXtoYY MuPt5Enriched

3.4. Monte Carlo Generator Studies 69

3.4 Monte Carlo Generator Studies

For sake of pronounced simulation studies, the separation of the events havebeen carried out according to the eight final states considered in this analy-sis. For this purpose, a filter code has been developed in framework of CMSofficial software: CMSSW.

In Figure 3.6, the generated invariant mass of Higgs is presented in com-parison with llττ visible invariant mass for signal samples of Higgs massesmH = 200 and 600 GeV, where all the possible final states has been takeninto account. A clear shift and broadening of peaks have been observed forall the llτhτh, llτlτh and llτlτl final states due to neutrino losses. The for-mer process involves the losses of tau neutrino and tau anti-neutrino, andthe neutrino loss increases with the increase in the number of taus decayingleptonically due to additional escape of lepton neutrino (and/or lepton anti-neutrino) for later processes. Thus, one should expect a widely spread Higgsmass distribution at the level of reconstruction peaking at lower side to thenominal mass.

Figure 3.6: Invariant llττ mass distribution for Higgs masses mH = 200 GeV(left) and mH = 600 GeV (right). A comparison is given of generated Higgsmass (green) and visible llτhτh (red), llτlτh (blue) and llτlτl (pink) masses.

The invariant mass of leading and sub-leading Z bosons which undergoesdi-lepton and di-tau decays is presented for signal samples of Higgs massesmH = 200 and 600 GeV in Figures 3.7 and 3.8, respectively. A good agree-ment is observed for leading generated Z boson and ll masses, in fact they


overlaid each other completely. The narrow peak suggests to define a masswindow around the nominal Z boson mass, 60 < mZ < 120 GeV, without theloss of signal events. Instead, the behavior of peak shifting has been observedfor sub-leading Z boson mass distributions due to neutrino losses. The effectenhances with the number of taus undergo leptonic decay increases. Hencethe widely spread sub-leading Z boson mass distribution is expected towardsthe lower side of nominal Z boson mass, and the final state dependent masswindow can also be defined.

Figure 3.7: Invariant ll mass distribution of leptons coming from leading Zdecay for Higgs masses mH = 200 GeV (left) and mH = 600 GeV (right). Acomparison is given of generated leading Z mass (green) and visible ll mass(red).

In high energy collisions, we expect the out-coming particles carrying highmomentum values due to high scale momentum transfers involved. The sameobservations have been made for leptons and leptonically or hadronically de-caying taus involve in this analysis, shown in Figure 3.9 and 3.10 for signalsamples of Higgs masses mH = 200 and 600 GeV, respectively. Green andblue distributions represent the first and second highest transverse momen-tum of leptons coming from leading Z boson decay, respectively. Blue andpink distributions represent the pT of taus decaying leptonically and hadron-ically for llτlτh final state, respectively, and the first and second highest pTof taus decaying leptonically for llτlτl final state, respectively. The shifts ofpT spectrums toward the higher pT values have been observed, for all thefour objects, with the increase in Higgs mass value. The sets of pT can there-fore be designed according to the different final states: [10, 10, 20, 20] GeV


Figure 3.8: Invariant ττ mass distribution of taus coming from sub-leadingZ boson decay for Higgs masses mH = 200 GeV (left) and mH = 600 GeV(right). A comparison is given of generated sub-leading Z mass (green) andvisible τhτh (red), τlτh (blue) and τlτl masses (pink).

for llτhτh, [10, 10, 10, 20] GeV for llτlτh and [10, 10, 10, 10] GeV for llτlτl finalstates5.

Furthermore, a certain separation of out-coming particles is expected inthe co-ordinate space of detector. The azimuthal angle φ separation and theseparation in η− φ space between leading and sub-leading Z bosons, leptonscoming from leading Z boson decay and taus coming from sub-leading Zboson decay have been studied. Observations are given in Figure 3.11, 3.12and 3.13 in terms of ∆φ, and Figures 3.14, 3.15 and 3.16 in terms of ∆R(=√

∆η2 + ∆φ2), for signal samples of Higgs mass mH = 200 and 600 GeV.A peaking behavior is observed for leading and sub-leading Z bosons in bothφ and η − φ space for all the mass points. It implies the back to back decayof Higgs boson into Z bosons. For the low mass values, the back to backseparation is also observed for leptons and taus but instead for high masses,the sharp peak behavior gets destroyed due to highly boosted Z boson decays,hence the large separation of leptons and taus coming from Z boson decaysdo not take place. In conclusion, the φ separation and the separation in η−φspace between out-coming particles, in particular between Z bosons, can be

5The simulation studies suggest to define a set of pT for all the four objects that havebeen re-checked at the level of reconstruction, described in Chapter 4. The lower pT thresh-olds involved in the reconstruction of respective physics objects, and the pT dependentprobabilities to be mimicked by other particles have also been taken into account.


Figure 3.9: pT distribution of leptons and taus coming from leading Z andsub-leading Z bosons decay, respectively, for Higgs mass mH = 200 GeV.Green and red distributions represents first highest and second highest pTof leptons. Blue and pink distributions represents first highest and secondhighest pT of taus (upper left: sub-leading Z → τhτh), pT of lepton andhadronic tau (upper right: sub-leading Z → τlτh), and first highest andsecond highest pT of leptons (lower: sub-leading Z→ τlτl).

a key observable for signal to background separation since one expect thedifferent format for 2 → 2 body decay (SM ZZ and WZ) and 2 → 3 bodydecay (Zbb and Zcc).


Figure 3.10: pT distribution of leptons and taus coming from leading Z andsub-leading Z bosons decay, respectively, for Higgs mass mH = 600 GeV.Green and red distributions represents first highest and second highest pTof leptons. Blue and pink distributions represents first highest and secondhighest pT of taus (upper left: sub-leading Z → τhτh), pT of lepton andhadronic tau (upper right: sub-leading Z → τlτh), and first highest andsecond highest pT of leptons (lower: sub-leading Z→ τlτl).


Figure 3.11: Azimuthal angle φ separation between Z bosons for Higgs massesmH = 200 GeV (left) and mH = 600 GeV (right).

Figure 3.12: Azimuthal angle φ separation between leptons coming fromleading Z boson decay for Higgs masses mH = 200 GeV (left) and mH = 600GeV (right).


Figure 3.13: Azimuthal angle φ separation between taus coming from sub-leading Z boson decay for Higgs masses mH = 200 GeV (left) and mH = 600GeV (right).

Figure 3.14: η − φ space separation, in terms of ∆R, between Z bosons forHiggs masses mH = 200 GeV (left) and mH = 600 GeV (right).


Figure 3.15: η−φ space separation, in terms of ∆R, between leptons comingfrom leading Z boson decay for Higgs masses mH = 200 GeV (left) andmH = 600 GeV (right).

Figure 3.16: η − φ space separation, in terms of ∆R, between taus comingfrom sub-leading Z boson decay for Higgs masses mH = 200 GeV (left) andmH = 600 GeV (right).

Chapter 4

Search for The SM HiggsBoson in H→ ZZ→ l+l−τ+τ−

Final States

In this chapter the H → ZZ → l+l−τ+τ− analysis performed using the datacollected by the CMS experiment in years 2011 at

√s = 7 TeV corresponding

to total integrated luminosity of L = 5.1fb−1, and 2012 at√s = 8 TeV cor-

responding to L = 12.2fb−1 is presented. In the first part, the identificationand the isolation of the objects involved in this analysis are described. Inaddition, the work carried out to establish the analysis selection criteria ispresented. Results for the final selection in terms of a comparison of data andsimulation predictions at each step of the selection criteria are given next toit. Afterwards, the complete process used to estimate the background is de-scribed. The last part describes the systematic uncertainties involved in thisanalysis. Final results in terms of the exclusion limits and the conclusionsare given in the next chapter.

4.1 Experimental Data Samples

The data collected with the CMS experiment, for which all the sub-detectorsperformed properly, have been used for this analysis. The datasets and thecorresponding primary datasets are given in Table 4.1. During the data tak-ing periods, the instantaneous luminosity which is known with a precision of4.5%[54], varied over the range 1029−1033 cm−2 s−1. The events correspond-ing to the given primary datasets were required to pass the ‘double muon’ or‘double electron’ high level triggers (HLTs) [Section 2.2.7] at the time of datacollection. HLT paths had been changed with the increasing instantaneous

77

4.2. Lepton Identification 78

luminosity delivered by the LHC, listed in Table 4.2. The triggers involvedwere based on the pT and some additional requirements for the muons andthe electrons. Two muons with minimum pT threshold value of 7 GeV inthe event were required for the particular event to satisfy the double muontrigger, in the starting period of pp collision in year 2011. The pT thresholdvalue increased asymmetrically to 13 and 8 GeV for the highest and secondhighest pT muons respectively, in the middle period of year 2011, and to 17and 8 GeV afterwards. The same pT threshold value had been continued fordata collection in year 2012. On the other hand, double electron events wereselected with more complicated criteria based on the pT of the electrons plusthe identification and isolation requirements.

The same trigger paths have also been required for MC simulated eventswhile performing the analysis with logical ‘OR’ requirement between HLTpaths corresponding to the years 2011 and 2012.

Table 4.1: Datasets corresponding to data collected by the CMS experimentin years 2011 and 2012.

Dataset Primary dataset Year

Run2012A-13Jul2012-v1 DoubleMu / DoubleElectron 2011Run2012A-recover-06Aug2012-v1 DoubleMu / DoubleElectron 2011Run2012B-13Jul2012-v4 DoubleMu 2012Run2012B-13Jul2012-v1 DoubleElectron 2012Run2012C-24Aug2012-v1 DoubleMu / DoubleElectron 2012Run2012C-PromptReco-v2 DoubleMu / DoubleElectron 2012

4.2 Lepton Identification

4.2.1 Muon Identification

The reconstructed muons [Section 3.2.3] collection contains a significant amo-unt of (un-decayed) charged hadrons, such as kaons and pions, which aremis-identified like muons. In order to have a pure sample of muons, the iden-tification requirements must be applied. The particle flow (PF) identificationhas been used for the muon identification in this analysis, which is based onthe PF event reconstruction[33]. The muons are required to be global ortracker muons as well. The PF identification uses the measurement of en-ergy released by the tracks in the calorimeter to identify the muons inside


Table 4.2: HLT paths used to select the final sample of 2011 and 2012 data.

HLT path Run range Year

µµ channelsHLT DoubleMu7 160431-163869 2011HLT Mu13 Mu8 165088-178380 2011HLT Mu17 Mu8 178420-180252 2011HLT Mu17 Mu8 190450-203002 2012

HLT Mu17 TkMu8 190450-203002 2012ee channels

HLT Ele17 CaloIdT CaloIsoVL TrkIdVL TrkIsoVL 160432-180252 2011Ele8 CaloIdL CaloIsoVL TrkIdVL TrkIsoVL

HLT Ele17 CaloIdT CaloIsoVL TrkIdVL TrkIsoVL 190450-197044 2012Ele8 CaloIdL CaloIsoVL TrkIdVL TrkIsoVL

HLT Ele17 CaloIdT TrkIdVL CaloIsoVL TrkIsoVL 190450-203002 2012Ele8 CaloIdT TrkIdVL CaloIsoVL TrkIsoVL

the jets with high efficiency and low mis-identification rate.

Each global muon gives rise to a PF identified muon if its combined mo-mentum of all the PF elements1 is compatible with that determined from thesole tracker within three standard deviations.

On the other hand, the other muons which have a track momentum sig-nificantly larger than the corresponding energy deposit in the calorimeterthereby making them incompatible with a charged hadron hypothesis, canalso be recovered. Firstly all the global muons, not already selected by thealgorithm and for which an estimate of the momentum exists with a preci-sion better than 25%, are treated as PF identified muons. The redundancyof the measurements in the tracker and the calorimeters thus allows a fewmore muons to be found without increasing the mis-identification rate. Thisredundancy is further exploited by progressively removing the tracks fromthe blocks ordered according to their measured pT uncertainty. The processstops when either all the tracks with the pT uncertainty in excess of 1 GeVhave been examined, or the removal of a track would render the total track

1A PF object is expected to give rise to several elements in the various CMS sub-detectors: one charged-particle track, and/or several calorimeter clusters, and/or onemuon track (in case of muons). The PF link algorithm provides a block after combiningthe following elements.


momentum smaller than the calibrated calorimetric energy. Less than 0.3%of the tracks are concerned by this procedure.

Furthermore, to ensure the high efficiency of the reconstruction in thetracker acceptance, a preselection is applied requiring the pµT > 5 GeV and|η| < 2.4. In addition, other sources of muon-like signature in the detectorare the cosmic, decay-in-flight and punch-through muons. The decay-in-flight muons are the real muons which originate from the decay of kaons andpions and give good hits in the muons chambers. On the other hand, thepunch-through muons are not real muons instead are the particles (hadrons)which do not undergo nuclear interactions upstream of the muon system.The selection steps are as following:

• The global track should have at least one good muon chamber hit, tosuppress the hadronic punch-through and the decay-in-flight muons;

• The global track should match to at least two muon stations, to sup-press the punch-through and the accidental track-to-segment matches.It also provides the consistency with the muon trigger, which requiresthe segments in at least two muon stations to obtain a meaningful es-timate of the muon pT . Moreover, it ensures the muons arbitration i.e.a track is uniquely associated to a muon segment;

• The tracker track should have at least one hit in the pixel detector, tosuppress the decay-in-flight muons;

• The tracker track should fire at least five tracker layers, to suppress thedecay-in-flight muons. It also guarantee a good pT measurement;

• The χ2/ndof of the global track fit is required to be less than 10, tosuppress the hadronic punch-through and the decay-in-flight muons;

• The transverse and the longitudinal impact parameters of the trackertrack, dxy and dz, as calculated with respect to the primary vertex, arerequired to satisfy the cuts: |dxy| < 0.2 cm, |dz| < 0.5 cm;

4.2.2 Electron Identification

After the reconstruction of electrons [Section 3.2.4], a further set of require-ments is introduced to distinguish between the prompt electrons and thecharged pions mis-identified like the electrons, and the electrons producedfrom photon conversions. The main handles on reducing the mis-identified


electron rate are the angular difference between the track and the superclus-ter, the ratio of HCAL to ECAL energy associated with the supercluster, andthe ECAL shower shape. The identification of electrons relies on a BoostedDecision Tree (BDT) multivariate technique. Twenty variables have beenused for the Multi Variate Analysis (MVA) training[45], listed as following:

track-ECAL matching variables:

• Esc/Pin - the ratio of the supercluster energy and the measured electrontrack momentum at the innermost track position;

• Ee/Pout - the ratio of the energy of the closest cluster to the electrontrack extrapolation to ECAL and the measured electron track momen-tum at the outermost track position;

• ∆ηin - the difference in η between the electron track and the superclus-ter at the vertex, and at the calorimeter surface;

• ∆φin - difference in φ between the electron track and the superclusterat the vertex;

• IoEmIoP = (1/energy of supercluster)−(1/momentum of electron);

electron-pion discrimination variables, based on the calorimeterenergy and the shower shape:

• H/E - the ratio of the supercluster HCAL energy to the ECAL energy.

• the ratio of the pre-shower energy and the uncorrected energy2 of thesupercluster;

• σiηiη - the RMS of energy along the η direction within the supercluster;

• σiφiφ - the RMS of energy along the φ direction within the supercluster;

• the width of the supercluster in the η and φ directions;

• 1−E1×5/E5×5 = 1−(energy inside 1×5 grid of crystals in η×φ aroundthe seed crystal) / (energy inside 5× 5 grid of crystals in η× φ aroundthe seed crystal);

2The lack of containment in the cluster reconstructed energy due to electronic noisecan be corrected as a function of the measured number of crystals which make up thecluster volume.

4.3. Lepton Isolation 82

• R9 - the ratio of the energy in the 3 × 3 grid of crystals around theseed crystal to the uncorrected energy of the supercluster;

pure tracking observables for further improvement of electron-piondiscrimination:

• the measured bremsstrahlung fraction from electron track: (measuredelectron track momentum at the innermost track position - measuredelectron track momentum at the outermost track position) / measuredelectron track momentum at the innermost track position;

• the normalized χ2 of the closest CTF track to the electron, and of theelectron track;

• the number of tracker layers fired by the closest CTF track to theelectron;

In addition, the pT of electron and the η of supercluster are used forthe MVA training. The thresholds for the BDT discriminator to identifyelectrons corresponding to two pT and three η values are given in Table 4.3.The electrons should have BDT discriminator value larger than optimizedvalue to be declared as identified electrons.

Table 4.3: Thresholds for the BDT discriminator to identify electrons[51].

Electron pT (GeV) |η| < 0.8 0.8 < |η| < 1.479 1.479 < |η|5 < pT < 10 0.47 0.004 0.295pT > 10 0.5 0.12 0.6

Furthermore, electron track is required to have no more than 1 missinghits in the pixel detector to ensure the rejection of electrons originated fromphoton conversion.

4.3 Lepton Isolation

In the LHC environment, a large number of particles are produced in thehigh energy pp collision. So the measurement of the isolated behavior of theobjects is very challenging at CMS. Muons and electrons from the H → ZZdecays are typically well isolated, while leptons from heavy flavor decays and

4.3. Lepton Isolation 83

decays in flights are expected to be poorly isolated due to be inside the jets.Moreover, muons and electrons coming form the decay of taus are also ex-pected to be isolated in the detector. Therefore, the proper computation ofthe lepton isolation is a must.

The PF based approach has been used for the isolation computationsfor both the electrons and muons. The tracker and the calorimeter infor-mation of PF particles have been used to calculate the isolation depositsaround the muons and electrons, so-called PF combined isolation. All thecharged particles are considered in the isolation calculations, while pho-tons and neutral hadrons are required to have ET > 0.5 GeV to be con-sidered in the isolation sum. The isolation variables sum up the particlesof the above types with ∆R < 0.4 with respect to the lepton axis, where∆R =

√(ηlep − ηiso)2 + (φlep − φiso)2 with subscript iso stands for the par-

ticles to be considered in isolation calculations. In case of electrons, innerveto cones of ∆R = 0.015 and ∆R = 0.08 are defined for the neutral hadronsand photons in endcap regions, respectively. The pT weighted PF combinedisolation is used in the analysis given by the following formula:

IPFrel =

∑(pchargedT + Eγ

T + EneutralT

)plT

(4.1)

where P chargedT is the charged hadron transverse momenta, Eγ

T and EneutralT

are the photon and neutral hadron transverse energies respectively. plT rep-resents the transverse momentum of the lepton.

Pile-up Corrections

The average number of pile-up (PU) interactions increased considerably alongwith the increment of the instantaneous luminosity in 2011 and 2012 run con-ditions of the LHC. Isolation variables are among the most pile-up sensitivevariables in this analysis. Pile-up leads to the increase in mean energy de-posited in the detector which further leads to the rise of the mean isolationvalues. Thus, the efficiency of a cut on isolation variables strongly dependson pile-up conditions. The pile-up effect is observed to be stronger in thecalorimeters and quite feeble in the tracking system. This is due to the re-quirement that the tracks contributing to the isolation cone originate froma common vertex. In order to have a pile-up robust analysis, the isolationvariable has to be corrected. Among several correction methods, the oneusing the FastJet[52, 53] energy density ρ in the event has been chosen toestimate the mean PU contribution within the isolation cone of a lepton for

4.4. Hadronic Tau Identification and Isolation 84

PF Isolation. A ρ variable is defined for each jet in a given event and themedian of the ρ distribution for each event is taken. The correction to theisolation variable is then applied according to the formula:

IPFrel (ρ) =

(∑pchargedT +max(0,

∑EγT +

∑EneutralT − ρ× Aeff )

)P lT

(4.2)

where effective area Aeff is the geometric area of the isolation cone timesa correction factor which accounts for residual dependence of the isolationon pile-up as a function of pseudo-rapidity[8].

4.4 Hadronic Tau Identification and Isolation

Hadronic tau identification[55] is needed to discriminate the backgroundscontributing to the signal region due to mis-identified objects (e, µ and jets)as described in Section 3.3. To discriminate against backgrounds where alepton can be mis-identified like a tau, the muon and the electron discrimi-nations are used. The HPS algorithm provides three working points for themuon discrimination, described as following:

• Loose Muon Rejection: Requiring that the highest pT track in thereconstructed tau should have no track segments in the muon detector.

• Medium Muon Rejection: Requiring that the highest pT track in thereconstructed tau should have no hits in the muon detector.

• Tight Muon Rejection: Requiring that the highest pT track in thereconstructed tau should have no hits in the muon detector. In theSingle Hadron category, it is further required that the ratio of thesum of energy deposits in the ECAL and HCAL associated to thisreconstructed tau and the track momentum of HPS tau should be largerthan 0.2, corresponding to a veto of the energy deposition signature ofa minimal ionizing particle.

For electron rejection, the PF multivariate electron discriminator is used(PF

e/γmva)[56]. The HPS algorithm provides three working points for electron

discrimination, described as following:

• Loose Electron Rejection: Requiring PFe/γmva < 0.6.

• Medium Electron Rejection: Requiring PFe/γmva < −0.1 and the pseudo-

rapidity 1.4442 > |η| > 1.5666.


• Tight Electron Rejection: Requiring PFe/γmva < −0.1 and the pseudo-

rapidity 1.4442 > |η| > 1.5666 plus the bremsstrahlung pattern re-quirements. In the Single Hadron category, the ratio H/P is requiredto be greater than 0.8, where H is the energy deposited by the onlytrack in HCAL and P is the track momentum. On the other hand, inthe Hadron Plus Strip category, the ratio Ebrem/Eγ should be largerthan 0.99, where Ebrem is the energy deposited by the PF gamma par-ticles in the HPS tau lying at a certain η separation with respect tothe highest PT track, and Egamma is the energy deposited by all the PFgamma particles in the HPS tau. An additional requirement on theHPS tau invariant mass is also used.

In addition, the HPS algorithm also provides another discriminator againstelectron identified by the MVA algorithm. It is based on the output of a mul-tivariate Boosted Decision Tree (BDT) considering the PF

e/γmva as the training

variable. The other variables are the following:

• the mean of ∆η and ∆φ of the neutral particles (form the leadingcharged hadron) in the reconstructed tau, weighted by their pT .

• the electromagnetic energy fraction of the highest pT charged hadronor photon of the reconstructed tau candidate in pT .

• the ratio of the HCAL energy of the highest pT charged hadron and itsmomentum.

• the number of neutral particles.

• the visible mass of the reconstructed tau3.

• The fraction of the visible energy of the reconstructed tau carried bythe neutral particles.

The discrimination of the backgrounds where the jets can be mis-identifiedlike taus, is mainly based on the isolation. The hadronic tau isolation iscalculated as the energy sum of the PF particles in a solid cone of ∆R =0.5 around the reconstructed tau four-vector. Pile-up correction is appliedin terms of the ∆β correction, which sums the energy of charged pile-upparticles with ∆R < 0.8 with respect to the leading charged track in the

3The particles with visible signature in the detector are used for hadronic tau recon-struction and therefore considered to compute the invariant mass of hadronic tau, so-calledvisible mass. The neutrinos produced in τh decay which escape the detection are not con-sidered.


signal cone4. A large cone is used so that there are more statistics availablefor the correction. The correction to the neutral isolation is given by thesummed energy, scaled by a correction factor, f∆β. The isolation is definedas

IPF (∆β) =∑(

pchargedT +max(0, EγT + Eneutral

T − f∆β × EPUT ))

(4.3)

where EPUT is the charged particle pT sum from pile-up vertices. The

correction factor f∆β is optimized from simulations defined as the ratio ofthe slope of energy sum of PF charged particles in cone of ∆R < 0.8 and theslope of energy sum of PF neutral particles in cone of ∆R < 0.5 as a functionof number of pile-up vertices. The optimized value is f∆β = 0.0729.

The HPS algorithm provides the following four working points for isola-tion:

• Very loose Combined Isolation: Requires sum of charged and ∆β-corrected gamma isolation contributions < 3 GeV.

• Loose Combined Isolation: Requires sum of charged and ∆β-correctedgamma isolation contributions < 2 GeV.

• Medium Combined Isolation: Requires sum of charged and ∆β-correctedgamma isolation contributions < 1 GeV.

• Tight Combined Isolation: Requires sum of charged and ∆β-correctedgamma isolation contributions < 0.8 GeV.

The isolation efficiency (ratio of number of of hadronic taus passing theisolation requirements to the total number of hadronic taus) for all the HPStau working points are presented in Figure 4.1, parametrized in generatedtau pT and number of pile-up vertices. The reconstructed taus that matchto the generated taus within the cone of ∆R < 0.1 with pT > 0 GeV and|η| < 2.3 are selected. In addition, the isolated taus are required to havepT > 20 GeV. The Medium and Tight combined isolation working points areused for this analysis [Section 4.6] with corresponding efficiency of 40–50%.A flat behavior of both the working points is observed with respect to pile-up

4All the decay products of tau are supposed to be found in the signal cone.

4.5. Establishing the Signal Selection Criteria 87

vertices. Similar studies have been performed using data and a systematicuncertainty of 6% on the hadronic taus reconstruction is estimated using aglobal fit[60].

Moreover the background reduction power of both the hadronic taus isola-tion working points where jets are mis-identified like hadronic taus, in contextof given analysis, is described in Section 4.7.2.

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Figure 4.1: Efficiency (from simulation) for the ∆β-corrected combined HPStau isolations as a function of generated τ pT (left) and reconstructed vertices(right) for

√s = 8 TeV.

4.5 Establishing the Signal Selection Criteria

This section presents the work that has been carried out to establish a se-lection criteria to select the signal-like events with strong power of the back-ground events reduction. All the information collected from the studies atgenerator level [Section 3.4] have been re-checked at reconstruction level.Only the identified leptons and the very loosely isolated hadronic taus thatsatisfy the loose electron and loose muon discriminators have been partici-pated in these studies. The η requirements for muon, electrons and hadronictaus are 2.4, 2.5 and 2.3 respectively.

Figure 4.2 represents the pT distributions of four highest pT leptons, andtwo highest pT hadronic taus in the event, for Higgs mass mH = 200 GeV at√s = 8 TeV, since this analysis involves four leptons and two hadronic taus


in the final states, llτlτl and llτhτh respectively. Moreover, the comparisonof the pT distributions of the four highest pT leptons for the signal and thebackground events is given in Figure 4.3. This comparison ultimately leadsto the cut value of pT > 10 GeV for all the four leptons, shown by the blackvertical line in all the plots.

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Figure 4.2: pT distributions for four highest pT leptons (left) and two highestpT hadronic taus (right) in the event, for Higgs mass mH = 200 GeV at√s = 8 TeV. Where the pT values decrease from pl1T to pl4T for leptons, and

from pτh1T to pτh2

T for the hadronic taus. The black vertical lines show thechosen cut values, 10 GeV for all the four leptons and 20 GeV for both thehadronic taus.

For first two highest pT leptons, the selection requirement results in thehuge reduction of ZZ and tt backgrounds with a small loss of signal events,since the kinematics of pp→ ZZ→ l+l−τ+τ− decay channel is different frompp → H → ZZ → l+l−τ+τ− decay channel and less energetic leptons areinvolved in the former. On the other hand, for tt background, the leptonscarry lower pT due to neutrino losses involved in this decay process. Dueto the requirement for the third highest pT lepton, the WZ + jets eventsalso get reduced due to the rejection of the lower pT lepton coming from thedecay of W boson. Requirement on the fourth highest pT lepton gives hugereduction of all the backgrounds due to the fact that the lepton is, in actual,the low pT jet mis-identified as a lepton or the lepton inside the quark jetcarrying a small fraction of jet momentum. In addition, the pT thresholdof 20 GeV is chosen for both the hadronic taus (shown by a black verti-cal line) due to the higher jet to hadronic tau and leptons to hadronic tau


mis-identified rates for lower pT as described in Section 4.7.2. Of course itleads to the huge signal losses but the loosening the threshold value results inthe increase of backgrounds that contribute due to the mis-identified objects.

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Figure 4.3: Comparison of the pT distributions of four highest pT leptonsin the event for the signal and the backgrounds: first highest (upper left),second highest (upper right), third highest (lower left) and forth highest(lower right). The black vertical lines show the pT threshold value of 10GeV.

Furthermore, the studies for isolation variable of the leptons have beencarried out. Figure 4.4a shows the isolation variable distributions of the fourleptons in the event with the corresponding four minimum isolation values,for Higgs mass mH = 200 GeV at

√s = 8 TeV. Two well isolated leptons


expected from the decay of Z boson are denoted as the best and the secondbest isolated leptons corresponding to the minimum and the second mini-mum isolation values respectively. The next two less isolated leptons aredenoted by the second worst and the worst isolated leptons corresponding tothe third and fourth minimum isolation values respectively. Figures 4.4b and4.4c represents the isolation variable distributions for the three muons andthree electrons in the event, respectively, with the corresponding three min-imum isolation values. The worst isolated muon(electron) is the one havingthe third minimum isolation value. A comparison of the isolation variablefor the signal and the background events is given in Figures 4.5 and 4.6 formuons and electrons respectively.

The isolation value for the best and the second best isolated leptons arerequired to be less than 0.25 for all the final states. It leads to the smallreduction in background events. For the final states with three leptons andone hadronic tau, llτlτh final states, the isolation requirement of the leptonwith third minimum isolation value highly affects the signal and backgroundseparation due to the huge reduction of backgrounds which contributes dueto the jets that are mis-identified like leptons, and expected to be poorlyisolated. The chosen cut values of isolation for muon and electron which arecombining with hadronic tau to reconstruct the sub-leading Z are 0.15 and0.1 respectively. The isolation values chosen for the final states with both thetaus undergo leptonic decays, llτhτh final states, both the second worst andworst isolated leptons are required to be less than 0.25. All the cut valuesare shown with the black vertical lines in all the plots.

Figure 4.7 shows a comparison of the signal and the background events forthe ∆R values between the two leptons which participate in the reconstruc-tion of the leading Z boson and the additional two objects which reconstructthe sub-leading Z boson. This variable does not provide a strong backgroundreduction power but, indeed, the ∆R > 0.3 has been chosen to ensure thatthe objects which participate in the final four objects final state give theseparate signature in the η − φ space.


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(c)

Figure 4.4: Isolation variable distributions for the four leptons (upper), forthe three muons (lower left) and the three electrons (lower right) in the eventwith minimum isolation values, for Higgs mass mH = 200 GeV at

√s = 8

TeV. The black vertical lines show the chosen cut values, 0.25 for all the fourleptons for llτlτl final state, and for two well isolated muons(electrons). Thevalue for the isolated muon(electron) with third minimum value is requiredto be less than 0.1(0.25) for llτlτh final states.


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Figure 4.5: Comparison of the isolation variable distributions for the threemuons in the event with minimum isolation values, the best isolation (upper),the second best isolation (lower left) and the worst isolation (lower right).The black vertical lines show the chosen cut values, 0.25 for the two wellisolated muons. The value for the isolated muon with third minimum valueis required to be less than 0.15 for llτµτh final states.

4.6. Event Selection 93

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Figure 4.6: Comparison of the isolation variable distributions for the threeelectrons in the event with minimum isolation values, the best isolation (up-per), the second best isolation (lower left) and the worst isolation (lowerright). The black vertical lines show the chosen cut values, 0.25 for thetwo well isolated electrons. The value for the isolated electron with thirdminimum value is required to be less than 0.1 for llτeτh final states.

4.6 Event Selection

The event selection requires the event to pass the trigger paths as explainedin Section 4.1. It ensures the presence of the two muons or the electronsthat could lead to the leading Z boson reconstruction. In addition, the eventshould have two more objects according to the decay of sub-leading Z toτhτh, τlτh and τlτl final states. All the four objects should satisfy the iden-


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Figure 4.7: Comparison of signal and background for the ∆R values betweenthe two leptons giving the reconstructed leading Z boson (left) and the twoobjects giving the reconstructed sub-leading Z boson (right).

tification requirements as described in Section 4.2, where the hadronic tausare required to be very loosely isolated. These four object combine to givethe reconstructed Higgs boson in the event (more than one combinatorics areallowed at this step). This section provides the detail of the complete set ofselection used for the leading and the sub-leading Z bosons. Moreover, theremoval of overlap with 4l (l = e, µ) final states is described (such overlapoccurs due to the one or two leptons which are mis-identified like hadronictaus and give the signature of llτlτh and the llτhτh final states).

4.6.1 Leading Z Boson Selection

Z→ µµ:

A pair of muons is selected if it satisfies the following requirements:

• the µ′s transverse momentum pT > 20 GeV (leading), 10 GeV (sub-leading);

• the µ′s absolute pseudo-rapidity |η| < 2.4;

• the µ′s PF combined relative isolation less than 0.25 with ρ correctionswith Aeff as described in Section 4.3;

• the µ′s should carry the opposite charge.


Z→ ee:

A pair of muons is selected if it satisfies the following requirements:

• the e′s transverse momentum pT > 20 GeV (leading), 10 GeV (sub-leading);

• the e′s absolute pseudo-rapidity |η| < 2.4;

• the e′s PF combined relative isolation less than 0.25 with ρ correctionswith Aeff ;

• the e′s should carry the opposite charge.

After these selection steps, between all the lepton pairs (e+e− or µ+µ−)satisfying the above requirements, a reconstructed Z boson is chosen withmass closest to the nominal Z mass. In addition, a mass window is de-fined 60 < mZ < 120 GeV that leads to a huge reduction of tt and all thenon-resonant backgrounds. tt background shows a long tail behavior of lead-ing Z mass towards the lower mass side due to neutrino losses involved intt → WbWb → l+l−ννbb decays process. The signal and other backgroundsget effected a little because of the presence of two good leptons in the event.

Figure 4.8 shows the leading Z benchmark plots for 2011 and 2012 data.A good data to simulations agreement has been observed for all the plots.The Z + jets background comprising almost the full contribution that hasa large cross-section value and hence the higher rate of production in ppcollision.

4.6.2 Sub-leading Z Boson Selection

Z→ τhτh:

In this decay process of sub-leading Z boson, there is a large backgroundcontribution in the signal region due to presence of two hadronic taus. TheZ + jets comprises the main contribution where jets are mis-identifying likehadronic taus. The following set of selection is applied for the backgroundreduction:

• the HPS τ ′s should satisfy the Tight Combined Isolation requirementwith ∆β correction as described in Section 4.4;

• the HPS τ discriminator against electron medium working point;

• the HPS τ discriminator against muon medium working point;


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Figure 4.8: Reconstructed invariant mass distribution of muons (left) andelectrons (right) coming from leading Z decay, for data 2011 and 2012 at√s = 7 (upper) and 8 TeV (lower) respectively.

• the HPS τ ′s transverse momentum pT > 20 GeV;

• the HPS τ ′s absolute pseudo-rapidity |η| < 2.3;

• the HPS τ ′s are required to be oppositely charged;

• 30 < mττ < 90 GeV.

Z→ τµτh:

Less background is involved for this decay process of sub-leading Z boson,because of the presence of a muon. Muons can be selected with strong


background reduction. Both the Z + jets and the WZ + jets backgroundscontributes in the signal region where one jet is mis-identifying like a muonand another like a hadronic tau for the former but the probability of a jetto fake a muon is smaller than to fake a hadronic tau. In addition, its alsopossible to have a real muon from the b quark decay. For WZ + jets, thereal muon comes from the decay of W boson and one jet is mis-identified ashadronic tau. The set of selection used is following:

• the µ transverse momentum pT > 10 GeV;

• the µ absolute pseudo-rapidity |η| < 2.4;

• the µ combined relative isolation less than 0.15 with ρ corrections withAeff ;

• the HPS τ should satisfy the Medium Combined Isolation requirementwith ∆β correction;

• the HPS τ discriminator against electron loose working point;

• the HPS τ discriminator against muon tight working point;

• the HPS τ transverse momentum pT > 20 GeV;

• the τ ′s absolute pseudo-rapidity |η| < 2.3;

• the µ and τ are required to be oppositely charged;

• 30 < mµτ < 90 GeV.

Z→ τeτh:

For this decay process of sub-leading Z boson, both the Z + jets and theWZ + jets backgrounds contributes. One jet mis-identified like an electronand another like hadronic tau give contribution of Z + jets. Like Z → τµτhfinal state, the WZ + jets contributes due to one real electron which comesfrom decay of W boson and another jet mis-identified like the hadronic tau.The selection used for background suppression is following:

• the e transverse momentum pT > 10 GeV;

• the e absolute pseudo-rapidity |η| < 2.5;

• the e combined relative isolation less than 0.1 with ρ corrections withAeff ;


• the HPS τ should satisfy the Medium Combined Isolation requirementwith ∆β correction;

• the HPS τ discriminator against electron identified by the MVA algo-rithm;

• the HPS τ discriminator against muon loose working point;

• the HPS τ transverse momentum pT > 20 GeV;

• the τ ′s absolute pseudo-rapidity |η| < 2.3;

• the e and τ are required to be oppositely charged;

• 30 < meτ < 90 GeV.

Z→ τeτµ:

In this decay mode of sub-leading Z boson, huge neutrino losses are involved.Therefore the extended mass window is used, 0 < meµ < 90 GeV. Thisdecay process has small ZZ background contribution due to the presence ofdifferent flavour leptons. The Z + jets background contributes due to mis-identification of one jet like electron and another jet like muon. On the otherhand, WZ + jets contributes where either lepton comes from W boson decayand one jet is mis-identifying like the other one. The selection criteria appliedfor background reduction is following:

• both the µ and the e transverse momentum pT > 10 GeV;

• the µ and the e absolute pseudo-rapidity |η| < 2.4 and 2.5 respectively;

• both the µ and the e combined relative isolation less than 0.25 with ρcorrections with Aeff ;

• the e and µ are required to be oppositely charged.

In addition to leading and sub-leading Z bosons selection, additional setof selections is applied. The difference between the longitudinal impact pa-rameters of all the possible two objects which participate in the four objectfinal state, should be dZ < 0.1 cm. It ensures that all the objects are com-ing from common vertex and hence provides a small rejection of the fake taubackground. Also all the possible two objects participating in the four objectfinal state should have separation is η − φ space i.e. ∆R > 0.3. It ensuresthat the objects involve are different from each other.


4.6.3 Removal of Overlap with 4l (l = e, µ) Analysis

A veto process is implemented as the last step of llττ selection. It requiresthe rejection of event if in addition to four objects, there is a muon with∆R > 0.3 with respect to four objects which participate in the four objectfinal state, satisfying the following loose selection criteria:

• the µ transverse momentum pT > 10 GeV and absolute pseudo-rapidity|η| < 2.4;

• the µ combined relative isolation less than 0.4 with ρ corrections withAeff ;

• the µ is loosely identified: is PF muon, and Global or tracker muon.

or there is an electron with ∆R > 0.3 with respect to four objects whichparticipate in the four object final state, satisfying the following loose selec-tion criteria:

• the e transverse momentum pT > 10 GeV and absolute pseudo-rapidity|η| < 2.5;

• the e combined relative isolation less than 0.4 with ρ corrections withAeff ;

• the e is identified as described in Section 4.2 without conversion removalcheck.

or there is a tau with ∆R > 0.3 with respect to four objects which par-ticipate in the four object final state, satisfying the following loose selectioncriteria:

• the HPS τ transverse momentum pT > 20 GeV and absolute pseudo-rapidity |η| < 2.3;

• the HPS τ satisfy the Medium combined isolation requirement with ∆βcorrection;

• the HPS τ discriminator against electron loose working point;

• the HPS τ discriminator against muon loose working point.

Moreover, the event is rejected if there is a muon with

• ∆R < 0.01 with respect to objects other than muon for all the eightfinal states and satisfying the loose muon selection criteria.


or an electron with

• ∆R < 0.01 with respect to objects other than muon and electron forall the eight final states except the llτlτl final states, and satisfying theloose electron selection criteria.

The data to simulations comparisons for some relevant physics observablesare given in Figures 4.9, 4.10 and 4.11 respectively. The isolation require-ments are relaxed for the objects which combine to reconstruct the sub-leading Z to get more statistics. For the pT comparison, the upper two (mid-dle two) plots give the comparisons for leading and sub-leading electrons(muons) coming from decay of leading Z boson. The final states, eeτhτh andeeτlτh for electrons and µµτhτh and µµτlτh for muons, are used for this com-parison. Similarly, the lower plot shows the comparison for hadronic taususing llτhτh final states. A good agreement is observed for all the plots.

Concerning the PF isolation variable in Figure 4.10, the upper two (lowertwo) plots show the comparisons for leading and sub-leading electrons (muons)coming from decay of leading Z boson. The final states, eeτhτh and eeτlτhfor electrons and µµτhτh and µµτlτh for muons, are used for this comparison.Furthermore, the η comparisons for electrons, muons and hadronic taus aregiven in Figure 4.11, using the final states, eeτhτh and eeτlτh for electronsand µµτhτh and µµτlτh for muons. The final states with two leptons and twohadronic taus has been considered for hadronic taus (lower plot). A gooddata to simulation agreement is observed for all the plots.

Furthermore, the Figures 4.12-4.19 are showing the data to simulationscomparisons for the signal, the background and as well as the data eventyields after several steps of selection criteria, for all the final states at

√s =

7 and 8 TeV. Corresponding yields are tabulated in Tables 4.4-4.11. Theselection steps can be described as following (at this step, more than onefour objects combinatorics per event exist):

• Preselection: Requiring the leptons to be identified [Section 4.2], andhadronic taus to satisfy the discriminators against electrons and muons,described in current section. In addition, all the four objects shouldsatisfy the pT and η requirements, described in this section;

• Leading Z: Requiring the event to have a reconstructed leading Z boson(at this step, the leading Z boson matching takes place for all thepossible combinatorics and the one which are made with Z boson otherthen chosen leading Z boson (with mass closest to the nominal Z mass)


get rejected. The leading Z mass window is not required at this selectionstep);

• mµµ and mee: Requiring the reconstructed leading Z boson to satisfythe mass window requirement;

• Qτhτh and Qτlτh : Requiring the reconstructed decay products of sub-leading Z boson to carry the charge opposite to each other;

• τh and τl Isolation: Requiring the reconstructed decay products of sub-leading Z boson to be isolated;

• mτhτh and mτlτh : Requiring the reconstructed sub-leading Z boson tosatisfy the mass window requirement;

• Cleaning: Requiring only one combinatoric to survive up-to the laststep of the full selection plus the 4l final states overlap veto. In case ofmore than one combinatoric surviving, the one with the highest pT ofthe reconstructed decay products of the sub-leading Z boson is selected.

A good agreement has been observed for data and MC simulations at eachselection step. All the backgrounds undergo a decrease after each selectionstep and, instead, WZ + jets and Z + jets show a huge decrease after thehadronic tau isolation requirement since they contribute due to mis-identifiedjets. Small discrepancies have been observed after the preselection due tocontribution of QCD backgrounds, which is not considered for these plots,and does not satisfy the leading Z selection since QCD jets are poorly isolated.Therefore a good agreement is observed after leading Z selection step. Atthe last steps of selection, only a few events survive and small discrepanciesare observed.


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Figure 4.9: Electron and muon (hadronic tau) pT : data to simulation com-parison for electrons and muons coming from leading Z decay (hadronic tauscoming from sub-leading Z decay). upper left: for leading electron; upperright: for sub-leading electron; middle left: for leading muon; middle right:for sub-leading muon; lower: for hadronic taus.


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Figure 4.10: Electron and muon (loose) isolation: data to simulation com-parison for electrons and muons coming from leading Z decay. upper left: forleading electron; upper right: for sub-leading electron; lower left: for leadingmuon; lower right: for sub-leading muon.


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Figure 4.11: Electron and muon (hadronic tau) η: data to simulation com-parison for electrons and muons coming from leading Z decay (hadronic tauscoming from sub-leading Z decay). upper left: for electrons; upper right: formuons; lower: for hadronic taus.


Table 4.4: Cut-flow data to MC comparisons for µµτhτh final state, for data 2011 and2012 at

√s = 7 (upper) and 8 TeV (lower) respectively.

Presel. Leading Z mµµ Qτhτh τh Iso. mτhτh Cleaning

Data 2011Data 38568 17377 14042 7144 0 0 0H200 3.91 2.67 2.57 1.54 0.176 0.172 0.161ZZ 7.42 6.05 5.51 3.72 0.792 0.748 0.681WZ+jets 41 29.9 25.7 13.5 0.0323 0.0224 0.0166Z+jets 1.81e+04 1.6e+04 1.53e+04 7.83e+03 0 0 0tt 2.95e+03 1.97e+03 811 409 0.0201 0.0201 0.0201

Data 2012Data 123217 53963 43357 21781 10 9 9H200 10.2 7.11 6.84 4.11 0.532 0.519 0.474ZZ 24.5 19.1 16.5 10.5 1.93 1.84 1.68WZ+jets 142 106 91.9 49.1 0.21 0.149 0.129Z+jets 5.28e+04 4.62e+04 4.43e+04 2.22e+04 6.96 4.64 4.41tt 9.59e+03 6.43e+03 2.62e+03 1.32e+03 0.0622 0.0311 0.0297

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Figure 4.12: Cut-flow data to MC comparisons for µµτhτh final state for data2011 and 2012 at

√s = 7 (left) and 8 TeV (right) respectively.


Table 4.5: Cut-flow data to MC comparisons for eeτhτh final state, for data 2011 and 2012at√s = 7 (upper) and 8 TeV (lower) respectively.

Presel. Leading Z mee Qτhτh τh Iso. mτhτh Cleaning

Data 2011Data 21496 17166 13949 6863 2 0 0H200 3.63 2.5 2.39 1.4 0.161 0.156 0.15ZZ 7.14 5.72 5.16 3.5 0.718 0.664 0.627WZ+jets 37.3 28.2 24.3 12.6 0.0298 0.00993 0.00909Z+jets 1.67e+04 1.56e+04 1.5e+04 7.62e+03 2.44 2.44 1.49tt 2.15e+03 1.83e+03 760 382 0.0201 0.0201 0.00437

Data 2012Data 59077 49322 40074 20246 14 10 10H200 8.89 6.42 6.12 3.69 0.46 0.447 0.412ZZ 21.7 16.9 14.7 9.24 1.74 1.64 1.54WZ+jets 126 97.6 84.4 44.7 0.258 0.136 0.13Z+jets 4.4e+04 4.11e+04 3.94e+04 2e+04 6.96 6.96 6.9tt 6.51e+03 5.64e+03 2.33e+03 1.17e+03 0.0622 0.0311 0.0297

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Figure 4.13: Cut-flow data to MC comparisons for eeτhτh final state for data2011 and 2012 at



Table 4.6: Cut-flow data to MC comparisons for eeτeτh final state, for data 2011 and 2012 at√s = 7 (upper) and 8 TeV (lower) respectively.

Presel. Leading Z mee Qτeτh τe Iso. τh Iso. mτeτh Cleaning

Data 2011Data 2451 888 652 330 65 3 3 3H200 12.2 3.67 3.48 1.95 1.49 0.223 0.191 0.167ZZ 24 8.31 7.78 4.76 3.8 0.993 0.806 0.711WZ+jets 72 33.8 30.5 17.5 14.3 0.184 0.109 0.0959Z+jets 1.2e+03 513 480 239 30.5 0 0 0tt 462 200 85.8 45.1 1.97 0.0403 0.0403 0.0381

Data 2012Data 6930 2794 2112 1108 193 12 7 7H200 31.8 10 9.53 5.41 4.19 0.715 0.596 0.504ZZ 85.5 30.6 26.3 15.4 11.7 2.55 2.02 1.73WZ+jets 268 126 115 66.7 54.6 1.08 0.631 0.589Z+jets 3.1e+03 1.41e+03 1.31e+03 645 76.6 2.32 0 0tt 1.33e+03 589 257 133 8.3 0.124 0.0622 0.0572

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Figure 4.14: Cut-flow data to MC comparisons for eeτeτh final state for data2011 and 2012 at



Table 4.7: Cut-flow data to MC comparisons for µµτeτh final state, for data 2011 and 2012at√s = 7 (upper) and 8 TeV (lower) respectively.

Presel. Leading Z mµµ Qτeτh τe Iso. τh Iso. mτeτh Cleaning

Data 2011Data 2750 898 663 364 47 3 1 0H200 6.31 4.9 4.78 2.6 2.17 0.246 0.199 0.175ZZ 12 10.5 9.54 5.67 4.68 0.965 0.783 0.678WZ+jets 37.1 32.2 29 17.2 14.2 0.151 0.0944 0.0825Z+jets 563 499 472 236 17.1 0 0 0tt 791 217 87.6 45.4 1.21 0.0403 0.0201 0.00998

Data 2012Data 9428 2975 2186 1118 187 4 2 2H200 17.9 14.1 13.7 7.57 6.29 0.806 0.634 0.504ZZ 47.1 39.2 33.1 18.9 14.9 2.67 2.07 1.68WZ+jets 140 121 111 64.6 53.8 0.895 0.468 0.429Z+jets 1.72e+03 1.43e+03 1.31e+03 633 62.6 0 0 0tt 2.48e+03 665 276 141 6 0.0933 0.0933 0.0826

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Figure 4.15: Cut-flow data to MC comparisons for µµτeτh final state for data2011 and 2012 at



Table 4.8: Cut-flow data to MC comparisons for µµτµτh final state, for data 2011 and 2012at√s = 7 (upper) and 8 TeV (lower) respectively.

Presel. Leading Z mµµ Qτµτh τµ Iso. τh Iso. mτµτh Cleaning

Data 2011Data 4405 1123 723 389 37 2 2 0H200 14.4 4.29 4.1 2.28 1.9 0.27 0.254 0.205ZZ 27.9 9.54 8.92 5.5 4.79 1.23 1.09 0.923WZ+jets 89.4 42 37.7 22.1 19.4 0.293 0.161 0.146Z+jets 988 455 444 238 1.22 0 0 0tt 1.34e+03 510 213 112 1.33 0 0 0

Data 2012Data 13600 3465 2303 1183 108 6 2 2H200 38.8 11.7 11.2 6.3 5.19 0.828 0.78 0.626ZZ 104 36.5 31 17.8 14.6 2.86 2.54 2.06WZ+jets 330 154 140 81.8 71.7 1.44 0.692 0.623Z+jets 2.58e+03 1.15e+03 1.09e+03 559 6.96 0 0 0tt 4.18e+03 1.61e+03 670 347 4.6 0.0311 0.0311 0

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Figure 4.16: Cut-flow data to MC comparisons for µµτµτh final state for data2011 and 2012 at



Table 4.9: Cut-flow data to MC comparisons for eeτµτh final state, for data 2011 and2012 at


Presel. Leading Z mee Qτµτh τµ Iso. τh Iso. mτµτh Cleaning

Data 2011Data 1512 1071 687 363 37 0 0 0H200 6.41 5.31 5.17 2.8 2.5 0.245 0.226 0.189ZZ 12.7 11.4 10.5 6.1 5.49 1.08 0.986 0.821WZ+jets 39.5 36 32.7 19 17 0.251 0.112 0.0954Z+jets 459 418 411 199 0 0 0 0tt 601 476 196 102 2.44 0 0 0

Data 2012Data 4595 3498 2255 1165 115 8 4 4H200 17 14.3 14 7.61 6.77 0.751 0.695 0.547ZZ 44.3 38.9 33.6 18.7 16 2.47 2.22 1.78WZ+jets 140 129 118 69.2 61.3 1.25 0.638 0.573Z+jets 1.08e+03 988 947 490 6.96 0 0 0tt 1.76e+03 1.44e+03 599 311 7.03 0.0311 0 0

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Table 4.10: Cut-flow data to MC comparisons for eeτeτµ final state, for data2011 and 2012 at


Presel. Leading Z mee Qτeτµ τe Iso. τµ Iso. Cleaning

Data 2011Data 170 57 32 21 4 0 0H200 0.75 0.348 0.283 0.231 0.186 0.164 0.123ZZ 2.71 1.39 1.14 0.965 0.785 0.722 0.527WZ+jets 2.12 0.981 0.574 0.318 0.124 0.0323 0.0325Z+jets 46.4 22 20.8 8.55 0 0 0tt 74.7 29.3 11.9 7.23 0.463 0 0

Data 2012Data 554 182 97 53 12 3 3H200 2.12 0.999 0.828 0.688 0.543 0.473 0.353ZZ 7.63 3.7 2.9 2.36 1.86 1.67 1.19WZ+jets 7.51 3.43 2.03 1.3 0.624 0.203 0.172Z+jets 90.5 46.4 32.5 27.8 6.96 0 0tt 192 78.9 30.7 18.8 1.87 0.0311 0.0272

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Presel. Leading Z mµµ Qτeτµ τµ Iso. τe Iso. Cleaning

Data 2011Data 329 57 33 14 4 3 3H200 0.768 0.323 0.274 0.232 0.196 0.157 0.133ZZ 2.86 1.37 1.15 0.985 0.883 0.741 0.585WZ+jets 2.29 1.03 0.589 0.36 0.201 0.0199 0.0155Z+jets 46.4 20.8 18.3 9.77 0 0 0tt 167 30.6 12.1 7.59 0.0806 0 0

Data 2012Data 1035 198 104 63 4 3 3H200 2.34 1.03 0.874 0.731 0.603 0.505 0.41ZZ 8.05 3.74 2.93 2.43 2.08 1.72 1.38WZ+jets 8.52 3.89 2.37 1.3 0.719 0.136 0.118Z+jets 90.5 44.1 39.4 20.9 2.32 0 0tt 492 92.6 36 22.9 0.28 0.0933 0.0797

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4.7. Background Estimation 113

4.7 Background Estimation

4.7.1 Irreducible ZZ Background Estimation

The estimation of irreducible ZZ background is based on a comparison to thewell-measured inclusive Z production cross-section. The number of observedZ events can be written as

N obsZ = σSM

Z · AZ · L (4.4)

where N obsZ is the number of observed events via inclusive Z production,

AZ is the analysis acceptance estimated using MC simulation including all theselection requirements and scaled by measured data to MC correction factors(for both the Z→ µµ and Z→ ee decay processes), L is the integrated lumi-nosity. σSM

Z is the SM cross-section for the inclusive Z production. Writing asimilar equation for the ZZ case one can use a following simple equation forestimating the number of ZZ events in the data:

N estimatedZZ = N obs

Z · σSMZZ · AZZ

σSMZ · AZ

(4.5)

where AZZ is the analysis acceptance for ZZ events. σSMZZ is the SM cross-

section for the ZZ production. Indeed, the data to MC correction factorshave been observed ∼ 1 which allows us to rely on the estimations from MCsimulation. The ZZ background estimation is therefore taken from the MCsimulations, scaled to the total integrated luminosity of the data collected byCMS experiment in years 2011 (L = 5.1fb−1) and 2012 (12.2fb−1) is givenin Table 4.12, for the eight final states considered for this analysis.

4.7.2 Reducible Background Estimation

A data-driven approach, so-called Fake-Rate (FR) method, has been usedto estimate the reducible backgrounds, since they occur due to the presenceof jets that can be mis-identified like the hadronic taus, and the leptons.The compete method consists of two steps, where the first step involvesthe measurement of the probability of the jet to be mis-identified like thehadronic tau, and the leptons, in the background control phase space regions,so-called the FR measurements. The second step is then the estimation of thebackground events contributing to the signal phase space region by applyingthe FR measurements to that region. The estimation has been performed bycategorizing the backgrounds that occur due to the jets faking the hadronic


Table 4.12: Estimated ZZ backgrounds for all the eight final states. Theerrors quoted here are only statistical.

Decay N estZZ (2011) N est

ZZ (2012)channel

µµτhτh 0.68 ± 0.02 1.68 ± 0.03eeτhτh 0.63 ± 0.02 1.54 ± 0.03eeτeτh 0.71 ± 0.02 1.73 ± 0.03µµτeτh 0.68 ± 0.02 1.68 ± 0.03µµτµτh 0.92 ± 0.02 2.06 ± 0.03eeτµτh 0.82 ± 0.02 1.78 ± 0.03eeτeτµ 0.53 ± 0.02 1.19 ± 0.03µµτµτe 0.59 ± 0.02 1.38 ± 0.03

TOTAL 5.55 ± 0.05 13.04 ± 0.07

taus, and the leptons.

Hadronic Tau Channels

The jet to hadronic tau FR measurements have been performed in the back-ground control regions using the llτhτh final states. The background controlregions contain the events consisting a leading Z which satisfies the baselineselection requirements described in Section 4.6, and two hadronic taus car-rying the same charge. The later requirement ensures the selected regionto be background dominated. The hadronic taus are required to satisfy thekinematic and acceptance requirements, pT > 10 GeV and |η| < 2.3. Themass window requirement for the invariant mass of sub-leading Z boson isrelaxed so that there are more statistics in the control region, leads to thesmall possibility of the statistical fluctuations. In addition to this, the tausare required to pass the muon and electron discriminators used for the base-line selection. No isolation check is required for both the hadronic taus andthe FR is then measured using the formula:

FRjet→τh =N isolatedjets

N totaljets

(4.6)

where N isolatedjets gives the number of jets which satisfy the HPS tau isola-

tion requirement, and N totaljets is the total number of jets in the background

control regions. Both the jets in the each event in the background control


region are considered independently to participate in the FR measurements.The FR measurements have been performed for both the HPS Medium Com-bined Isolation and HPS Tight Combined Isolation working points, used inthis analysis. Figure 4.20-4.23 are showing the data to MC comparison of thenumber of events in the background control regions, in terms of visible llτhτhinvariant mass. The comparison is given separately for both the µµτhτh andeeτhτh final states for 2011 and 2012 data. A good agreement of data and MCsimulations have been observed. Few discrepancies have been observed dueto lack of statistics for the Z+jets background simulation events. This is oneof the main reason to perform the estimation of reducible backgrounds fromdata itself. Indeed, the background control regions are mainly dominated byZ + Jets background for both the final states with the signal contaminationof less than 0.1% due to charge mis-measurements.

The FR measurements are then combined for the two final states and fitwith a function of the hadronic tau pT given as:

F (pT (τ)) = C0 + C1e−C2pT (τh) (4.7)

The combined FR measurements parametrized in the hadronic tau pT forboth the isolation working points along with the fit results are given in Figure4.24 for 2011 and 2012 data. An exponential decrease in FR with increase inhadronic tau pT is observed. Further studies have been performed in termsof total energy sum of the jets in the event, leading to the fact that in case oflow pT jets, the events consist of a small number of activities and have smallenergy sums. Therefore less isolation deposits are found to sum up in theisolation cone around the jets and hence show the isolated behavior, and theisolation is getting destroyed with the increase in pT of jets. A comparisonof FR measurements from data and MC simulations is also given. A goodagreement has been observed, specially for pT > 20 GeV, which is the con-sidered threshold for hadronic taus in this analysis.

A pT independent FR of 1.2(1.5)% and 1.5(2)% have been observed forTight(Medium) Combined Isolation working point, from 2011 and 2012 datarespectively.


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Figure 4.20: Data to simulation comparison for the background estimationcontrol regions for µµττ with selection: same sign and no isolation require-ments for both the τ ′s (top), same sign and isolation for the highest pT τ(middle and lower left), same sign and isolation on the second highest pT τ(middle and lower right) for 2011 data and simulation. Middle (lower) plotsare obtained with Medium (Tight) isolation working point for tau.


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Figure 4.21: Data to simulation comparison for the background estimationcontrol regions for µµττ with selection: same sign and no isolation require-ments for both the τ ′s (top), same sign and isolation for the highest pT τ(middle and lower left), same sign and isolation on the second highest pT τ(middle and lower right) for 2012 data and simulation. Middle (lower) plotsare obtained with Medium (Tight) isolation working point for tau.


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Figure 4.22: Data to simulation comparison for the background estimationcontrol regions for eeττ with selection: same sign and no isolation require-ments for both the τ ′s (top), same sign and isolation for the highest pT τ(middle and lower left), same sign and isolation on the second highest pT τ(middle and lower right) for 2011 data and simulation. Middle (lower) plotsare obtained with Medium (Tight) isolation working point for tau.


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Figure 4.23: Data to simulation comparison for the background estimationcontrol regions for eeττ with selection: same sign and no isolation require-ments for both the τ ′s (top), same sign and isolation for the highest pT τ(middle and lower left), same sign and isolation on the second highest pT τ(middle and lower right) for 2012 data and simulation. Middle (lower) plotsare obtained with Medium (Tight) isolation working point for tau.


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Next step is to apply the FR measurements in the signal region whichcontains the events satisfying the baseline selection except the mass windowrequirement for the sub-leading Z boson, and the two objects in addition toleading Z boson are required to be anti-isolated. Where anti-isolation meansthat the object that are not passing the isolation requirement. The numberof background events in the signal region, NB, are then estimated using theformulas given ahead5

• For fully-hadronic final states:

NB =NSF (pT (τ 1

h))F (pT (τ 2h))

1− F (pT (τ 1h))F (pT (τ 2

h))(4.8)

• For semi-leptonic final states:

NB =NSF (pT (τh))F (l)

1− F (pT (τh))F (l)(4.9)

where NS represents the number of events in the signal region and F (l)is the jet to lepton FR described next.

Electron and Muon Channels

Similar method has been used for jet to leptons FR measurements. Themeasurements have been performed in the background control regions usingthe llτµτh final state for jet to muon FR and the llτeτh final state for jet toelectron FR. The events in the background control regions should contain aleading Z satisfying the baseline selection requirements, and an additionallepton and a hadronic tau carrying the same charge. The lepton should alsosatisfy the baseline kinematic and acceptance requirements. No mass win-dow for the invariant mass of sub-leading Z boson and no isolation and pT

5Since the total number of jets are given as the sum of the number of isolated jets andthe number of anti-isolated jets. Mathematically

N totaljets = N isolated

jets +Nanti−isolatedjets

where isolated jets are contributing to signal region. Furthermore using the Equation 4.6and dropping the subscript jet→ τh

N isolatedjets

FR= N isolated

jets +Nanti−isolatedjets

N isolatedjets =

Nanti−isolatedjets .FR

1− FR


selection for hadronic tau are required. The hadronic tau pseudo-rapidityshould be |η| < 2.3. In addition to these requirements, it is also requiredthat the Emiss

T in the event is less then 20 GeV to limit the real lepton fromthe decay of W boson in the WZ+jets background events. Furthermore, thehadronic tau is required to pass the discriminators as per baseline selection,and no isolation is required for the lepton. The jet to lepton FR is thenmeasured as the number of jets passing the lepton isolation divided by thetotal number of jets.

The FR measurements have been performed for both the ‘Tight’ and‘Loose’ working points for the muons (0.15 and 0.25) and the electrons (0.1and 0.25). The simulation comparison to data for the number of events inthe background control regions, in terms of visible llτlτh invariant mass, aregiven in Figure 4.25 and 4.26 for 2011 and 2012 data. A good agreement isobserved with small discrepancies due to lack of statistics for the Z + jetsbackground simulated events. The main dominating contributions come fromZ + jets background along with a considerable contribution from WZ + jetsbackground.

The measured FR parametrized in the lepton pT are shown in Figures4.27 and 4.28 for 2011 and 2012 data. Instead in case of jet to leptons FR,a random behavior has been observed and the statistics is low, and hence itis not possible to fit a curve. Therefore the pT independent FR is appliedto the signal region. A FR of 8(20)% and 16(29)% have been observed forTight(Loose) electron working points, from 2011 and 2012 data respectively.The probability of jets to fake muons is observed to be 3.6(4.3)% and 5(8)%for Tight(Loose) working points, from 2011 and 2012 data respectively.

The events in the signal regions are required to satisfy the baseline se-lection except the mass window requirement for the sub-leading Z boson.In addition, the leptons coming from the decay of sub-leading Z boson arerequired to be anti-isolated. The number of background events in the signalregion are then estimated using the formula:

NB =NSF (l1)F (l2)

1− F (l1)F (l2)(4.10)

where F (l1) and F (l2) correspond to the measured FR values for first andsecond leptons coming from the decay of sub-leading Z boson, respectively.The F (l1) and F (l2) are different since the analysis involves the final stateswith two leptons of different flavour.


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Final Estimation:

The equations 4.8, 4.9 and 4.10 account the reducible background estimationwhere both the objects (O1 and O2) coming from the decay of sub-leadingZ boson are the mis-identified jets. Moreover, the proper WZ + jets back-ground estimation is also important and needs to be performed. Hence thesignal regions are divided into three categories based on isolation require-ments for the objects coming from the decay of sub-leading Z boson, sinceother requirements are the same as baseline selection except mass windowrequirement for the sub-leading Z boson.

• Category 0: Requiring O1 and O2 to be anti-isolated. This categoryis dominated by the Z + jets background events. The backgroundcontribution is estimated as follows:

N0B =

NSF (O1)F (O2)

1− F (O1))F (O2))(4.11)

• Category 1: Requiring the O1 to be anti-isolated and the O2 to beisolated. This category is dominated by the WZ + jets backgroundevents in addition to the Z + jets background events, where one reallepton is coming from the decay of W boson and should be isolated.The background contribution is estimated as follows:

N1B =

NSF (O1)

1− F (O1)(4.12)

• Category 2: Requiring the O1 to be isolated and the O2 to be anti-isolated. This category is the same as the category 1 but differs in thesense that the object which is isolated for the former is anti-isolated forthe later and vise-versa. Similarly, this category is dominated by theWZ + jets background events in addition to the Z + jets backgroundevents, where one real lepton is coming from decay of the W bosonand should be isolated. The background contribution is estimated asfollows:

N2B =

NSF (O2)

1− F (O2)(4.13)

Afterwards, background estimations in all the categories are added, how-ever the contamination of category 0 in the two other categories needs to betaken into account. Thus, the final formula for the background estimation,

4.8. Line-shape Re-weighting for High Higgs Masses 128

by dropping the subscript B, is given as:

N estreducible = N0 × F1 × F2 + (N1 −N0 × F2)× F1 + (N2 −N0 × F1)× F2

= N1 × F1 +N2 × F2 −N0 × F1 × F2 (4.14)

where the first term (N0 × F1 × F2) gives the estimation for the Z +jets background, the second term ((N1 − N0 × F2) × F1) gives the numberof WZ + jets background events with one real isolated objects from thedecay of W boson minus the number of Z + jets background events with one“fake” isolated jet and similarly the third term can be defined. After somemathematical exercise, the final formula ends up with:

N estreducible = N est

cat1 +N estcat2 −N est

cat0 (4.15)

The results of the reducible background estimation for all the eight finalstates are given in Table 4.13 for 2011 and 2012 data. The number of eventssurviving in each category are also given. The category 0 has the maximumnumber of entries since both the jets are required to be anti-isolated followedby the category 2 where the tau anti-isolation is required, since the reduciblebackgrounds contribute mainly due to jets faking the hadronic taus. Indeed,the final states with two hadronic taus, llτhτh, have the main contribution.

4.8 Line-shape Re-weighting for High Higgs

Masses

The current searches for a heavy Higgs boson at LHC assume the on-shell(stable) Higgs boson production, describing the Higgs line-shape with a Breit-Wigner distribution. This approximation breaks down at high Higgs bosonmass (typically > 400 GeV) due to the very large Higgs width (> 70 GeV).As discussed in Reference [57], a more correct approach to describe the Higgsmass distribution has been proposed, known as Complex Pole Scheme (CPS).For this thesis, those updated values for the total cross-section are consideredand a new functionality developed, described in POWHEG[29], in order tore-weight the Higgs-signal samples to match the Higgs line-shape predictedin the CPS approach has been exploited6. Moreover the interference betweenthe Higgs signal and the gg → ZZ background, which leads to the biasingfor the ZZ invariant mass distribution for high Higgs boson masses is taken

6The weights have been computed by LHC Cross-Section Working Group, and propa-gated to each event corresponding to the generated Higgs boson mass for this analysis.


Table 4.13: Estimate of reducible background in different categories and thefinal estimate using 2011 and 2012 data. The numbers in the parenthesis arenumber of events in each category.

Decay Category 0 Category 1 Category 2 Estimatedchannel background

2011µµτhτh 0.66(3600) 0.60(49) 0.68(36) 0.62 ± 0.14eeτhτh 0.66(3404) 0.47(40) 0.65(35) 0.47 ± 0.13eeτeτh 0.20(146) 0.09(1) 0.57(31) 0.47 ± 0.14µµτeτh 0.26(190) 0.45(5) 0.38(21) 0.58 ± 0.22µµτµτh 0.07(230) 0.08(4) 0.19(12) 0.20 ± 0.07eeτµτh 0.06(210) 0.04(2) 0.27(20) 0.25 ± 0.07eeτeτµ 0.08(12) 0.49(2) 0.11(3) 0.52 ± 0.36µµτµτe 0.06(9) 0.0(0) 0.25(1) 0.18 ± 0.25

TOTAL 3.29 ± 0.55

2012µµτhτh 2.89(10250) 2.91(195) 3.44(159) 3.45 ± 0.35eeτhτh 2.84(10147) 3.45(228) 3.50(163) 4.11 ± 0.36eeτeτh 1.53(511) 3.91(21) 1.81(92) 4.20 ± 0.88µµτeτh 1.54(512) 2.05(11) 1.44(73) 1.95 ± 0.64µµτµτh 0.55(636) 0.56(11) 0.93(48) 0.94 ± 0.22eeτµτh 0.59(676) 0.61(12) 1.14(60) 1.15 ± 0.23eeτeτµ 0.62(26) 1.99(5) 0.81(9) 2.17 ± 0.94µµτµτe 0.96(40) 0.63(7) 0.40(1) 0.96 ± 0.15

TOTAL 18.93 ± 1.56


into account. A better description can be found elsewhere[51].

In Figure 4.29 the Higgs line-shape before and after the CPS plus inter-ference re-weighting is shown for Higgs mass of 600 and 1000 GeV. For 600GeV, there is a small effect of re-weighting on the Higgs line-shape but in-stead for the higher masses, effect is more pronounced. Moreover, the Higgsline-shapes including the systematics are shown in Figure 4.30 for Higgsmass of 600 and 1000 GeV, where the effect of systematics is very small. Thereconstructed llττ invariant mass distributions after CPS plus interferencere-weighting are given in Figure 4.31. The alternative shapes to describe theline-shape systematics are also shown.

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Figure 4.29: Invariant mass distribution for generated Higgs boson for Higgsmass of 600 GeV (left) and 1000 GeV (right). The line-shapes before (red)and after (blue) the CPS re-weighting are shown.


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Figure 4.30: Invariant mass distribution for generated Higgs boson after(blue) the CPS re-weighting for Higgs mass of 600 GeV (left) and 1000 GeV(right). The alternative shapes to describe the line-shape uncertainties arealso shown.

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Figure 4.31: Reconstructed llττ invariant mass distribution after (blue) theCPS plus interference re-weighting for Higgs mass of 600 GeV (left) and 1000GeV (right). The alternative shapes to describe the line-shape uncertaintiesare also shown.

4.9. Systematic Uncertainties 132

4.9 Systematic Uncertainties

4.9.1 Theoretical Uncertainties

• Uncertainty on the signal cross-section: systematic uncertainties onthe total signal cross-section for each production mechanism and forwhole Higgs boson mass range are computed and are taken from Ref-erence [18, 19]. It depends on PDF+σs systematics and on QCD scaleuncertainties. These two sources of uncertainties are treated as uncor-related. Furthermore, systematic uncertainty on BR(H → 4l) is takento be 2%[58].

• Uncertainties on the signal acceptance: uncertainties on the signalacceptance[59] are evaluated using MCFM and varying QCD renor-malisation (µR) and factorization (µF ) scales up and down by a fac-tor of two with respect to the default µR = µF = mZ. The varia-tions in the acceptance are 0.1% (NLO ZZ) and 0.4% (gg → ZZ) andcan be neglected. Phenomenological uncertainties (PDF+αs) are eval-uated following the PDF4LHC prescription and using the PDF setsCT10, MSTW08, NNPDF sets and found to be 4% (NLO ZZ) and 5%(gg → ZZ).

4.9.2 Experimental Uncertainties

• FR uncertainties: the uncertainty on jet to hadronic tau FR comesfrom the η dependence and the usage of different functions to fit thefake rate. In addition, the uncertainty comes by using a pT -independentfake rate, or a pT -independent and η-dependent fake rate. Based onthose facts the total uncertainty on jet to hadronic tau FR is estimatedto be 30%. The uncertainty on the jet to leptons FR is estimated to be30% too, which is due to the difference of jet to leptons FR in differentcontrol regions. It has been observed that the jet to leptons (leptonsbeing electron and muon) FR gets highly effected by the presence ofextra tau in the event and, moreover, by the pT requirement for thehadronic tau the lepton is pairing with. Indeed, the presence of anothertau can lead more activities in the event so affecting the probability ofan identified electron or muon to pass the isolation requirement.

• Uncertainties on the trigger efficiencies: uncertainties on trigger ef-ficiencies are evaluated from data, using Tag-and-Probe (T&P) tech-nique [51]. The uncertainties on the trigger efficiency is measured tobe 1.5%.

4.9. Systematic Uncertainties 133

• Uncertainties on the leptons related efficiencies: uncertainties on theleptons related efficiencies are evaluated from data using T&P tech-nique [51]. Uncertainties on leptons reconstruction and identificationefficiencies are evaluated to be 2–3% and isolation efficiencies to be 2%.The uncertainty of 0.5% is evaluated on energy-momentum calibration.

• Uncertainties on the hadronic tau related efficiencies: uncertainty, rec-ommended by CMS Tau Physics Object Group, on the hadronic taureconstruction and identification is 6%, and on energy scale is about3% for τh[60]. The later contributes to the variation in the shape of themass spectrum.

In Addition, the uncertainties due to data and MC efficiencies mis-matchfor leptons are taken into account. It is 1–2% for lepton identification andisolation efficiencies and propagated to each event. Moreover, systematicuncertainty evaluated on the integrated luminosity are 2.2% and 4.4% for2011 and 2012 data respectively[8].

Chapter 5

Final Results and theStatistical Interpretation

Results for the signal selection and the background estimation that are pre-sented in Chapter 4, and the number of l+l−τ+τ− candidate events observedin data are summarized in Table 5.1. Both the statistical and systematicerrors are also quoted.

• Six l+l−τ+τ− candidate events have been observed in 2011 data corre-sponding to an integrated luminosity of 5.1fb−1 and 8.85 ± 1.6 back-ground events are expected in total. The expected events for Higgssignal of mass 200 GeV are 1.3± 0.02, summing all the final states.

• In 2012 data, forty events have been observed, corresponding to anintegrated luminosity of 12.2fb−1 and 31.97 ± 5.95 background eventsare expected. The expected events for Higgs signal of mass 200 GeVare 3.84± 0.02, summing all the final states.

• Tables 5.2 gives the expected signal events taken from the simulationin 2011 and 2012, for few Higgs masses.

Figures 5.1 and 5.2 report the event displays of eeτeτh and eeτeτµ candi-date events in the CMS experiment. Both the event candidates consist threewell isolated electrons with tracks (light blue) in the CMS tracker systemand the energy deposits in the calorimeter system (red). The former eventcandidate consists one hadronic tau with green track and the energy depositsin HCAL, and the later consists fourth object which is a muon with a cleantrack signature in tracker as well as in muon chamber. The solid red arrowrepresents the direction of Emiss

T . Furthermore, the details of observed eventsare given in Tables 5.3 for year 2011 and 2012.

134

135

Figure 5.1: Events display for a eeτeτh candidate events in 2012 data.

Figure 5.2: Events display for a eeτeτµ candidate events in 2012 data.

136

Table 5.1: The estimated ZZ, reducible backgrounds and events observed in data at√

7 and 8 TeV, Thenumber of signal events expected for the SM Higgs boson with a mass of mH = 200 GeV is also given.

Decay N estZZ Other Total mH Observed

channel backgrounds backgrounds 200 GeV

2011µµτhτh 0.68± 0.02± 0.09 0.62± 0.14± 0.17 1.30± 0.14± 0.28 0.16 ± 0.01 0eeτhτh 0.63± 0.02± 0.08 0.47± 0.13± 0.16 1.10± 0.13± 0.24 0.14 ± 0.01 0eeτeτh 0.71± 0.02± 0.09 0.47± 0.14± 0.10 1.18± 0.14± 0.17 0.17 ± 0.01 3µµτeτh 0.68± 0.02± 0.09 0.58± 0.22± 0.18 1.26± 0.22± 0.19 0.18 ± 0.01 0µµτµτh 0.92± 0.02± 0.12 0.20± 0.07± 0.07 1.12± 0.07± 0.13 0.21 ± 0.01 0eeτµτh 0.82± 0.02± 0.11 0.25± 0.07± 0.05 1.07± 0.07± 0.11 0.19 ± 0.01 0eeτeτµ 0.53± 0.02± 0.07 0.52± 0.36± 0.36 1.05± 0.36± 0.35 0.13 ± 0.01 0µµτµτe 0.59± 0.02± 0.08 0.18± 0.25± 0.12 0.77± 0.25± 0.14 0.13 ± 0.01 3Total 5.55± 0.05± 0.72 3.29± 0.55± 1.34 8.85± 0.55± 1.52 1.31 ± 0.02 6

2012µµτhτh 1.68 ± 0.03 ± 0.22 3.45 ± 0.35 ± 0.93 5.13 ± 0.35 ± 1.56 0.47 ± 0.01 9eeτhτh 1.54 ± 0.03 ± 0.20 4.11 ± 0.36 ± 1.36 5.65 ± 0.36 ± 2.01 0.41 ± 0.01 10eeτeτh 1.73 ± 0.03 ± 0.23 4.20 ± 0.88 ± 0.87 5.93 ± 0.88 ± 1.15 0.50 ± 0.01 7µµτeτh 1.68 ± 0.03 ± 0.22 1.95 ± 0.64 ± 0.62 3.63 ± 0.64 ± 0.54 0.50 ± 0.01 2µµτµτh 2.06 ± 0.03 ± 0.27 0.94 ± 0.22 ± 0.32 3.00 ± 0.22 ± 0.38 0.63 ± 0.01 2eeτµτh 1.78 ± 0.03 ± 0.23 1.15 ± 0.23 ± 0.22 2.93 ± 0.23 ± 0.41 0.55 ± 0.01 4eeτeτµ 1.19 ± 0.03 ± 0.16 2.17 ± 0.94 ± 1.50 3.36 ± 0.94 ± 0.92 0.35 ± 0.01 3µµτµτe 1.38 ± 0.03 ± 0.18 0.96 ± 0.15 ± 0.66 2.34 ± 0.15 ± 0.51 0.41 ± 0.01 3

TOTAL 13.04 ± 0.07 ± 1.70 18.93 ± 1.56 ± 5.48 31.97 ± 1.56 ± 5.74 3.82 ± 0.02 40

137

Table 5.2: Expected Standard Model Higgs event yields for 5.1 and 12.2 fb−1, taken fromsimulation in 2011 and 2012 respectively. Errors quoted are statistical only.

Decay mH mH mH mH mH mH

channel 200 GeV 250 GeV 300 GeV 400 GeV 500 GeV 800 GeV

2011µµτhτh 0.16± 0.01 0.18± 0.01 0.17± 0.01 0.16± 0.01 0.07± 0.01 0.005± 0.004eeτhτh 0.14± 0.01 0.17± 0.01 0.18± 0.01 0.15± 0.01 0.07± 0.01 0.006± 0.004eeτeτh 0.17± 0.01 0.20± 0.01 0.17± 0.01 0.16± 0.01 0.08± 0.01 0.007± 0.004µµτeτh 0.18± 0.01 0.19± 0.01 0.18± 0.01 0.16± 0.01 0.07± 0.01 0.006± 0.004µµτµτh 0.21± 0.01 0.21± 0.01 0.21± 0.01 0.18± 0.01 0.08± 0.01 0.007± 0.004eeτµτh 0.19± 0.01 0.21± 0.01 0.20± 0.01 0.18± 0.01 0.08± 0.01 0.007± 0.004eeτeτµ 0.13± 0.01 0.13± 0.01 0.13± 0.01 0.12± 0.01 0.06± 0.01 0.008± 0.004µµτeτµ 0.13± 0.01 0.14± 0.01 0.14± 0.01 0.13± 0.01 0.06± 0.01 0.008± 0.004

2012µµτhτh 0.47 ± 0.01 0.54 ± 0.01 0.57 ± 0.01 0.51 ± 0.01 0.26 ± 0.01 0.02 ± 0.01eeτhτh 0.41 ± 0.01 0.53 ± 0.01 0.52 ± 0.01 0.54 ± 0.01 0.25 ± 0.01 0.02 ± 0.01eeτeτh 0.50 ± 0.01 0.56 ± 0.01 0.53 ± 0.01 0.51 ± 0.01 0.25 ± 0.01 0.02 ± 0.01µµτeτh 0.50 ± 0.01 0.56 ± 0.01 0.54 ± 0.01 0.52 ± 0.01 0.27 ± 0.01 0.03 ± 0.01µµτµτh 0.63 ± 0.01 0.69 ± 0.01 0.65 ± 0.01 0.58 ± 0.01 0.28 ± 0.01 0.03 ± 0.01eeτµτh 0.55 ± 0.01 0.64 ± 0.01 0.58 ± 0.01 0.58 ± 0.01 0.27 ± 0.01 0.03 ± 0.01eeτeτµ 0.35 ± 0.01 0.41 ± 0.01 0.40 ± 0.01 0.36 ± 0.01 0.22 ± 0.01 0.03 ± 0.01µµτµτe 0.41 ± 0.01 0.41 ± 0.01 0.43 ± 0.01 0.40 ± 0.01 0.22 ± 0.01 0.03 ± 0.01

138

Table 5.3: List of observed l+l−τ+τ− candidates and their properties in 2011and 2012 data.

Decay mZ1 mZ2 ml+l−τ+τ− Decay mZ1 mZ2 ml+l−τ+τ−

channel channel

2011eeτeτh 74.42 46.12 200.80 µµτµτe 92.38 37.27 167.72eeτeτh 92.55 52.71 179.33 µµτµτe 94.10 63.24 259.73eeτeτh 92.54 57.95 233.68 µµτµτe 60.59 46.58 108.99

2012eeτhτh 86.85 69.21 163.88 eeτhτh 92.97 45.60 165.15eeτhτh 89.45 71.65 204.56 eeτhτh 94.52 54.94 206.81eeτeτh 73.88 72.15 220.91 eeτhτh 84.22 47.86 186.73eeτeτh 91.57 38.57 194.42 eeτhτh 91.29 58.33 288.74eeτeτh 80.60 35.49 171.61 eeτhτh 91.29 42.52 173.05eeτeτh 109.28 58.73 267.34 eeτeτh 88.67 43.13 146.80eeτµτh 87.32 64.23 546.76 eeτeτh 88.32 43.15 174.06eeτµτh 94.14 68.96 313.48 eeτeτh 97.29 51.10 237.54eeτeτµ 89.66 8.97 148.81 eeτµτh 93.93 44.018 154.12eeτeτµ 90.83 67.01 171.76 eeτµτh 94.38 43.96 204.30eeτeτµ 88.24 82.91 187.57 µµτhτh 91.28 58.89 195.99µµτhτh 88.45 82.99 177.50 µµτhτh 99.94 80.34 250.33µµτhτh 90.70 63.72 224.90 µµτhτh 68.20 34.67 134.73µµτhτh 91.74 65.54 210.29 µµτhτh 61.10 87.90 312.89µµτµτh 88.08 54.14 153.99 µµτhτh 105.31 50.07 320.62µµτeτh 67.13 62.39 131.68 µµτhτh 89.77 66.66 181.96µµτeτh 88.92 52.35 153.68 µµτµτh 92.75 72.06 251.28eeτhτh 87.86 64.50 310.96 µµτµτe 90.54 32.04 127.92eeτhτh 92.11 36.99 237.30 µµτµτe 92.11 44.61 334.34eeτhτh 90.63 47.66 217.33 µµτµτe 90.37 37.96 163.05

5.1. l+l−τ+τ− Invariant Mass Distributions 139

5.1 l+l−τ+τ− Invariant Mass Distributions

The l+l−τ+τ− invariant mass is shown in Figure 5.3 for the 2011 data analy-sis, the 2012 one and the combination of 2011 and 2012 analysis. The Higgsmass range, 100 < mH < 625 GeV, is considered since only the visible invari-ant mass is considered and we expect the broad mass spectrum towards thelower side with respect to the nominal mass [Section 3.4]. No event candidatehas been found above mass of 625 GeV. A good agreement has been observedfor data and the expected backgrounds with in the statistical uncertainties.The light blue shaded area represents the contribution of SM ZZ backgroundwhere the events are clustered at mass of 200 GeV and has a long tail onleft hand side going up to 400 GeV. The green shaded area represents the re-ducible backgrounds contribution. Expected Higgs signal of mass 400 is laidover the backgrounds given by red line. Moreover, the distribution of theobserved events in 2011 and 2012 data in the plane (mZ1 , mZ2) is providedin Figure 5.4. The events are mainly clustering around the nominal Z mass.

5.2 Exclusion Limits

The observed and expected upper limits at 95% confidence level are derivedusing the shape analysis[61], where the distributions of the four lepton in-variant mass are used as the discriminating observables. The signal andbackground shape templates are taken from simulation, where the SM ZZand reducible background yields are normalized to the estimated backgroundyields given in Table 5.1, at

√s = 7 TeV and 8 TeV. Due to lack of statistics

for the simulated samples, the reducible background shape template is takenfrom data with relaxed isolation requirements on the objects reconstruct thesub-leading Z boson. In addition, two additional shape templates per eachsignal and backgrounds are taken in the limit calculations to account thehadronic tau energy scale uncertainties.

The normalizations for backgrounds float within the uncertainties fromthe estimation techniques. All systematics [Section 4.9] are included in thelikelihood with log-normal distributions. The CLs method (see Appendix A)is used to calculate the limits. The expected and the observed upper limitson σ95%CL/σSM from all the final states at

√s =7 TeV, 8 TeV, and combined

for 7 and 8 TeV are shown in Figure 5.5, as a function of mH. The redcurve shows the observed limit at 95% CL and the median of the expectedlimit at 95% CL is given by the black dashed curve. The green and yellowbands (±1σ and ±2σ) give the 68% and 95% ranges for the expected limits

5.2. Exclusion Limits 140

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Figure 5.3: Visible l+l−τ+τ− invariant mass derived by using the 2011 only,the 2012 only statistics and combining combining the 2011 and 2012 dataand the MC selection.

respectively.

No evidence is found for a significant deviation from SM expectationsanywhere in the Higgs mass range considered in this analysis. The differences

5.3. Combination with H→ ZZ(∗) → 4l (l = e, µ) Analysis 141

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Figure 5.4: Distribution of the observed events in 2011 and 2022 data in theplane (mZ1 ,mZ2).

between the observed and expected limits are found consistent with statisticalfluctuations and the observed limits reside within 68% band of the expectedone. The upper limit of two times the SM expectations has been observedfor Higgs mass 200 < mH < 500 GeV. A summary of the observed upperlimit on σ95%CL/σSM is reported Table 5.4.

5.3 Combination with H→ ZZ(∗) → 4l (l = e, µ)

Analysis

Since taus are massive leptons which undergo further decay into lighter par-ticles (leptons or hadrons). Therefore the search for SM Higgs Boson, whereHiggs boson decays to two Z bosons and their further decays ultimately givefour leptons final states, has been performed separately at the CMS exper-iment: final states with four leptons (electrons and muons only) and finalstates with two leptons and two taus (llτhτh, llτlτh and llτlτl). The twoanalysis are then merged to complete the Higgs searches with four leptons


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Figure 5.5: CLs limits on σ(95%)/σSM from combined τ final states with2011 data at


√s =8 TeV.

(electrons, muons and taus) in the final states.

The details of analysis with only electrons and muons in the final statesand the Higgs mass in the range of 110 < mH < 1000 GeV is discussed inReference [8]. The upper limits are obtained separately from the four leptons


Table 5.4: The expected and the observed upper limit on σ(95%CL)/σSM.

mH Observed Expected 68% band 95% band(Gev)

2011200 2.67 4.38 [3.16, 6.08] [2.38, 8.08]250 3.24 4.38 [3.16, 6.08] [2.38, 8.07]300 3.22 4.01 [2.90, 5.58] [2.18, 7.41]400 2.47 3.56 [2.58, 4.95] [1.93, 6.57]500 4.48 6.11 [4.41, 8.49] [3.32, 11.3]800 41.8 50.2 [36.2, 69.7] [27.2, 92.6]

2012200 3.15 2.59 [1.87, 3.60] [1.41, 4.78]250 2.32 2.60 [1.88, 3.62] [1.41, 4.80]300 1.85 2.32 [1.67, 3.22] [1.26, 4.28]400 2.00 1.74 [1.26, 2.43] [0.95, 3.23]500 3.13 2.63 [1.90, 3.66] [1.43, 4.86]800 23.1 16.3 [11.8, 22.6] [8.83, 30.0]

2011 + 2012200 2.03 2.16 [1.56, 2.99] [1.17, 3.98]250 1.72 2.20 [1.59, 3.05] [1.20, 4.06]300 1.45 1.93 [1.39, 2.68] [1.05, 3.56]400 1.48 1.45 [1.05, 2.02] [0.79, 2.68]500 2.39 2.18 [1.58, 3.03] [1.18, 4.03]800 18.3 13.3 [9.62, 18.5] [7.24, 24.6]

final states, where the leptons being electrons and muons only, and collec-tively the electrons, muons and taus, shown in Figure 5.6 as a function ofmH. The solid black curve shows the observed limit at 95% CL and bluedashed curve represents the median of expected limit at 95% CL. The greenand yellow bands (±1σ and ±2σ) give the 68% and 95% ranges for the ex-pected limits respectively. The combined results exclude the SM Higgs bosonat 95% CL in the ranges 113− 116 GeV and 129− 720 GeV. For mH > 200GeV, the differences between the observed and expected limits are consistentwith statistical fluctuations since the observed limits are generally within thegreen 68% or yellow 95% bands. The analysis with final states including onlyelectrons and muons is powerful analysis over the whole mass range since ithas clean signature of leptons and the strong background reduction power.The broad excess seen for mH < 200 GeV is attributed to the new observedboson with a mass near 125 GeV[5]. The local p-values[61], representing


the significance of local excesses relative to the background expectation, areshown as a function of mH in Figure 5.7, for the final states with electrons andmuons only, and electrons, muons and taus collectively. The minimum of thelocal p-value is reached at low mass around 125.9 GeV and corresponds to alocal significance of 4.5σ with respect to the predictions for the backgrounds.


[GeV]Hm100 200 300 400 500 1000

SM

)τ 4

l+2l

2→

ZZ

→(Hσ/

95%

CL

)τ 4

l+2l

2→

ZZ

→(Hσ

-110

1

10

CMS preliminary -1 = 8 TeV, L = 12.2 fbs -1 = 7 TeV, L = 5.1 fbs

ObservedExpected

σ 1±Expected

σ 2±Expected

Figure 5.6: CLs limits on σ(95%)/σSM as a function of mH from the fourleptons final states: (upper) leptons being electrons and muons only, (lower)leptons being electrons, muons and taus collectively, with 2011 data at

√s =7

TeV and 2012 data at√s =8 TeV.


Figure 5.7: Significance of the local excess with respect to the SM backgroundexpectation as a function of mH with 2011 data at

√s =7 TeV and 2012 data

at√s =8 TeV, for four leptons final states: (upper) leptons being electrons

and muons only, (lower) leptons being electrons, muons and taus collectively.

Conclusions

A search for the SM Higgs boson is performed in the decay mode H→ ZZ→l+l−τ+τ− (l = e, µ) with the CMS experiement at center-of-mass energyof 7 and 8 TeV. The discovery of Higgs boson, which is the only missingparticle of SM, in particular, would shed light on the mechanism of sponta-neous breaking of the electroweak symmetry. The given analysis is one ofthe promising analyses performed for the search for SM Higgs boson at theCMS experiment, due to comparable cross-sections and branching ratios tothe decay mode with four leptons in the final states (where leptons beingelectron and muons), the ‘golden channel’. Indeed, the analysis with taus inthe final states provides the completion to the four leptons analysis.

The data collected by the CMS experiment in year 2011 at√s = 7 TeV

and 2012 at√s = 8 TeV, has been used. It corresponds to the integrated

luminosity of 5.1fb−1 and 12.2fb−1 respectively. Eight final states have beenconsidered according to the leptons that might be electrons and muons, andthe hadronic and leptonic decays of taus. The highly efficient physics objectsreconstruction algorithms, designed within the CMS collaboration and, fromtime to time, retuned according to the increasing luminosities and pile-upscenarios at LHC, have been used for the leptons and the hadronic tau re-constructions. The hadronic taus reconstructed using HPS algorithm havebeen used with Tight and Medium Combined Isolation working points withthe corresponding reconstruction efficiency of 40–50%, and a flat behaviorwith respect to pile-up vertices.

A selection criteria has been established to select the signal-like eventsand validated by data and simulation comparisons after each selection step.The estimation of SM ZZ background for each final state, where four realleptons coming from the decay of Z bosons give a signal-like signature, hasbeen carried out from the simulations. Instead the reducible backgrounds,Z + jets, WZ + jets and tt, which contribute due to mis-identification ofQCD jets as leptons and hadronic taus, have been estimated using data-

147

driven method, named Fake-Rate (FR) method.

In the FR method, the probabilities have been measured for a jet to bemis-identified like leptons and hadronic taus separately (in terms of the prob-ability of jets to pass the isolation requirements). The measurements havebeen performed in the background dominating regions with the signal con-tribution of less than 0.1%. The events that contribute in this region shouldhave a leading Z boson as per the baseline selection, and two more objectswith the same charge. The hadronic tau FR has been measured using thefinal states with two leptons and two hadronic taus, llτhτh, and observedto be 1.2(1.5)% and 1.5(2)% for Tight(Medium) Combined Isolation work-ing point, from 2011 and 2012 data respectively. The probability of jets topass the Tight(Loose) isolation requirements for electrons is observed to be8(20)% and 16(29)%, and for muons is observed to be 3.6(4.3)% and 5(8)%,from 2011 and 2012 data respectively. The measurements have been per-formed using the final states with three leptons and one hadronic tau, llτeτhfor electrons and llτµτh for muons. Afterwards, the reducible backgroundshave been estimated by applying the observed FR to the signal regions. Theestimations are carried out separately for all the eight final states where theevents contributing in the corresponding signal regions are required to havea leading Z boson and two additional objects carrying the opposite charges.

The expected and the observed exclusion upper limits have been derivedon σ95%CL /σSM using CLs method, taking into account the statistical andsystematic uncertainties. No excess of events is observed in the consideredHiggs mass range of 190 < mH < 1000 GeV, with respect to the back-ground expectations. The upper limit of two times the SM expectations isobserved for the Higgs mass range of 200 < mH < 500 GeV. Finally, theanalysis has been merged with the analysis performed for SM Higgs searchin H→ ZZ(∗) → 4l (l = e, µ) decay channel to provide the completion to theSM Higgs boson searches at the CMS experiment with four leptons in thefinal states.

148

Appendix A

Statistical tools

A.1 CLs Statistical Method

For calculations of exclusion limits, the modified frequentist criterion CLs[62,63] is used. To fully define the method, one needs to make a choice of thetest statistic, which is used to determine how signal or background-like theexperimental observations are. It is based on the profile likelihood ratio andthe likelihood L(data|µ, θ) to be used in constructing the test statistic isdefined as

L(data|µ, θ) = Poisson(obs|µ · s(θ) + b(θ)) · p(θ|θ) (A.1)

where s stands for the expected signal under the SM Higgs hypothesis,µ is a signal strength modifier and it scales the signal SM cross-section ofall production channels by the same factor, i.e. σ = µ · σSM. b stands forthe backgrounds, and θ are the nuisance parameters which are describingthe systematic uncertainties. The probability density function p(θ|θ) is theprobability of measuring a set of nuisance parameters θ, given its true valueθ. And obs can be the actual observation or pseudo-data from toy MC sim-ulated experiments.

The explicit form of the poissonian term in equation A.1 for the productof probabilities of observing ni events in the ith bin is given by

Poisson(obs|µ · s(θ) + b(θ)) =∏i

(µ · si(θ) + bi(θ))ni

n!· eµ·si(θ)+bi(θ) (A.2)

149

A.1. CLs Statistical Method 150

A.1.1 Case of Discovery

The test statistic q0 used to quantify the statistical significance of an excessof events over the background-only expectation is defined as

q0 = −2lnL(obs|b(θµ))

L(obs|µ · s(θ) + b(θ))(µ ≥ 0) (A.3)

Both the denominator and numerator are maximized. In the numerator,µ remains fixed and only the nuisance parameters θ are allowed to float.Their values at which L reaches the maximum are denoted as θµ. In the

denominator, both µ and θ are allowed to float in the fit, and µ and θ areparameters at which L reaches its global maximum.

The value of the test statistic for the actual observation will be denotedas qobs0 . The probability of getting a q0 value as large as qobs0 or larger in thebackground-only hypothesis is called p-value.

To quote significance, Z, we choose a ‘one-sided Gaussian’ convention forassociating p-value and significance as follows:

p0 = P (q0 > qobs0 |b) =

∫ ∞Z

e−x2/2

√2π

dx (A.4)

This local p-value is used to search for a signal excess in the background-only hypothesis across the whole explored mH range.

A.1.2 Case of Exclusion

As the µ = 0 subscript indicates, q0 is used to look for a signal under thehypothesis of pure background. On the contrary, if one wants to exclude thepresence of a given signal one can assume that the signal strength is µ anddefine qµ as

qµ = −2lnL(obs|µ · s(θµ) + b(θµ))

L(obs|µ · s(θ) + b(θ))(µ ≥ µ ≥ 0) (A.5)

Similarly to equation A.4, two p-values can be defined under the hypoth-esisof signal plus background (s+ b) and of background only (b):

CLs+b = P (qµ > qobsµ |s+ b) (A.6)

CLb = P (qµ > qobsµ |b) (A.7)

A.1. CLs Statistical Method 151

A quantity called CLs is then defined as:

CLs =CLs+bCLb

(A.8)

An upper limit on the signal strength µ can then be set by finding the µvalue that corresponds e.g. to CLs = 0.05 for a 95% confidence level.

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