Measurement of Angular Correlation in b Quark Pair Production at the LHC as a Test of ...

225 Pages·2013·10.01 MB·English

Measurement of Angular Correlation
in b Quark Pair Production at the LHC
as a Test of Perturbative QCD
by
Brian Lee Dorney
Bachelor of Science, Applied Physics
Kettering University
2009
Master of Science, Physics
Florida Institute of Technology
2011
A dissertation submitted to
Florida Institute of Technology
in partial fulfillment of the requirements
for the degree of
Doctor of Philosophy
in
Physics
Melbourne, Florida
July 2013
' 2013 Brian Lee Dorney
All Rights Reserved
The author grants permission to make single copies
We the undersigned committee hereby recommends that the attached document be
accepted as fulfilling in part the requirements for the degree of
Doctor of Philosophy in Physics.
“Measurement of Angular Correlation in b Quark Pair Production at the LHC as a
Test of Perturbative QCD” a dissertation by Brian Lee Dorney
Marc Baarmand, Ph.D.
Professor, Physics and Space Sciences
Major Advisor
Ugur Abdulla, Ph.D.
Professor, Mathematical Sciences
Outside Committee Member
Daniel Batcheldor, Ph.D.
Director Olin Observatory
Assistant Professor, Physics and Space Sciences
Committee Member
Marcus Hohlmann, Ph.D.
Associate Professor, Physics and Space Sciences
Committee Member
Ming Zhang, Ph.D.
Professor, Physics and Space Sciences
Committee Member
Joseph Dwyer, Ph.D.
Professor, Department Head, Physics and Space Sciences
Abstract
Measurement of Angular Correlation in b Quark Pair Production at
the LHC as a Test of Perturbative QCD
by Brian Lee Dorney
Dissertation Advisor: Marc Baarmand, Ph.D.
Beauty quarks are pair-produced by strong interactions in multi-TeV proton-
proton(pp)collisionsattheCERNLargeHadronCollider(LHC).Suchinteractionsallow
for a test of perturbative Quantum Chromodynamics (QCD) in a new energy regime.
The primary beauty-antibeauty quark bb pair production mechanisms in perturbative
QCDarereferredtoasflavorcreation, flavorexcitation, andgluonsplitting. Thesethree
mechanisms produce bb pairs with characteristic kinematic behavior, which contribute
differently to the shape of the differential bb production cross section with respect to
the difference in the azimuthal angle ∆φ and the combined separation variable ∆R =
(cid:112)
∆φ2+∆η2 between the beauty and antibeauty quarks (b and b, respectively); with
∆η being the change in the pseudorapidity η = −ln(tan(θ/2)), θ being the polar angle.
These ∆φ and ∆R variables are collectively referred to as angular correlation variables
and hence forth referred to as ∆A. By measuring the shape and absolute normalization
of the differential production cross section distributions with respect to ∆A a test of the
predictions of perturbative QCD can be performed.
Thisdissertationdescribesameasurementofthedifferentialproductioncrosssec-
tions with respect to the ∆A between two hadronic jets arising from the hadronization
iii
and decay of b or b (referred to as b hence forth) produced in pp collisions at the LHC
observed with the Compact Muon Solenoid (CMS) detector. Hadronic jets are identified
as originating from b quarks, i.e. b-tagged, based on the presence of high impact param-
eter tracks with respect to the primary pp interaction point in events in which a muon
is also produced. The study presented in this dissertation corresponds to an integrated
luminosityof3pb−1 collectedin2010bytheCMSexperimentatacenter-of-massenergy
of 7 TeV.
The visible kinematic phase-space of the differential production cross sections
probed in this study is given by the requirement of two b-tagged hadronic jets with
pjet > 30 GeV and (cid:12)(cid:12)ηjet(cid:12)(cid:12) < 2.4, with an angular separation of ∆R > 0.6 between them,
T
one of these jets has a muon within its constituents with pµ > 8 GeV and |ηµ| < 2.1.
T
The results obtained in data are compared with predictions based on perturbative QCD
calculations given by Cascade, MadGraph/MadEvent, and Pythia Monte Carlo
event generators. The predictions of perturbative QCD are found to be in agreement
the measured differential cross sections within uncertainties.
iv
Table of Contents
List of Figures xi
List of Tables xxxiv
List of Abbreviations xxxvii
Acknowledgements xl
Dedicatory xliii
1 Introduction 1
1.1 Theoretical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1.1 The Lagrangian . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1.2 The Strong Coupling Constant . . . . . . . . . . . . . . . 6
1.1.1.3 Color Confinement . . . . . . . . . . . . . . . . . . . . . . 10
1.1.1.4 Perturbation Theory . . . . . . . . . . . . . . . . . . . . . 11
1.1.1.5 Hadronization . . . . . . . . . . . . . . . . . . . . . . . . 14
1.1.1.6 Parton Distribution Functions . . . . . . . . . . . . . . . 15
v
1.1.1.7 Fragmentation . . . . . . . . . . . . . . . . . . . . . . . . 18
1.1.2 B Phyiscs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.1.2.1 Hadroproduction of bb Pairs . . . . . . . . . . . . . . . . 19
1.1.2.2 Properties of B hadrons . . . . . . . . . . . . . . . . . . . 21
1.2 Monte Carlo Event Generators . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2.1 Pythia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.2.1.1 Parton Shower in Pythia . . . . . . . . . . . . . . . . . . 25
1.2.1.2 The Underlying Event and its Simulation by Pythia . . 28
1.2.2 MadGraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.2.2.1 Matrix-Element Simulation in MadGraph . . . . . . . . 30
1.2.2.2 Jet Matching in MadGraph . . . . . . . . . . . . . . . . 35
1.2.3 Cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1.2.3.1 Showering via Backwards Evolution . . . . . . . . . . . . 38
1.3 Previous bb Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.3.1 Tevatron Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.3.2 LHC Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.4 Proposed Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2 The CMS Detector 50
2.1 Inner Tracking Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1.1 Silicon Pixel Detector . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1.2 Silicon Strip Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.1.3 Track Parameter Resolution . . . . . . . . . . . . . . . . . . . . . . 54
vi
2.2 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.2.1 The Crystal ECAL . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
2.2.1.1 ECAL Barrel . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.2.1.2 ECAL Preshower . . . . . . . . . . . . . . . . . . . . . . 56
2.2.1.3 ECAL Endcap . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.1.4 ECAL Energy Resolution . . . . . . . . . . . . . . . . . . 58
2.2.2 The Brass HCAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.2.2.1 HCAL Barrel . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.2.2.2 HCAL Endcap . . . . . . . . . . . . . . . . . . . . . . . . 61
2.2.2.3 HCAL Outer . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.2.2.4 HCAL Forward. . . . . . . . . . . . . . . . . . . . . . . . 62
2.2.2.5 HCAL Energy Resolution . . . . . . . . . . . . . . . . . . 62
2.3 Solenoid Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
2.4 The Muon Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3 Jet Reconstruction And B-Tagging 68
3.1 Particle-Flow Event Reconstruction. . . . . . . . . . . . . . . . . . . . . . 71
3.1.1 Origin of Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.1.1.1 Iterative Tracking . . . . . . . . . . . . . . . . . . . . . . 72
3.1.1.2 Calorimeter Clustering . . . . . . . . . . . . . . . . . . . 73
3.1.2 Linking and Block Formation . . . . . . . . . . . . . . . . . . . . . 74
3.1.2.1 Links Between Tracks and Calorimeter Clusters . . . . . 75
3.1.2.2 Links Between Calorimeter Clusters . . . . . . . . . . . . 76
vii
3.1.2.3 Links Between Tracks . . . . . . . . . . . . . . . . . . . . 76
3.1.3 Particles Reconstruction and Identification . . . . . . . . . . . . . 77
3.1.3.1 Particle-Flow Muons and Electrons . . . . . . . . . . . . 78
3.1.3.2 Particle-Flow Hadrons and Photons . . . . . . . . . . . . 78
3.2 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2.1 The k Clustering Algorithm . . . . . . . . . . . . . . . . . . . . . 81
T
3.2.1.1 k Clustering Procedure . . . . . . . . . . . . . . . . . . 82
T
3.2.2 The Anti-k Clustering Algorithm . . . . . . . . . . . . . . . . . . 83
T
3.2.2.1 Properties of the Anti-k Clustering Algorithm . . . . . . 84
T
3.2.3 Particle-Flow Anti-k Jets. . . . . . . . . . . . . . . . . . . . . . . 87
T
3.3 B-Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.1 Signed Impact Parameter Significance . . . . . . . . . . . . . . . . 88
3.3.2 The Track Counting Algorithm . . . . . . . . . . . . . . . . . . . . 89
4 Angular Correlation Measurement 91
4.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.1 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.1.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.2 Physics Object Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2.1 Muon Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2.2 Jet Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.2.2.1 Simulated Jet Flavor Definition . . . . . . . . . . . . . . 97
4.2.2.2 B Hadron Branching Fraction Scale Factor . . . . . . . . 97
viii
4.2.2.3 Jet Energy Scale and Resolution . . . . . . . . . . . . . . 98
4.2.2.4 Muon and Jet Association . . . . . . . . . . . . . . . . . 99
4.3 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3.1 Online Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.3.2 Offline Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.2.1 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.3.2.2 B-Tagging . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.3.3 Resolution and Response . . . . . . . . . . . . . . . . . . . . . . . 107
4.3.4 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.4.1 Online Efficiency . . . . . . . . . . . . . . . . . . . . . . . 112
4.3.4.2 Online Plus Offline Efficiency . . . . . . . . . . . . . . . . 116
4.4 Signal Purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.4.1 System4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.4.2 κ Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
ij
4.4.2.1 Binned by pjet . . . . . . . . . . . . . . . . . . . . . . . . 124
T
(cid:12) (cid:12)
4.4.2.2 Binned by (cid:12)ηjet(cid:12) . . . . . . . . . . . . . . . . . . . . . . . 125
4.4.2.3 Track Mismatching . . . . . . . . . . . . . . . . . . . . . 126
4.4.2.4 Poorly Reconstructed Jets . . . . . . . . . . . . . . . . . 132
4.4.3 System4 Toy Method . . . . . . . . . . . . . . . . . . . . . . . . . 137
4.4.3.1 Closure Tests . . . . . . . . . . . . . . . . . . . . . . . . . 138
4.4.3.2 System4 Solution From Data . . . . . . . . . . . . . . . . 140
4.5 Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
ix