Precision QCD corrections to gluon-initiated diphoton-plus-jet production at the LHC

2025-05-02 0 0 7.43MB 178 页 10玖币
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Precision QCD corrections to
gluon-initiated diphoton-plus-jet
production at the LHC
Ryan Iain Moodie
A Thesis presented for the degree of
Doctor of Philosophy
Institute for Particle Physics Phenomenology
Department of Physics
Durham University
United Kingdom
April 2022
arXiv:2210.07115v1 [hep-ph] 13 Oct 2022
Precision QCD corrections to
gluon-initiated diphoton-plus-jet
production at the LHC
Ryan Iain Moodie
Submitted for the degree of Doctor of Philosophy
April 2022
Abstract:
In this thesis, we present recent advances at the precision frontier of
higher-order quantum chromodynamics (
QCD
) calculations. We consider massless
two-loop five-point amplitudes, with a particular focus on diphoton-plus-jet pro-
duction through gluon fusion. We build a library of infrared functions up to at
most next-to-next-to-leading order (
NNLO
) in
QCD
, which can be used to validate
amplitudes and construct counterterms in subtraction schemes at
NNLO
. We review
progress in the novel use of machine learning technology to optimise the evaluation
of amplitudes in hadron collider simulations. We present the full-colour virtual
QCD
corrections to diphoton-plus-jet production through gluon fusion, discussing
the new techniques developed to calculate these non-planar two-loop amplitudes.
We use these amplitudes to compute the next-to-leading order
QCD
corrections to
the differential cross sections of diphoton-plus-jet production through gluon fusion
at the Large Hadron Collider. We also present the leading-colour double-virtual
corrections to hadronic trijet production. All derived amplitudes are made available
in a public implementation that is ready for further phenomenological application.
Contents
Abstract ii
List of Abbreviations vi
1 Introduction 1
1.1 The Standard Model . . . . . . . . . . . . . . . . . . 3
1.1.1 Quantum electrodynamics . . . . . . . . . . . . . 3
1.1.2 Quantum chromodynamics . . . . . . . . . . . . . 5
1.2 Observables . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Factorisation theorem . . . . . . . . . . . . . . . 8
1.2.2 Cross sections . . . . . . . . . . . . . . . . . 9
1.2.3 Beyond fixed order . . . . . . . . . . . . . . . . 11
1.3 Amplitudes . . . . . . . . . . . . . . . . . . . . . 12
1.3.1 Properties . . . . . . . . . . . . . . . . . . . 13
1.3.2 Infinities . . . . . . . . . . . . . . . . . . . 14
1.4Colour....................... 15
1.4.1 Colour decomposition . . . . . . . . . . . . . . . 15
1.4.2 Colour matrices . . . . . . . . . . . . . . . . . 19
1.5 Kinematics . . . . . . . . . . . . . . . . . . . . . 22
1.5.1 Degrees of freedom . . . . . . . . . . . . . . . . 23
1.5.2 Representations . . . . . . . . . . . . . . . . . 25
1.5.3 Weyl spinors . . . . . . . . . . . . . . . . . . 25
1.5.4 Spinor-helicity formalism . . . . . . . . . . . . . 27
1.5.5 Helicity amplitudes . . . . . . . . . . . . . . . 31
1.5.6 Recursion . . . . . . . . . . . . . . . . . . . 32
1.5.7 Momentum twistor variables . . . . . . . . . . . . 33
1.6 On-shell methods and integral reduction . . . . . . . . . . 35
1.6.1 Loops . . . . . . . . . . . . . . . . . . . . 35
1.6.2 Unitarity cuts . . . . . . . . . . . . . . . . . 36
1.6.3 Generalised unitarity . . . . . . . . . . . . . . . 38
1.6.4 Integrand reduction . . . . . . . . . . . . . . . 41
Contents iv
1.6.5 Integration-by-parts identities . . . . . . . . . . . . 42
1.7 Finite fields . . . . . . . . . . . . . . . . . . . . . 44
1.7.1 Definition . . . . . . . . . . . . . . . . . . . 44
1.7.2 Reconstruction . . . . . . . . . . . . . . . . . 45
1.7.3 Recovering rationals . . . . . . . . . . . . . . . 47
1.8 Phenomenology . . . . . . . . . . . . . . . . . . . 48
1.8.1 Fixed-order perturbation theory . . . . . . . . . . . 49
1.8.2 Estimating uncertainty . . . . . . . . . . . . . . 51
1.8.3 Diphoton production . . . . . . . . . . . . . . . 54
1.9 Structure of this thesis . . . . . . . . . . . . . . . . . 55
2 Infrared behaviour 56
2.1 Infrared limits . . . . . . . . . . . . . . . . . . . . 56
2.1.1 Cuts..................... 57
2.1.2 Poles..................... 58
2.2 Infrared factorisation . . . . . . . . . . . . . . . . . 58
2.2.1 Collinear limits . . . . . . . . . . . . . . . . . 59
2.2.2 Soft limits . . . . . . . . . . . . . . . . . . . 61
2.2.3 Beyond NLO . . . . . . . . . . . . . . . . . . 64
2.2.4 Utility . . . . . . . . . . . . . . . . . . . . 65
2.3 Infrared subtraction . . . . . . . . . . . . . . . . . . 65
2.4 Implementation . . . . . . . . . . . . . . . . . . . 67
2.4.1 Validation . . . . . . . . . . . . . . . . . . . 68
2.4.2 Example code . . . . . . . . . . . . . . . . . 71
3 Matrix element neural networks 78
3.1 Background . . . . . . . . . . . . . . . . . . . . . 78
3.2 Amplitudes . . . . . . . . . . . . . . . . . . . . . 79
3.3 Phase space partitioning . . . . . . . . . . . . . . . . 81
3.4 Model architecture . . . . . . . . . . . . . . . . . . 82
3.5Pipeline ...................... 83
3.6Results....................... 85
3.7Summary...................... 88
4 Virtual QCD corrections to the gg →γγg amplitude 90
4.1 Background . . . . . . . . . . . . . . . . . . . . . 91
4.2 Kinematics and amplitude conventions . . . . . . . . . . . 92
4.3 Computational setup and amplitude reduction . . . . . . . . 95
4.4 Momentum twistor parametrisation . . . . . . . . . . . . 98
4.5 Analytic reconstruction over finite fields . . . . . . . . . . . 100
Contents v
4.5.1 Linear relations among the rational coefficients . . . . . 100
4.5.2 Matching factors on univariate slices . . . . . . . . . 101
4.5.3 Univariate partial fraction decomposition over finite fields . 102
4.5.4 Summary and impact of the reconstruction strategy . . . 106
4.6 Compact analytic expressions for the all-plus configuration . . . . 108
4.7 Implementation and performance . . . . . . . . . . . . . 110
4.8Summary......................115
5 NLO QCD corrections to gg →γγg distributions 117
5.1 Background . . . . . . . . . . . . . . . . . . . . . 117
5.2 Computational setup . . . . . . . . . . . . . . . . . . 118
5.3Results.......................120
5.4 Computational cost . . . . . . . . . . . . . . . . . . 128
5.5Summary......................129
6 Leading-colour double-virtual QCD corrections to pp →3j130
6.1 Stability and timing . . . . . . . . . . . . . . . . . . 130
6.2 Infrared performance . . . . . . . . . . . . . . . . . . 132
7 Conclusion 134
Bibliography 136
Index 166
摘要：

PrecisionQCDcorrectionstogluon-initiateddiphoton-plus-jetproductionattheLHCRyanIainMoodieAThesispresentedforthedegreeofDoctorofPhilosophyInstituteforParticlePhysicsPhenomenologyDepartmentofPhysicsDurhamUniversityUnitedKingdomApril2022PrecisionQCDcorrectionstogluon-initiateddiphoton-plus-jetproductio...

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