Abstract
Contents
1 Introduction 1
1.1 The Standard Model of particle physics................................................................................ 3
1.2 Motivations and hints for new physics ................................................................................ 5
1.2.1 Muon anomalous magnetic moment ...................................................................... 6
1.2.2 Lepton-flavor-universality violation......................................................................... ?
1.3 Effective field theories.............................................................................................................. ?
1.4 The Standard Model as an effective theory......................................................................... 10
2 Standard Model effective field theory 12
2.1 Operator bases........................................................................................................................... 12
2.1.1 Redundant operators ................................................................................................. 13
2.1.2 The Warsaw basis....................................................................................................... 19
2.1.3 Further bases.............................................................................................................. 21
2.1.4 Higher-dimensional operators................................................................................... 22
2.2 The size of the Wilson coefficients....................................................................................... 22
2.2.1 Power counting and dimensional analysis............................................................... 22
2.2.2 Loop-level versus tree-level generated operators.................................................. 24
2.3 Constraints and validity.......................................................................................................... 25
2.3.1 Convergence of the 1/A expansion and the EFT validity range....................... 25
2.3.2 Unitarity violation and positivity constraints........................................................ 26
2.3.3 Gauge anomalies and reparametrization invariance............................................... 27
3 Low-energy effective field theory 28
3.1 Electroweak-symmetry breaking in the SMEFT.......................... 29
3.2 Integrating out the weak-scale particles in SMEFT............................................................ 32
4 Global symmetries 34
4.1 Baryon and lepton number ..................................................................................................... 35
4.2 Flavor symmetries.............................................. 35
4.2.1 The U(3)5 symmetry and minimal flavor violation................................................ 36
4.2.2 The U(2)5 symmetry and minimal breaking ......................................................... 40
4.2.3 Employing flavor symmetries for high-pr searches at theLHC............................ 47
4.2.4 Further symmetry options and renormalization groupeffects............................... 50
4.3 Custodial symmetry................................................................................................................ 52
5 One-loop matching of effective field theories 57
5.1 Diagrammatic matching......................................................................................................... 58
5.1.1 Off-shell and on-shell matching................................................................................. 58
5.1.2 Dimensional regularization: the method of regions and 75 in D dimensions . . 61
5.1.3 Example: leptonic dipole operators in the Si leptoquark model....................... 65
5.2 Functional matching................................................................................................................ 68
5.2.1 Supertrace evaluation with the covariant derivative expansion.......................... 70
5.2.2 Example: a toy model with a heavy vectorlike fermion........................................ 75
5.2.3 Example: the Si leptoquark model........................................................................ 78
5.2.4 Matchete: matching effective theories efficiently................................................. 80
5.3 Evanescent operators........................................................................................................... 82
5.3.1 Evanescence-free renormalization schemes........................................................... 83
5.3.2 Evanescent operators in the SMEFT..................................................................... 86
6 Beyond the Standard Model phenomenology: leptonic dipole operators in the SMEFT 92
6.1 The workflow of SMEFT analyses........................................................................................ 92
6.2 Renormalization group evolution ........................................................................................ 95
6.3 Low-energy constraints in the LEFT .................................................................................. 96
6.4 Flavor alignment of the leptonic dipole operators...................................................................100
6.4.1 Dynamical alignment mechanisms............................................................................... 103
6.4.2 Alignment through flavor symmetries......................................................................... 104
6.4.3 Alignment in an explicit new-physics model ............................................................106
7 Drell-Yan tails in the SMEFT 109
7.1 Drell-Yan tails beyond the Standard Model.............................................................................Ill
7.1.1 General form-factor decomposition.............................................................................112
7.1.2 Matching form factors to new-physics models.........................................................114
7.1.3 Cross-section calculation ............................................................................................ 120
7.1.4 Collider observables......................................................................................................122
7.1.5 HighPT: high-py tails...................................................................................................126
7.2 Phenomenological analyses......................................................................................................127
7.2.1 Single parameter fits...................................................................................................... 127
7.2.2 Lepton-flavor violation in a leptoquark model .........................................................131
7.2.3 Drell-Yan tails in light of the Rd^i anomalies.........................................................132
7.2.4 Implications of the quark-flavor alignment............................................................... 140
7.3 EFT validity and higher-dimensional operators......................................................................141
7.4 Confronting the vector leptoquark hypothesis with pp -> tt and b —> cru measurementsl50
7.4.1 Flavor structure of the Ui leptoquark model............................................................151
7.4.2 Low-energy analysis...................................................................................................... 155
7.4.3 High-energy analysis...................................................................................................... 157
8 Conclusion 165
A Matchete 168
A.l Defining a model..........................................................................................................................168
A.2 Simplification of the EFT operator basis............................................................................... 171
A.3 The vectorlike fermion toy model in Matchete......................................................................174
A. 4 Matching the Si leptoquark model to the SMEFT............................................................... 176
B HighPT 182
B. l The full flavor likelihood for the d < 8 SMEFT......................................................................183
B.2 Analyzing lepton-flavor violation in leptoquarkmodels..................... 186
B.3 Determining the EFT validity for leptoquark models....................... 187
Scientific publications 189
Acknowledgments 190
Bibliography igi
Wilsch, Felix