Abstract
Contents
I Theoretical and experimental overview 3
1 The Standard Model 4
1.1 Particles and symmetries................................................................................................ 4
1.2 Electromagnetic interaction......................................................................................... 6
1.3 Strong interaction............................................................................................................ 8
1.4 Electroweak unification................................................................................................... 9
1.4.1 Charged and neutral currents.......................................................................... 11
1.4.2 The Higgs mechanism ...................................................................................... 12
1.4.3 CKM matrix...................................................................................................... 16
1.5 Beyond the Standard Model......................................................................................... 17
2 The B° K*°e+e~ decay 19
2.1 Flavour changing neutral current ................................................................................ 19
2.2 Effective field theory...................................................................................................... 19
2.2.1 Computation of observables............................................................................. 21
2.3 Angular definitions......................................................................................................... 22
2.4 Differential decay rate................................................................................................... 23
2.5 Angular observables......................................................................................................... 25
2.6 Experimental status ...................................................................................................... 28
2.6.1 Differential branching fractions ...................................................................... 28
2.6.2 Angular analyses................................................................................................ 29
2.6.3 Lepton flavour universality tests...................................................................... 29
2.6.4 Global fits............................................................................................................. 31
II The LHCb detector at the LHC 34
3 The LHC 35
4 The LHCb detector 38
4.1 Tracking system................................................................................................................ 40
4.1.1 Dipole magnet...................................................................................................... 40
4.1.2 Vertex locator...................................................................................................... 41
4.1.3 Tracking stations................................................................................................ 42
4.1.4 Track reconstruction......................................................................................... 44
4.1.5 Primary vertex reconstruction.......................................................................... 47
4.2 Particle identification system......................................................................................... 49
4.2.1 Ring imaging Cherenkovdetectors..................................................................... 50
4.2.2 The calorimeter system...................................................................................... 50
4.2.3 Muon system...................................................................................................... 54
4.2.4 Particle identificationmethods............................................................................ 55
4.3 Trigger system ................................................................................................................... 59
4.3.1 Hardware trigger................................................................................................... 60
4.3.2 Software trigger...................................................................................................... 61
III Angular analysis of B° —>K*°e+e~ decays 63
5 Analysis strategy 64
6 Samples 67
6.1 Simulation generation anddata processing................................................................... 67
6.2 Data...................................................................................................................................... 68
6.3 Simulation ............................................................................................................................. 70
6.3.1 Truth matching..................................................................................................... 70
6.4 Trigger selection.................................................................................................................. 71
6.5 Corrections to thesimulation .......................................................................................... 72
6.5.1 Particle identification variables ........................................................................ 72
6.5.2 Trigger cuts alignment........................................................................................ 74
6.5.3 Trigger efficiency corrections.............................................................................. 76
6.5.4 Reconstruction, kinematic and multiplicity corrections ............................. 80
7 Candidates selection 84
7.1 Preselection........................................................................................................................ 84
7.2 Specific backgrounds........................................................................................................ 86
7.2.1 > 4>e+e~ background..................................................................................... 86
7.2.2 B+ —> K+e+e~ background.............................................................................. 86
7.2.3 Charmonium contributions................................................................................. 88
7.2.4 Signal kaon-pion swaps........................................................................................ 91
7.2.5 Semileptonic decays with h —> e misidentification....................................... 92
7.2.6 Partially reconstructed decays........................................................................... 92
7.2.7 Double semileptonic background........................................................................ 93
7.3 Multivariate analysis........................................................................................................ 93
7.3.1 Input features........................................................................................................ 94
7.3.2 Signal and background samples........................................................................ 94
7.3.3 Training and results ........................................................................................... 95
7.3.4 Response uniformity........................................................................................... 96
7.3.5 Threshold optimisation.......................................................................................... 100
7.4 Low efficiency regioncut......................................................................................................104
7.5 Multiple candidates..............................................................................................................105
7.6 Summary of selections....................................................................................................... 105
8 Elements of the angular analysis 107
8.1 Effective acceptance ............................................................................................................107
8.1.1 Parametrisation.......................................................................... 107
8.1.2 Sample choice.......................................................................................................... 109
8.1.3 Effective acceptance function ............................................................................. 109
8.1.4 Validation.................................................................................................................115
8.2 Components modelling......................................................................................................119
8.2.1 Rare mode............................................................................................................... 119
8.2.2 Control mode......................................................................................................... 127
8.3 Angular fit................................... 130
8.3.1 Weighted unbinned maximum likelihood fit......................................................130
8.3.2 Fit strategy............................................................................................................ 131
8.3.3 Weighted fit features............................................................................................ 132
8.4 Pseudoexperiment studies............................................................................................... 138
8.4.1 Component yields.................................................................................................. 138
8.4.2 Signal and background models............................................................................ 138
8.4.3 Sensitivity............................................................................................................... 141
9 Data fits 143
9.1 Control mode validation.................................................................................................. 143
9.1.1 Angular fit............................................................................................................... 143
9.1.2 Control mode systematic uncertainties............................................................ 144
9.1.3 Results and discussions......................................................................................... 149
9.2 Systematic uncertainties...................................................................................................154
9.2.1 Background models............................................................................................... 155
9.2.2 Effective acceptance parametrisation................................................................160
9.2.3 Control mode leakage............................................................................................ 165
9.2.4 Charmonium combinatorial ................................................................................165
9.2.5 B+ —> K+e+e~ veto ............................................................................................ 166
9.2.6 Peaking backgrounds............................................................................................ 167
9.3 Results and discussions......................................................................................................169
10 Conclusion and outlook 174
Appendix 177
A Simulation correction order 177
B Main MVA threshold optimisation configuration 179
B.l Mass fit set-up .................................................................................................................. 179
B. 2 Pseudoexperiment configuration..................................................................................... 179
C Additional details on systematic uncertainties 183
C. l Alternative combinatorial and DSL modelling strategy........................................... 183
C.1.1 Combinatorial and DSL-like backgrounds......................................................... 183
C.1.2 Modified DSL model............................................................................................ 184
C.1.3 Alternative data fit............................................................................................... 187
C.2 Control mode leakage modelling..................................................................................... 188
C.3 Charmonium combinatorial modelling........................................................................... 188
References 191
Wang, Zhenzi