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New aspects of flavour model building in supersymmetric grand unification [Elektronische Ressource] / vorgelegt von Martin Spinrath

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New Aspects of Flavour Model Buildingin Supersymmetric Grand Uni cationMartin SpinrathM unchen 2010New Aspects of Flavour Model Buildingin Supersymmetric Grand Uni cationMartin SpinrathDissertationan der Fakult at fur Physikder Ludwig{Maximilians{Universit atMunc henvorgelegt vonMartin Spinrathaus M onchengladbachMunc hen, den 19. Mai 2010Erstgutachter: PD Dr. Georg Ra eltZweitgutachter: Prof. Dr. Gerhard BuchallaTag der mundlic hen Prufung: 23. Juli 2010ContentsZusammenfassung xiiiAbstract xivI Introduction 11 Introduction 3II Theoretical Framework 72 The Standard Model of Particle Physics 92.1 Gauge Interactions and Field Content . . . . . . . . . . . . . . . . . . . . . 92.2 The Flavour Sector of the Standard Model . . . . . . . . . . . . . . . . . . 112.3 Open Questions in the Model . . . . . . . . . . . . . . . . . . . . 142.3.1 Neutrino Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3.2 The Hierarchy Problem . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.3 Charge Quantisation and Anomaly Cancellation . . . . . . . . . . . 162.3.4 The Flavour Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Supersymmetry 193.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Some Formal Aspects of Supersymmetry . . . . . . . . . . . . . . . . . . . 203.2.1 The Supersymmetry Algebra . . . . . . . . . . . . . . . . . . . . . . 203.2.2 Superspace and Super elds . .

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New Aspects of Flavour Model Building
in Supersymmetric Grand Uni cation
Martin Spinrath
M unchen 2010New Aspects of Flavour Model Building
in Supersymmetric Grand Uni cation
Martin Spinrath
Dissertation
an der Fakult at fur Physik
der Ludwig{Maximilians{Universit at
Munc hen
vorgelegt von
Martin Spinrath
aus M onchengladbach
Munc hen, den 19. Mai 2010Erstgutachter: PD Dr. Georg Ra elt
Zweitgutachter: Prof. Dr. Gerhard Buchalla
Tag der mundlic hen Prufung: 23. Juli 2010Contents
Zusammenfassung xiii
Abstract xiv
I Introduction 1
1 Introduction 3
II Theoretical Framework 7
2 The Standard Model of Particle Physics 9
2.1 Gauge Interactions and Field Content . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Flavour Sector of the Standard Model . . . . . . . . . . . . . . . . . . 11
2.3 Open Questions in the Model . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Neutrino Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 The Hierarchy Problem . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 Charge Quantisation and Anomaly Cancellation . . . . . . . . . . . 16
2.3.4 The Flavour Puzzle . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Supersymmetry 19
3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Some Formal Aspects of Supersymmetry . . . . . . . . . . . . . . . . . . . 20
3.2.1 The Supersymmetry Algebra . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Superspace and Super elds . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Supersymmetric Lagrangians . . . . . . . . . . . . . . . . . . . . . . 25
3.3 The Minimal Supersymmetric Extension of the Standard Model . . . . . . 27
3.3.1 Field Content of the MSSM . . . . . . . . . . . . . . . . . . . . . . 28
3.3.2 R-Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.3 MSSM Spectrum and Soft SUSY Parameters . . . . . . . . . . . . . 30
3.4 Supersymmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4.1 General Aspects of SUSY Breaking . . . . . . . . . . . . . . . . . . 32vi CONTENTS
3.4.2 Minimal Anomaly Mediated Supersymmetry Breaking . . . . . . . 34
3.4.3 Gauge Sup . . . . . . . . . 34
3.4.4 Constrained Minimal Supersymmetric Standard Model . . . . . . . 35
4 Grand Uni ed Theories 37
4.1 Introduction to SU(5) and Field Content . . . . . . . . . . . . . . . . . . . 37
4.2 Charge Quantisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Uni cation of Gauge Couplings . . . . . . . . . . . . . . . . . . . . . . . . 40
4.4 Proton Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.5 Symmetry Breaking and Fermion Masses . . . . . . . . . . . . . . . . . . . 43
III New GUT Predictions for Yukawa Coupling Ratios 45
5 New GUT Predictions for Yukawa Coupling Ratios 47
5.1 Conditions for Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2 b Uni cation and Georgi{Jarlskog Relations . . . . . . . . . . . . . . . 48
5.3 New GUT Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.3.1 from SU(5) Uni cation . . . . . . . . . . . . . . . . . . 50
5.3.2 Predictions from Pati{Salam Uni cation . . . . . . . . . . . . . . . 52
IV The Case of Medium and Large tan 57
6 Supersymmetric Threshold Corrections to the Yukawa Couplings 59
6.1 E ective Field Theory Approach . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2 Formulas and Numerical Values . . . . . . . . . . . . . . . . . . . . . . . . 63
7 Yukawa Couplings at the GUT Scale: A First Glance 67
7.1 Renormalisation Group Running from the EW to the GUT Scale . . . . . 68
7.2 Semianalytic Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3 Parameter Dependencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.3.1 Dependence on and tan . . . . . . . . . . . . . . . . . . . . . . 70
7.3.2 Dep on M and A . . . . . . . . . . . . . . . . . . . . . 71SUSY t
7.3.3 Right-handed Neutrino Threshold E ects . . . . . . . . . . . . . . . 74
7.3.4 Impact of the Sparticle Spectrum . . . . . . . . . . . . . . . . . . . 74
8 Yukawa Couplings at the GUT Scale: A Phenomenological Approach 81
8.1 SUSY Breaking Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 81
8.2 Numerical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.3 Experimental Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.3.1 Direct Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
8.3.2 Electroweak Precision Observables . . . . . . . . . . . . . . . . . . 84
8.3.3 BR(b!s ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84CONTENTS vii
+8.3.4 BR(B ! ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85s
8.3.5 Anomalous Magnetic Moment of the Muon . . . . . . . . . . . . . . 85
8.3.6 Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8.4 Allowed Quark and Lepton Mass Ratios at the GUT Scale . . . . . . . . . 86
8.4.1 mAMSB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.4.2 mGMSB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.4.3 CMSSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
8.5 Allowed GUT Scale Ratios Compared to Theory Predictions . . . . . . . . 89
8.5.1 GUT Predictions in the mAMSB Scenario . . . . . . . . . . . . . . 89
8.5.2 GUT in the mGMSB and CMSSM Scenarios . . . . . . 91
8.5.3 Comparison with the Previous Approach . . . . . . . . . . . . . . . 92
9 Implications for GUT Model Building and a Concrete Application 95
9.1 for GUT Model . . . . . . . . . . . . . . . . . . . . . 95
9.1.1 Comparison with Previous Studies . . . . . . . . . . . . . . . . . . 96
9.1.2 GUT Scale Ratios for the First Fermion Generation . . . . . . . . . 96
9.1.3 Charged Lepton Corrections to Neutrino Mixing Angles . . . . . . . 97
9.2 A GUT Flavour Model for Large tan . . . . . . . . . . . . . . . . . . . . 98
9.2.1 Symmetries and Field Content . . . . . . . . . . . . . . . . . . . . . 99
9.2.2 The SO(3)SU(5) Symmetric Superpotential . . . . . . . . . . . . 99
9.2.3 Vacuum Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9.2.4 Numerical Fit to the SM Fermion Masses and Mixings . . . . . . . 103
9.2.5 The Neutrino Sector . . . . . . . . . . . . . . . . . . . . . . . . . . 107
V The Case of Small tan