無R宇稱超對稱裡的輕子味違反希格斯衰變｜國立中央大學博碩士論文系統

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研究生：	鄭逸凡 Yifan Cheng
論文名稱：	無R宇稱超對稱裡的輕子味違反希格斯衰變 Lepton Flavor Violating Higgs Decays in Supersymmetry without R Parity
指導教授：	江祖永 Otto C. W. Kong
口試委員:
學位類別：	博士 Doctor
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	192
中文關鍵詞：	超對稱、R宇稱
外文關鍵詞：	Supersymmetry, R parity
相關次數：	點閱：11 下載：0
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在這篇論文裡，我徹底地檢視了希格斯玻色子藉由違反R宇稱的耦合作用而衰變到tau與渺子的現象。利用完整的一階環狀費曼圖計算，我發現即使已知的實驗限制----尤其像是約小於1電子伏特的中微子質量，給予了R宇稱參數嚴峻的限制，在合理的參數範圍內該衰變仍可佔有顯著的比例。因此，輕子味違反希格斯衰變不僅不該被忽略，也值得後續的實驗關注。基於上述研究分析，我也就希格斯到電子與渺子、以及希格斯到電子與tau此兩種衰變，做個概述。

In this dissertation I examine thoroughly the Higgs boson to µτ decay via processes involving R-parity violating couplings. By means of full one-loop diagrammatic calculation, I found that even if known experimental constraints, particularly including the stringent sub-eV neutrino mass bounds, give strong restrictions on R-parity violating parameters, the branching ratio could still achieve notable value in the admissible parameter space. Therefore, the ﬂavor violating leptonic Higgs decay may be of interest and should not be overlooked in future experiments. Based on the analysis, I give some comments on the key features of h → eµ and h → eτ also.

1 Introduction                                                                   1

1.1 The Standard Model and Lepton Flavor Conservation . . . . . . . . . . . .    1
1.2 Lepton Flavor Violation in Supersymmetry . . . . . . . . . . . . . . . . . . 1
1.3 Supersymmetry without R Parity . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Methodology and Outline . . . . . . . . . . . . . . . . . . . . . . . . . . .3

2 Minimal Supersymmetric Standard Model without R Parity                         5

2.1 Basic Formulation and Parametrization . . . . . . . . . . . . . . . . . . . .5
2.2 Color-Singlet Fermion Mass Matrices . . . . . . . . . . . . . . . . . . . . .6
2.3 Quark and Squark Mass Matrices . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Color-Singlet Scalar Mass Matrices . . . . . . . . . . . . . . . . . . . . . 8
2.5 Higgs Potential and Tadpole Equations . . . . . . . . . . . . . . . . . . . 10
2.6 Loop Corrections to Higgs Boson Masses . . . . . . . . . . . . . . . . . . .11

3 Calculations and Numerical Results                                            13

3.1 Contribution from B_i B_j Combinations . . . . . . . . . . . . . . . . . . .16
3.2 Contribution from B_i µ_j Combinations . . . . . . . . . . . . . . . . . . .17
3.3 Contribution from B_i λ  Combinations . . . . . . . . . . . . . . . . . . .19
3.4 Contribution from B_i λ' Combinations . . . . . . . . . . . . . . . . . . .22
3.5 Contribution from B_i A^λCombinations . . . . . . . . . . . . . . . . . . .23
3.6 Contribution from µ_i µ_j Combinations . . . . . . . . . . . . . . . . . . .24
3.7 Contribution from µ_i λ  Combinations . . . . . . . . . . . . . . . . . . .25
3.8 Contribution from µ_i λ' Combinations . . . . . . . . . . . . . . . . . . .26
3.9 Contribution from λ  λ  Combinations . . . . . . . . . . . . . . . . . . .27
3.10 Contribution from λ' λ'Combinations . . . . . . . . . . . . . . . . . . .28

4 Summary                                                                       31

  Bibliography                                                                  33

A One-Loop Feynman Diagrams for φ→ µτ                                        39

B Lagrangian of the Supersymmetric Model without R Parity                       41

B.1 Kinetic Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
B.1.1 Kinetic Term | D_µ φ|^2. . . . . . . . . . . . . . . . . . . . . . . . . 42
B.1.2 Kinetic Term iψ^{†i}\bar{σ}^µ D_µ ψ_i . . . . . . . . . . . . .. . . . 45
B.2 Yukawa Coupling Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
B.3 Gauge Coupling Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
B.4 Scalar Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51

C Effective Couplings                                                           53

D Feynman Diagram Calculations for φ → µτ                                    61

D.1 Type 1 Triangular Diagrams: 2 Vertual Fermions + 1 Vertual Scalar . . . .   61
D.2 Type 2 Triangular Diagrams: 2 Vertual Scalars + 1 Vertual Fermion . . . .   65
D.3 Type 3-1 Triangular Diagrams: 1 Vertual Scalar, Fermion and Gauge Boson     67
D.4 Type 3-2 Triangular Diagrams: 1 Vertual Scalar, Fermion and Gauge Boson     70
D.5 Type 4 Triangular Diagrams: 2 Vertual Fermions + 1 Vertual Gauge Boson      72
D.6 Type 5 Triangular Diagrams: 2 Vertual Gauge Bosons + 1 Vertual Fermion      76
D.7 Type 6 Diagrams: 2 Vertual Fermions + 1 Vertual Scalar on µ . . . . . . .   78
D.8 Type 7 Diagrams: 2 Vertual Fermions + 1 Vertual Scalar on τ . . . . . . .  81
D.9 Type 8 Diagrams: 2 Vertual Fermions + 1 Vertual Gauge Boson on µ . . .      84
D.10 Type 9 Diagrams: 2 Vertual Fermions + 1 Vertual Gauge Boson on τ . . .    87

E Deacy Width of φ → µτ                                                      91

F Derivatives of Quark and Squark Masses                                        93

F.1 Quark Mass Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
F.2 Squark Mass Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . .94
F.3 Quark Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
F.4 Squark Derivatives with Respect to Neutral Higgs Fields . . . . . . . . . . 97
F.5 Squark Derivatives with Respect to Charged Higgs Fields . . . . . . . . . .100
                                

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