A Mathematica based Version of the CKMfitter Package

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58 Chapter 7. Conclusions and Perspectives Since all the present data from experiments in quark-flavor physics is well described by the Standard Model, the space for New Physics contributions is significantly constrained. Nevertheless, there is still enough space for possible New Physics effects, which have been quantified in this thesis in two different extensions of the Standard Model. Possible New Physics contributions to neutral meson oscillations have been implemented model-independently to the B-meson systems as well as to the Kaon system. The allowed ranges for the NP parameters (r 2 d ,2ϑd) in the Bd system have been found to: r 2 d = 1.02 +0.50 −0.42 and 2ϑd = −0.094 +0.049 −0.123 (at 68 % CL), (7.3) which is in good agreement with the Standard Model. The small bias in 2ϑd results from the slight disagreement of the measurements of |Vub|incl and sin 2β. Since a significant constraint on possible New Physics in B 0 - ¯ B 0 mixing is obtained from the observable ASL, its theoretical prediction has been implemented including LO QCD corrections as well as NLO QCD corrections. A preliminary comparison of their SM predictions is given in this thesis. Contributions of charged Higgs bosons to the branching fraction of leptonic B-meson decays have been implemented in the framework of Two-Higgs-Doublet Models. Since only the decay B + → τ + ντ is currently experimentally accessible, the constraint on (tan β,m H +) is still loose. An additional fit input from B → Xsγ transitions would provide an additional constraint, but has not been implemented yet. To guarantee the stability of the fit results by using the Mathematica based CKMfitter package, several comparison tests with the original package have been performed. As a benefit to the CKMfitter group, a user guide has been written during this thesis as well as a tutorial on the coding of theory packages. After more than one year of development, the Mathematica based version of the CKMfitter package has been used for the first time to produce the fit results for a large conference (ICHEP 2006). Nevertheless, a lot of features available in the original CKMfitter package are still missing. A Wolfenstein parameter independent prediction of B(B + → l + νl) as well as the theory of rare Kaon decays need to be implemented. Due to its modular structure, the new Mathematica based version of the CKMfitter package is not only restricted to the CKM matrix analysis. Further applications, e. g. a leptonic mixing matrix analysis could be easily added.
Appendix A The Inami-Lim Functions The Inami-Lim functions are defined by [74]: where S (xi) = � 1 xi 4 + 9 4 (1 − xi) − 3 2 (1 − xi) 2 � − 3 S (xi, xj) i�=j = � �3 xi ln xi 2 1 − xi �� 1 xixj 4 + 3 2 (1 − xi) − 3 4 (1 − xi) 2 � 1 ln(xi) xi − xj � 1 + 4 + 3 2 (1 − xj) − 3 4 (1 − xj) 2 � − 1 ln(xj) xj − xi 3 � 1 , 4 (1 − xi) (1 − xj) xi = m2 i m 2 W with i = c, t . The quark masses are used in the MS scheme, which are perturbatively calculated in LO from the pole masses by: � ¯mi(mi) = mi 1 − 4 � �� αS(mi) . (A.1) 3 π The QCD correction factor ηcc to the Inami-Lim functions has been parametrized through [37]: � � �� ¯mc(mc) ηcc � (1.46 ± δcc) 1 − 1.2 − 1 [1 + 52 (αS(mZ) − 0.118)] (A.2) 1.25 GeV/c2 with an uncertainty from higher-order corrections parametrized by: � � �� ¯mc(mc) δcc = 0.22 1 − 1.8 − 1 [1 + 80 (αS(mZ) − 0.118)] . (A.3) 1.25 GeV/c2 59
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A Mathematica based Version of the
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Kurzfassung Das CKMfitter Software-
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vi CONTENTS 6 New Physics Beyond th
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viii LIST OF FIGURES B.6 Constraint
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x LIST OF TABLES
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2 Chapter 1. Introduction Unfortuna
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4 Chapter 2. Theory the bosons of t
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6 Chapter 2. Theory VCKM is a compl
Page 18 and 19: 8 Chapter 2. Theory 2.4 Neutral Mes
Page 20 and 21: 10 Chapter 2. Theory b u,c,t d 0 B
Page 22 and 23: 12 Chapter 2. Theory CP violation i
Page 24 and 25: 14 Chapter 3. CKMfitter The quantit
Page 26 and 27: 16 Chapter 3. CKMfitter
Page 28 and 29: 18 Chapter 4. A Mathematica based V
Page 40 and 41: 30 Chapter 5. Probing the Standard
Page 60 and 61: 50 Chapter 6. New Physics Beyond th
Page 70 and 71: 60 Appendix A. The Inami-Lim Functi
Page 72 and 73: 62 Appendix B. Additional Figures o
Page 74 and 75: 64 Appendix B. Additional Figures o
Page 76 and 77: 66 Appendix C. Testjob } globalMinS
Page 78 and 79: 68 Appendix D. Source Code else k =
Page 80 and 81: 70 Appendix D. Source Code do i = 1
Page 82 and 83: 72 Appendix E. User Guide E.2 Datac
Page 84 and 85: 74 Appendix E. User Guide scanMin T
Page 86 and 87: 76 Appendix E. User Guide E.3 Input
Page 88 and 89: 78 Appendix E. User Guide
Page 108 and 109: 98 BIBLIOGRAPHY [12] L. Wolfenstein
Page 110 and 111: 100 BIBLIOGRAPHY [43] A. G. Akeroyd
Page 112 and 113: 102 BIBLIOGRAPHY [74] T. Inami and
Page 115: Erklärung Hiermit versichere ich,
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