A Mathematica based Version of the CKMfitter Package

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44 Chapter 5. Probing the Standard Model In addition to the Standard Global CKM Fit, several fits for different classes of constraints have been performed in this thesis. Each plot of Figure 5.8 shows the 95 % CL belts for the individual constraints and the allowed area from the combined fits. In the first row, the fit results, obtained from the CP-violating observables α, sin 2β, γ and |ɛK| are compared with those obtained from the CP-conserving constraints |Vub|, ∆md and ∆md & ∆ms. An important observation is that a non-real CKM matrix with ¯η �= 0 and thus CP violation is also obtained from CP-conserving constraints. The crucial input in this constraint is the recent measurement of ∆ms by CDF, presented at the winter conferences 2006. The second row shows the impact of theoretical uncertainties. The allowed area from the fit using only the UT angle constraints α, sin 2β and γ is much smaller than the area obtained from the constraints |Vub|, |ɛK|, ∆md and ∆md & ∆ms which depend on additional QCD parameters. The left figure of the third row shows the fit results from constraints which are dominated by tree-level contributions. Beside |Vub|, a combined constraint from α and β is used which allows to extract γ. Assuming no New Physics contributions to the ∆I = 3/2 part of b → d transitions in the extraction of α leads in combination with β, measured in tree-level B → Mc¯c transitions, to a cancellation of a possible New Physics mixing phase ϑd (see Chapter 6). That gives a determination of γ = π − β − α independent from possible New Physics in B 0 - ¯ B 0 mixing. Compared to that, the right plot shows constraints from the loop-dominated observables sin 2β, |ɛK|, ∆md and ∆md & ∆ms. Since all fits are consistent with the Standard Global CKM Fit and the allowed (¯ρ,¯η) range is quite small, the space for possible New Physics effects is significantly constrained. A more detailed discussion of possible NP contributions in B 0 - ¯ B 0 mixing is described in the next chapter.
5.2. Standard Model Fit Results 45 η η η 0.6 0.5 0.4 0.3 0.2 excluded area has CL > 0.95 γ sin2β εK α 0.1 α γ β 0 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0.6 0.5 0.4 0.3 0.2 excluded area has CL > 0.95 γ sin2β ρ εK sol. w/ cos2β < 0 (excl. at CL > 0.95) CKM f i t t e r ICHEP 2006 α γ η 0.6 0.5 0.4 0.3 0.2 excluded area has CL > 0.95 Δmd Δms & Δmd α 0.1 γ Vub/Vcb β 0 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 (a) (b) α 0.1 α γ β 0 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0.6 0.5 0.4 0.3 0.2 excluded area has CL > 0.95 (c) γ( α) α ρ ρ sol. w/ cos2β < 0 (excl. at CL > 0.95) CKM f i t t e r ICHEP 2006 0.1 γ Vub/Vcb β 0 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 (e) α CKM γ f i t t e r ICHEP 2006 η η 0.6 0.5 0.4 0.3 0.2 excluded area has CL > 0.95 εK Δmd α ρ Δms & Δmd ρ CKM f i t t e r ICHEP 2006 CKM f i t t e r ICHEP 2006 0.1 γ Vub/Vcb β 0 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 0.6 0.5 0.4 0.3 0.2 sin2β εK Δmd (d) Δms & Δmd α 0.1 γ β 0 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 ρ εK εK sol. w/ cos2β < 0 (excl. at CL > 0.95) Figure 5.8: Confidence level in the (¯ρ,¯η) plane for several global CKM fits. (a) CP-violating observables vs. (b) CP-conserving observables, (c) theoretically clean observables vs. (d) observables with significant theory errors from non-perturbative QCD parameters and (e) tree dominated observables vs. (f) loop dominated observables. In the plot from pure tree observables, the constraint on α has been used assuming there are no New Physics contributions to the ∆I = 3/2 part of b → d transitions. In the combination of this constraint with β from B → Mc¯cKS modes the New Physics mixing phase ϑd cancels, so that it gives a New Physics free determination of γ = π − β − α. excluded area has CL > 0.95 (f) CKM f i t t e r ICHEP 2006
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A Mathematica based Version of the
Page 3: Kurzfassung Das CKMfitter Software-
Page 6 and 7: vi CONTENTS 6 New Physics Beyond th
Page 8 and 9: viii LIST OF FIGURES B.6 Constraint
Page 10 and 11: x LIST OF TABLES
Page 12 and 13: 2 Chapter 1. Introduction Unfortuna
Page 14 and 15: 4 Chapter 2. Theory the bosons of t
Page 16 and 17: 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 68 and 69: 58 Chapter 7. Conclusions and Persp
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
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94 Appendix E. User Guide
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96 Appendix E. User Guide
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98 BIBLIOGRAPHY [12] L. Wolfenstein
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100 BIBLIOGRAPHY [43] A. G. Akeroyd
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102 BIBLIOGRAPHY [74] T. Inami and
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Erklärung Hiermit versichere ich,
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