A Mathematica based Version of the CKMfitter Package

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30 Chapter 5. Probing the Standard Model 5.1.2 |Vus| The matrix element |Vus| has been extracted from semileptonic Kaon decays (Kl3), e. g. K + → π 0 e + νe. Its current world average (WA) is [9]: |Vus|Kl3 = 0.2257 ± 0.0021gauss . (5.2) |Vus| as well as |Vud| are the main inputs to constrain the Wolfenstein parameter λ. However, |Vus| depends on large theoretical uncertainties from the determination of the form factor f+(0). Other possibilities to determine |Vus| involve for instance leptonic Kaon and Pion decays, semileptonic Hyperon decays or hadronic τ decays. 5.1.3 |Vcb| The magnitude of |Vcb| is determined from exclusive and inclusive measurements 1 of semileptonic B-meson decays to charmed final states (b → clν). Because of theoretical uncertainties on the form factor calculation, the exclusive determination is less precise compared to the inclusive one and thus not used in this work. Due to the large statistics, the inclusive WA [9]: |Vcb|incl = (41.7 ± 0.7gauss) · 10 −3 (5.3) is already below the 2% level. It is the main input to constrain the Wolfenstein parameter A. 5.1.4 |Vub| Analogous to |Vcb|, the CKM matrix element |Vub| is determined from exclusive and inclusive measurements of b → ulν transitions. The inclusive determination suffers from large B → Xclν background and uses therefore phase space regions where the charm background is kinematically suppressed. Hadronic effects enter in leading order (LO) via one non-perturbative shape function, which has been extracted from the photon energy spectrum in B → Xsγ. For the inclusive WA, the BLNP [28] calculation is chosen [29] 2 : |Vub| incl. = (4.48 ± 0.24gauss ± 0.39theo) · 10 −3 , (5.4) The theoretical error is obtained by adding linearly the contributions from weak annihilation, subleading shape functions and the Heavy-Quark Expansion (HQE) uncertainty on the b-quark mass. Direct measurements of exclusive channels depend significantly on form factor calculations. The form factors can be calculated using unquenched Lattice QCD (LQCD) or QCD Sum Rules, which still leads to larger theoretical uncertainties compared to the inclusive determination. 1 Exclusive means the full reconstruction of a single mode, e. g. B + → ¯ D 0 e + νe, where inclusive measurements integrate over all possible final states, B → Xclν. 2 The central value has been shifted after the ICHEP06 conference to 4.49 · 10 −3 .
5.1. Fit Inputs 31 1 – CL 1.2 1 0.8 0.6 0.4 0.2 C K M f i t t e r ICHEP 06 B → ππ B → ρπ B → ρρ Combined CKM fit 0 0 20 40 60 80 100 120 140 160 180 α (deg) WA 1 – CL 1.2 1 0.8 0.6 0.4 0.2 C K M f i t t e r FPCP 06 Full frequentist treatment on MC basis CKM fit no γ meas. in fit D ( * ) K ( * ) GLW + ADS D ( * ) K ( * ) WA GGSZ Combined 0 0 20 40 60 80 100 120 140 160 180 γ (deg) Figure 5.1: Left: Confidence level on the UT angle α obtained from the combination (green shaded) of B → ππ (green curve), B → ρπ (red curve) and B → ρρ (blue curve). Right: Confidence level on the UT angle γ obtained from the combination (green shaded) of the GLW, ADS and GGSZ methods (see text). 5.1.5 The UT angle α The direct constraint on the UT angle α is obtained from charmless B decays. The best current knowledge comes from a combination of the two body isospin analysis [10] of B → ππ and B → ρρ decays and the Dalitz-plot analysis [10] of B → ρπ decays. Figure 5.1 (left) shows the confidence level on α from the combined constraint of these three measurements. The isospin analysis as well as the α extraction from B → ρπ have been performed by the CKMfitter group using the most recent results of BABAR and Belle. Due to its non-gaussian shape, the χ 2 -contour is used as a LUT input file as described in Chapter 4. 5.1.6 sin 2β The currently best constraint on (¯ρ,¯η) comes from determination of the CP-violating parameter sin 2β. It is measured with high precision at the B-factories from the interference between decays with and without mixing in b → c¯cs transitions. The current world average is obtained by combining the measurements of B → (c¯c)K 0 (BABAR) and B → J/ψKS,L (Belle) and yields [30]: sin 2β = 0.675 ± 0.026gauss . (5.5)
Page 1 and 2: 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 42 and 43: 32 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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80 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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