A Mathematica based Version of the CKMfitter Package

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28 Chapter 4. A Mathematica based Version of the CKMfitter Package The test job, used for the fit time comparison, is the Standard Global CKM Fit. Its Mathematica datacard is shown in detail in Appendix C and the result is the yellow area around the apex of the Unitarity Triangle in Figure 4.3. The fit time needed using the original CKMfitter package is about 23 hours, whereas the same result can be obtained by the Mathematica based version in only ten minutes. This is a reduction of the fit time of more than a factor 100 for the Standard Global CKM Fit. Original CKMfitter package ≈ 23 h Mathematica based CKMfitter ≈ 10 min Table 4.7: Fit time comparison of test job runs Since the fit time depends on the hard- and software conditions, the performance of the Mathematica based CKMfitter package is tested for several configurations. The results for the test job are summarized in Table 4.8. Hardware MHz Compiler Operation System Fit time / min AMD Opteron 2194 f77 -O Scientific Linux 3.0.7 04 : 42 Intel P M 1497 ifort -O2 SUSE Linux 10.0 05 : 25 Intel P M 1497 f77 -O SUSE Linux 10.0 07 : 06 Intel P III 1266 ifort -O2 Scientific Linux 3.0.3 09 : 10 Intel P III 1266 f77 -O Scientific Linux 3.0.3 10 : 18 Table 4.8: Hardware and software performance tests The most important conclusion is, that the fit results are independent of the used hard- and software conditions. Using a high developed hardware system in combination with an optimized FORTRAN compiler leads to a further fit time reduction. With a fit time reduction of more than a factor 100, the goal of the Mathematica based CKMfitter development has been achieved.
Chapter 5 Probing the Standard Model After a brief discussion of the relevant fit inputs, the most important results of the global CKM matrix analysis in the framework of the Standard Model are presented. 5.1 Fit Inputs In this section, the SM predictions and measurement methods of the most relevant observables are described. If not stated otherwise, the expressions given are used in the Mathematica based version of the CKMfitter package. The input values are quoted in form of a central value and its uncertainties, where contributions of gaussian distributed experimental, statistical and theoretical uncertainties are quadratically added and labeled with “gauss”. Theoretical systematics, labeled with “theo”, are added linearly and treated in the Rfit scheme. In the case of constraints with ambiguous solutions (as for the UT angles α and γ), the experimental likelihood function is directly used as fit input. Since a complete review of the input measurements is beyond the scope of this thesis, more detailed informations can be obtained from the References [4, 8, 9] and references therein. The values of the fit inputs are the most recent results as presented at ICHEP 2006 and are summarized in Table 5.1. The final plots have been prepared by Vincent Tisserand using the macros as described in Chapter 4. 5.1.1 |Vud| The most precise determination of |Vud| stems from superallowed nuclear beta decays. Taking the average of the most precise experimental results yields [27]: |Vud| = 0.97377 ± 0.00027gauss . (5.1) Superallowed nuclear beta decays are pure weak vector transitions (0 + → 0 + ). Thus, the extraction of |Vud| is theoretically very clean, since theoretical uncertainties in electroweak radiative corrections, isospin violating electromagnetic effects and nuclear structure dependence are under good theoretical control. 29
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 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
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78 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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