A Mathematica based Version of the CKMfitter Package

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18 Chapter 4. A Mathematica based Version of the CKMfitter Package The core of Mathematica is the kernel, which interactively performs the calculation. The user interacts with the kernel via a front-end, where a graphical version is available as well as a commandline interface. Since the terminology of Mathematica is used in this work, Appendix E.1 gives a short overview about relevant terms and commands. A more detailed documentation is provided on the Mathematica website [22]. 4.2 Package Structure The Mathematica based version of the CKMfitter package is modularly composed of several Mathematica notebooks and packages. Furthermore, there are FORTRAN files from the minimization routine and datacards in ASCII format. In Table 4.1, the content of the most relevant directories is shown. CKMfitter Directory File Content analysis/ datacards fortran/ minimir.f, fit.f, dmnfg.f, specialfunctions.f inputs/ input datacards, χ 2 -input tables, PDG.m lib/ AnalysisLib.m, FitLib.m theories/ theory packages, TheoryTutorial.nb tools/ CreateInputTable.nb CKMfitter.nb Table 4.1: Directory structure of the Mathematica based CKMfitter package The user interface is the CKMfitter.nb notebook. It is located in the main directory, but should be copied to another analysis specific directory, outside of the CKMfitter package. For the sake of clarity, complex functions and subroutines are sourced out from the user interface to library packages. The AnalysisLib package contains all relevant subroutines for the data processing inside the Mathematica environment, e. g. subroutines to load datacards and theory packages. The second library package is named FitLib and includes all functions for the interaction of CKMfitter.nb with the FORTRAN minimization routine. It provides for example a subroutine, which translates the Mathematica expressions to FORTRAN code. As in the original CKMfitter package, a fit is userfriendly driven by datacards. Since these are ASCII text files, they can be edited without using Mathematica in a plain text editor. In a datacard, all flags and options of a selected analysis are set, e. g. the context name, the fit variables and the scan granularity. A more detailed description of the relevant fit options and settings is given in Appendix E.2.
4.3. CKMfitter.nb 19 An important flag in the datacards is the specification of the input files. These files contain the numerical input for each measurement xexp and model parameter ymod. The values are provided in the “inputs” list, where each element is again a list, one per measurement or model parameter. According to the different error types of a measurement, there exist different input types, e. g. “Range” or “GaussRange”. It is also possible to specify the name of a file, which contains a χ 2 -contour of a measurement xexp. The different input types are distinguished using explicit syntaxes in the list. A brief description of the syntax for each possible input type is provided in Appendix E.3. Furthermore, the theoretical expressions xtheo depend on fixed inputs, e. g. physical constants. They are listed in a separate package, called PDG, which is also located in the inputs directory. Its content is the “fixedinputs” list, where each entry is a “rule”, which replaces a symbol through its numerical value, e. g. mB → 5.2794 for the B-meson mass. 4.3 CKMfitter.nb The CKMfitter analysis notebook is the user front-end of the Mathematica based version. It sources all relevant information from datacards and theory packages, translates the χ 2 -function in FORTRAN format, runs the minimization and exports the fit results. In addition, the CKMfitter notebook provides several checks and the opportunity to monitor the fit process. Running a fit, the user only needs to select an analysis datacard, where all job options are set before. Afterwards the analysis is executed step by step as shown in Figure 4.1. In the first part, all relevant informations are loaded, e. g. library packages and physical constants. After loading the theory packages and input files as specified in the datacard, the χ 2 -function and their partial derivatives are symbolically calculated during the fit preparation. These expressions are transformed in FORTRAN code format using the Mathematica intrinsic function FortranForm and written to the file minimirChi2.f. This file is compiled and linked to the minimization subroutines and the executable minimir is built. The fit starts through running minimir, which performes the global minimization as well as the one- and two-dimensional scans. The fit results are written to the file minimir.output and then loaded from CKMfitter.nb, where the fit results are plotted. Finally, plots and data files are exported. Remark: To interrupt the fit process, there is the possibility to quit the Mathematica kernel. Since minimir is a stand alone executable, it needs to be aborted separately by the user!
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 30 and 31: 20 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
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68 Appendix D. Source Code else k =
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70 Appendix D. Source Code do i = 1
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72 Appendix E. User Guide E.2 Datac
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74 Appendix E. User Guide scanMin T
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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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