Appendix A: Maximum Likelihood Fits

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1 Appendix A: Maximum Likelihood Fits L. Caminada, Study of the Inclusive Beauty Production at CMS and Construction and Commissioning of the CMS Pixel Barrel Detector, Springer Theses, DOI: / , Ó Springer-Verlag Berlin Heidelberg

2 140 Appendix A: Maximum Likelihood Fits A.1 Bins in Muon Transverse Momentum A.1.1 Fit Result Fig. A.1 Fit result obtained by dividing the MC sample into two independent subsamples and using the approximate fitting method. The dashed and the dotted line are the b- and cudsgtemplate, respectively. The full circles correspond to the data distribution, while the solid line is the result of the fitting procedure. The data distribution is scaled to an integrated luminosity of 1pb -1. All bins in muon transverse momentum are shown

3 Appendix A: Maximum Likelihood Fits 141 A.1.2 Fit Deviation in the Approximate Method Fig. A.2 Deviation of the fitted scale factor a b fit in b-events from the true value a b when using the approximate fitting method. The results are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1pb -1. All bins in muon transverse momentum are shown

4 142 Appendix A: Maximum Likelihood Fits A.1.3 Pull Distributions of the Approximate Method Fig. A.3 b-fraction pull distributions resulting from the approximate fitting method. The pull distributions are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1 pb -1. All bins in muon transverse momentum are shown

5 Appendix A: Maximum Likelihood Fits 143 A.1.4 Fit Deviation in the Full Treatment Fig. A.4 Deviation of the fitted scale factor a b fit in b-events from the true value a b when using the full treatment in the fitting procedure. The results are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1 pb -1. All bins in muon transverse momentum are shown

6 144 Appendix A: Maximum Likelihood Fits A.1.5 Pull Distributions of the Full Treatment Fig. A.5 b-fraction pull distributions resulting from the full treatment in the fitting procedure. The pull distributions are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1 pb -1. All bins in muon transverse momentum are shown

7 Appendix A: Maximum Likelihood Fits 145 A.2 Bins in Muon Pseudorapidity A.2.1 Fit Result Fig. A.6 Fit result obtained by dividing the MC sample into two independent subsamples and using the approximate fitting method. The dashed and the dotted line are the b-and cudsgtemplate, respectively. The full circles correspond to the data distribution, while the solid line is the result of the fitting procedure. The data distribution is scaled to an integrated luminosity of 1pb -1. All bins in muon pseudorapidity are shown

8 146 Appendix A: Maximum Likelihood Fits A.2.2 Fit Deviation in the Approximate Method Fig. A.7 Deviation of the fitted scale factor a b fit in b-events from the true value a b when using the approximate fitting method. The results are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1pb -1. All bins in muon pseudorapidity are shown

9 Appendix A: Maximum Likelihood Fits 147 A.2.3 Pull Distributions of the Approximate Method Fig. A.8 b-fraction pull distributions resulting from the approximate fitting method. The pull distributions are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1 pb -1. All bins in muon pseudorapidity are shown

10 148 Appendix A: Maximum Likelihood Fits A.2.4 Fit Deviation in the Full Treatment Fig. A.9 Deviation of the fitted scale factor a b fit in b-events from the true value a b when using the full treatment in the fitting procedure. The results are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1 pb -1. All bins in muon pseudorapidity are shown

11 Appendix A: Maximum Likelihood Fits 149 A.2.5 Pull Distributions of the Full Treatment Fig. A.10 b-fraction pull distributions resulting from the full treatment in the fitting procedure. The pull distributions are obtained from repeated pseudo experiments with data statistics generated by appropriate random variations corresponding to an integrated luminosity of 1 pb -1. All bins in muon pseudorapidity are shown

12 Appendix B: Systematic Uncertainties B.1 Limited MC Statistics Table B.1 Systematic uncertainties due to limited MC and data statistics Relative error of fitted b-fraction (L =1pb -1 ) l p T 5 6 GeV 0.5% 6 7 GeV 0.5% 7 8 GeV 0.5% 8 10 GeV 0.5% GeV 0.6% GeV 0.6% GeV 1% GeV 1% GeV 1.2% GeV 3% g l (-2, -1.8) 0.8% (-1.8, -1.5) 0.7% (-1.5, -1.2) 0.7% (-1.2, -0.9) 0.7% (-0.9, -0.6) 0.7% (-0.6, -0.3) 0.7% (0.3, 0) 0.7% (0, 0.3) 0.7% (0.3, 0.6) 0.7% (0.6, 0.9) 0.7% (0.9, 1.2) 0.7% (1.2, 1.5) 0.7% (1.5, 1.8) 0.7% (1.8, 2.1) 0.8% L. Caminada, Study of the Inclusive Beauty Production at CMS and Construction and Commissioning of the CMS Pixel Barrel Detector, Springer Theses, DOI: / , Ó Springer-Verlag Berlin Heidelberg

13 Appendix C: Preliminary p ffiffi Results of First Collisions at s = 7 TeV C.1 p \ rel Distribution in Bins of Muon Transverse Momentum Fig. C.1 p rel \ distribution measured in data. Eight bins in muon transverse momentum are shown. The result of the maximum likelihood fit and the simulated template distributions are overlaid on the p rel \ distribution in data. The dashed and the dotted line are the b- and cudsgtemplate, respectively. The full circles correspond to the data distribution, while the solid line is the result of the fitting procedure L. Caminada, Study of the Inclusive Beauty Production at CMS and Construction and Commissioning of the CMS Pixel Barrel Detector, Springer Theses, DOI: / , Ó Springer-Verlag Berlin Heidelberg

14 154 Appendix C: Preliminary Results of First Collisions at C.2 p \ rel Distribution in Bins of Muon Pseudorapidity p ffiffi s = 7 TeV Fig. C.2 p \ rel distribution measured in data. Seven bins in muon pseudorapidity are shown. The result of the maximum likelihood fit and the simulated template distributions are overlaid on the p \ rel distribution in data. The dashed and the dotted line are the b- and cudsgtemplate, respectively. The full circles correspond to the data distribution, while the solid line is the result of the fitting procedure

15 Curriculum Vitae Personal Data Name: Lea Michaela Caminada Date of Birth: December 30, 1981 Place of Birth: Zürich (ZH) Nationality: Swiss Citizen of Vrin (GR) and Zürich (ZH) Education Doctoral studies at ETH Zürich and PSI Research at the CMS experiment at the CERN LHC 2006 Diploma in Physics at ETH Zürich summa cum laude Diploma Thesis at the H1 experiment at DESY in Hamburg in the group of Prof. R. Eichler Title: Implementation of a Trigger for the Decay b? e+xon the Third Trigger Level at the H1 experiment Exchange year at the Strathclyde University in Glasgow Studies of Physics at ETH Zürich 2001 Eidgenössische Matura Typus B Gymnasium in Zürich-Oerlikon Primary School in Zürich-Höngg Awards 2010 CMS Thesis Award 2010 Medallie der ETH Zürich for an excellent PhD thesis 2006 Diploma in Physics at ETH Zürich summ cum laude L. Caminada, Study of the Inclusive Beauty Production at CMS and Construction and Commissioning of the CMS Pixel Barrel Detector, Springer Theses, DOI: / , Ó Springer-Verlag Berlin Heidelberg

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