Violation in Mixing

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184 Analysis of the time-dependent �È -violating asymmetry in � � � � decays Variables �� MC Ã� MC ÃÃ MC bkg MC (GSB) Run 1 (SB) Ñ�Ë� ¡� � � � � � � � � �� Ñ�Ë� � � � � �� Ñ�Ë�� Ñ�Ë�� Ñ�Ë� ¡Ø � �� Ñ�Ë��¡Ø � � � � �� ¡�� ¡�� ¡�� ¡��¡Ø � � � � � �� ¡��¡Ø � � � �� ¡Ø � �� ¡Ø � � � � �� ¡Ø � � � �� ¡Ø � � � � �� ¡Ø � �� ¡Ø � � � �� ¡Ø� �¡Ø � � � � �� Table 7-14. Linear correlation coefficients for the variable set �Ñ �Ë� ¡�� ¡Ø� �¡Ø�. The grand side-band (GSB) region is defined as (�� Ñ�Ë � �� , �¡�� Î), and “SB” refers to the normal side-band region. dependence, which is properly taken into account in the PDF definition. Incorporating the correlation into the toy Monte Carlo generator, we have confirmed that there is no bias in the fit yields. The � correlation between the Fisher discriminant and the error on ¡Ø in the background samples is not yet understood. However, signal yields change only slightly between fits with and without ¡Ø, which gives some confidence that the correlation does not significantly affect the yield estimate. MARCELLA BONA
7.8 Validation studies 185 Figure 7-9. Left plots: pull plots for signal yields and the Ã� charge asymmetry in �� toy experiments generated with fb equivalent luminosity. Right plots: pull plots for background yields and the Ã� charge asymmetry in �� toy experiments generated with fb equivalent luminosity. 7.8 Validation studies Numerous studies using toy Monte Carlo, simulation, and real data have been performed to optimize and validate the analysis strategy. Figures 7-9 through 7-11 show pull plots for all free fit parameters in �� toy experiments corresponding to the nominal �È fit. Signal and background yields are generated according to a Poisson distribution with means equal to the PRL result scaled to fb . The yield for signal ÃÃ is generated with zero branching fraction and fit with the constraint ÆÃÃ � . Random values of �� are generated between ¦ and random values of Ë�� are generated within the bounds given by the selected value of ��. The numbers of � and � tags are consistent with the generated value of ��. The most probable �È asymmetry fit errors are �Ë�� and �� (Fig. 7-12). 7.8.1 Toy Monte Carlo Due to the two-body nature of the decay, the daughter tracks in � � � � are essentially anticorrelated in momentum and polar angle. First two plots in Fig. 7-13 show scatter plots of these two variables for tracks in signal �� Monte Carlo. In addition, the assignment of the pion mass to all tracks leads to a systematic shift in the mean ¡�, which is momentum dependent due to the boost (see right plot in Fig. 7-13). This underlying momentum dependence of � and ¡� is the source of the large correlations between these variables reported in Table 7-14. ANALYSIS OF THE TIME-DEPENDENT �È -VIOLATING ASYMMETRY IN � � � � DECAYS
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ÍÒ�Ú�Ö×�Ø��
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Contents Introduction . ...........
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4 Strategy and Tools for Charmless
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7.2 Branching fraction � � �
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Introduction The main goal of the B
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1 �È Violation in the �� Sys
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1.2 Neutral � Mesons 7 Note, howe
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1.2 Neutral � Mesons 9 Applying t
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1.2 Neutral � Mesons 11 �È �
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1.2 Neutral � Mesons 13 ��
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1.2 Neutral � Mesons 15 � ¡�
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1.2 Neutral � Mesons 17 and � a
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1.2 Neutral � Mesons 19 given tim
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1.3 The Three Types of �È Violat
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1.4 �È Violation in the Standard
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1.5 Determination of « 37 1.5 Dete
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1.5 Determination of « 39 Assuming
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1.5 Determination of « 41 Figure 1
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1.5 Determination of « 43 b q (a)
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1.5 Determination of « 45 � �
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2 The BABAR Experiment 2.1 Physics
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2.1 Physics at � � B Factory op
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2.2 The BABAR detector. 51 Integrat
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2.2 The BABAR detector. 53 The dete
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2.2 The BABAR detector. 55 two oute
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2.2 The BABAR detector. 57 SVT Effi
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2.2 The BABAR detector. 59 324 1015
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Efficiency 2.2 The BABAR detector.
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2.2 The BABAR detector. 63 2.2.4 Th
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entries per mrad 2.2 The BABAR dete
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2.2 The BABAR detector. 67 entries
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2.2 The BABAR detector. 69 energies
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2.2 The BABAR detector. 71 The main
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Efficiency 2.2 The BABAR detector.
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2.2 The BABAR detector. 75 Table 2-
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3 Ã Ë reconstruction and efficien
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3.3 Studies on data 79 19.5° BINS
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3.3 Studies on data 81 ¯ off-reson
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3.3 Studies on data 83 0.504 0.502
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3.3 Studies on data 85 0.03 0.025 0
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3.3 Studies on data 87 0.504 0.502
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3.3 Studies on data 89 N(π + π -
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3.3 Studies on data 91 0.508 0.506
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3.3 Studies on data 93 Figure 3-13.
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3.3 Studies on data 95 0.508 0.506
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4 Strategy and Tools for Charmless
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4.2 Event selection 99 channel sele
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4.2 Event selection 101 ÀÐ �
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4.2 Event selection 103 Figure 4-2.
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4.3 Background fighting 105 Figure
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4.4 PID selection 107 In the case o
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4.4 PID selection 109 θ c Cut Effi
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4.5 Tracking Corrections 111 Ë�
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4.6 Analysis methods 113 Ñ�Ë si
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4.6 Analysis methods 115 Events/2.5
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4.6 Analysis methods 117 Figure 4-1
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4.6 Analysis methods 119 θ c radia
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5 Measurement of Branching Fraction
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5.2 Ã Ë reconstruction 123 1 0.8
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5.3 Analysis Strategy 125 0.35 0.3
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5.4 Background Suppression and PDF
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Page 139 and 140: 5.5 Maximum likelihood analysis 133
Page 151 and 152: 5.6 Counting analysis 145 Table 5-1
Page 153 and 154: 5.7 Determination of branching frac
Page 155 and 156: 6 Measurement of Branching Fraction
Page 157 and 158: 6.3 The maximum likelihood analysis
Page 163 and 164: 6.4 Counting analysis 157 120 100 8
Page 165 and 166: 6.5 Analysis choice 159 6.5 Analysi
Page 167 and 168: 6.6 Results on the Run1 data-set 16
Page 169 and 170: 6.7 Determination of the branching
Page 171 and 172: 7 Analysis of the time-dependent
Page 173 and 174: 7.3 Analysis strategy 167 Parameter
Page 175 and 176: 7.4 Data samples and event selectio
Page 177 and 178: 7.4 Data samples and event selectio
Page 179 and 180: 7.5 Background characterization 173
Page 181 and 182: 7.5 Background characterization 175
Page 189: 7.7 The maximum likelihood analysis
Page 193 and 194: 7.8 Validation studies 187 100 75 5
Page 195 and 196: 7.8 Validation studies 189 Figure 7
Page 197 and 198: 7.8 Validation studies 191 Paramete
Page 199 and 200: 7.9 Results 193 Parameter Fit Resul
Page 201 and 202: 7.9 Results 195 Events/2 MeV/c 2 Ev
Page 203 and 204: 7.10 Systematic studies 197 Categor
Page 205 and 206: 7.11 Summary 199 �Ã� Ë��
Page 207 and 208: 7.11 Summary 201 �Ã� Ë��
Page 209 and 210: 7.11 Summary 203 Variation �Ã�
Page 211 and 212: BIBLIOGRAFIA 205 Bibliografia Chapt
Page 213 and 214: BIBLIOGRAFIA 207 [38] J. Charles, P
Page 215 and 216: BIBLIOGRAFIA 209 Chapter 7 [67] D.
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Violation in Mixing

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