Violation in Mixing

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166 Analysis of the time-dependent �È -violating asymmetry in � � � � decays In the case of imperfect tagging, Eq. 7.1 must be modified to include the mis-tag probabilities: � � Ø�� Û � Û� � � Ø�� Û � Û� (7.4) where Û (Û) is the probability that a true � (� ) meson is tagged as a � (� ). Defining the dilutions, � � Û and � � Û , the average dilution ��, and the dilution difference ¡� � � �� the mistag probabilities can be written as Û � �� ¡� The decay rate distributions, assuming perfect vertex resolution, are then � � Ø�� Ø�� ¡Ø�� ¡Ø�� ¡� � � � (7.5) Û� �� ¡� � (7.6) ¡� �� Ë�×�Ò ¡Ñ�� ¡Ø �� Ó× ¡Ñ�� ¡Ø � ¡� �� Ë�×�Ò ¡Ñ�� ¡Ø �� Ó× ¡Ñ�� ¡Ø � � � � (7.7) The observed distribution � ¡Ø is the convolution of � ¡Ø with the signal vertex resolution function Ê×�� ¡Ø � � Ø�� Ø�� ªÊ×�� Ø�� Ø�� ªÊ×�� (7.8) In neutral � meson decays to the Ã ¦ � § final state the flavor of the parent meson is tagged by the charge of the kaon. For a � � Ã � (� � Ã � ) decay the event is therefore known to be a mixing event if the tag side is a � (� ). The maximum likelihood fit includes the effect of mixing in the Ã� term. The decay rate distributions for mixed and unmixed events when the tag side is a � or � are (cf. Ref. [72]): �¡Ø�� Ñ�Ü�� Ø�� ¡� � ��Ó× ¡Ñ�� ¡Ø �¡Ø�� ÙÒÑ�Ü�� Ø�� ªÊ×�� ¡� � ��Ó× ¡Ñ�� ¡Ø �¡Ø�� Ñ�Ü� � Ø�� ªÊ×�� ¡� � ��Ó× ¡Ñ�� ¡Ø � ªÊ×�� ÙÒÑ�Ü� � Ø�� ¡Ø�� ¡� � �� Ó× ¡Ñ�� ¡Ø 7.2 Branching fraction � � � � analysis results � ªÊ×�� (7.9) Given data and selection described in Chapter 4, BABAR has published the results of the � � � � branching fraction in Ref. [6]. The unbinned maximum likelihood fit and the parameterizations of the PDFs MARCELLA BONA
7.3 Analysis strategy 167 Parameter Fit Result Æ�� ¦ ÆÃ� �Ã� ÆÃÃ �� ¦ � � � ¦ � �� Æ�� ¦ �� Æ�Ã� �� ¦ � ��Ã� � ¦ � � Æ�ÃÃ � � ¦ �� Table 7-1. Results from the maximum likelihood fit. have been described in detail in Sec. 4.6.1. The fit is performed using the unbinned maximum likelihood fit including all events which pass the preselection and the PID cuts. The sample consists of � candidates. The results from the fit are given in Table 7-1. The statistical significances of the signals are determined to be �� for � � , �� for Ã � and � � for Ã Ã . The systematic uncertainties in the fit results due to modelling of the PDFs are summarized in Tables 7-2 for the branching ratio. Par. bkg Ñ�Ë bkg ¡� bkg � �Ñ�Ë� � Ñ�Ë �¡�� ¡� � � � � Tot. Æ�� ¦�� ¦ � ¦ ÆÃ� ¦ �� ¦ � ¦ � ÆÃÃ ¦ ¦ � ¦ � �� ¦ �� ¦�� ¦ �� ¦ � ¦ � �� ¦ �� ¦ � ¦� Table 7-2. Systematic errors ( ) on the branching ratio results from the maximum likelihood fit. For the decay modes � � � � and � � Ã � we measure the branching fractions to be �� ¦ � �� ×Ø�Ø ¦ �� ×Ý×Ø ℄ ¡ and � ��¦ �� ×Ø�Ø � ×Ý×Ø ℄ ¡ , respectively. The statistical significance is �� standard deviations for the � � Ã � decay. We do not find a significant signal yield in the mode � � Ã Ã and measure a � confidence level upper limit branching fraction of �� ¢ � . The asymmetry in the � � Ã � and � � Ã � decay rates is measured to be � � ¦ � ¦ � . These results have been published as Ref. [6] and they are referred to as the PRL results. 7.3 Analysis strategy Applying the cuts described in Chapter 4 for the branching fraction analysis and considering the PRL results for the yields, the expected number of tagged �� events is �� fb ,or� �� in fb (see Sec. 7.2). The 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
Page 121 and 122: 4.6 Analysis methods 115 Events/2.5
Page 123 and 124: 4.6 Analysis methods 117 Figure 4-1
Page 125 and 126: 4.6 Analysis methods 119 θ c radia
Page 127 and 128: 5 Measurement of Branching Fraction
Page 129 and 130: 5.2 Ã Ë reconstruction 123 1 0.8
Page 131 and 132: 5.3 Analysis Strategy 125 0.35 0.3
Page 133 and 134: 5.4 Background Suppression and PDF
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: 7 Analysis of the time-dependent
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 191 and 192: 7.8 Validation studies 185 Figure 7
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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