Violation in Mixing

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176 Analysis of the time-dependent �È -violating asymmetry in � � � � decays Sample Lepton Kaon NT1 NT2 Untagged � � MC � ¦ �� ¦ �� ¦ � �� ¦ �� ¦ �� Ã � MC �� ¦ �� ¦ �� ¦ � �� ¦ �� ¦ �� Ã Ã MC �� ¦ �� ¦ �� ¦ � �� ¦ �� ¦ �� Run 1 � � �� ¦ �� ¦ �� ¦ �� ¦ � �� ¦ �� Run 2 � � � ¦ �� ¦ �� ¦ � �� ¦ �� ¦ �� Run1+2Breco � ¦ � �� ¦ �� ¦ � �� ¦ �� ¦ �� Table 7-8. Efficiency ( ) for each tag category in signal � � Monte Carlo, the Run 1 and Run 2 � � fit region, and the Run 1 + 2 Breco sample. The latter (highlighted) is used in the fit. 7.6 Signal characterization The tagging performance and vertex resolution of the tag side in a �� event do not depend on the decay channel of the fully reconstructed � meson. With this assumption, the tagging efficiencies, dilutions, and ¡Ø resolution function (Ê×��) for ��, Ã�, and ÃÃ decays are obtained from the high statistics sample of fully-reconstructed �’s (Breco sample). Table 7-8 compares the tagging efficiency in signal Monte Carlo, the Run 1 + 2 Breco sample, and the � � fit region. The latter is obtained by floating the signal tag fractions in a �È -blind fit 2 . No significant difference is observed between different species in signal Monte Carlo, and the on-resonance signal region gives consistent tagging efficiencies. Table 7-9 summarizes the average dilution and difference for each category as determined in the Run 1+2Breco sample. The signal ¡Ø resolution function is parameterized by the sum of three Gaussians (core, tail, outlier), where the core bias is a function of the tag category and the error on ¡Ø. Table 7-10 lists the resolution function parameters obtained from a fit to the Run 1+2Breco tagged + untagged sample. 2 We blind the �È parameters by adding a random offset between ¦� and randomly flipping the sign of the asymmetries. Breco Run 1 + 2 Breco MC �� MC Category �� ¡� �� ¡� �� ¡� Lepton �� ¦ � � � ¦ � �� Kaon �� ¦ � � � ¦ � �� NT1 �� ¦ � � � ¦ � �� NT2 � ¦ � � � � ¦ � �� Table 7-9. Average dilution and difference determined from the Run 1+2Breco sample. For comparison we show the parameters determined from Breco and �� MC. MARCELLA BONA
7.7 The maximum likelihood analysis 177 Parameter Run 1 Breco Run 2 Breco MC Breco Scale (core) �� ¦ � �� ¦ � � � � ¦ � Æ ¡Ø lepton (core) � ¦ � � � �� ¦ � � � � ¦ � Æ ¡Ø kaon (core) � ¦ � �� ¦ � �� ¦ � � Æ ¡Ø NT1 (core) � �� ¦ � �� ¦ � � � � ¦ � � Æ ¡Ø NT2 (core) � �� ¦ � � � �� ¦ � � � � ¦ � Æ ¡Ø notag (core) � � ¦ � �� ¦ � � � ¦ � � Scale (tail) � ¦ � � ¦ � �� ¦ � � Æ ¡Ø (tail) �� ¦ �� ¦ � � �� ¦ � � �(tail) � � ¦ � � � � ¦ � � � � ¦ � � �(outlier) � ¦ � � ¦ � � � ¦ � Table 7-10. Parameters for Ê×�� obtained from the Run 1 and Run 2 Breco tagged + untagged samples. The Breco MC results are shown for comparison. 7.7 The maximum likelihood analysis An unbinned maximum likelihood fit is used to simultaneously extract yields and �È asymmetry parameters from combined tagged and untagged � � sample. The only new feature of the fitting technique relative to the branching fraction analysis is the addition of a PDF describing the time dependence in each component and tagging category. 7.7.1 Likelihood function The overall construction of the likelihood function Ä is similar to the branching fraction analysis. For this analysis, the sample consists of signal and background components for the three species (��,Ã�, and ÃÃ), separated by the flavor and category of the tag side. In addiction to the usual variables Ñ�Ë, ¡�, the Fisher discriminant � and the � ��Ö�Ò�ÓÚ angle, the ¡Ø measurement facilitates provides additional background rejection. The probability È�� for a single event � in tag category is the sum of probabilities over all components, È�� Æ�� Æ � �� È �� ÆÃÃ Æ �ÃÃÈ ÃÃ �� ÆÃ� Æ �Ã� Æ�� Æ � �� È �� Æ�ÃÃ Æ � �ÃÃ È �ÃÃ �� Ã� È Ã � �� Æ�Ã� �Ã� � Æ ��Ã� È �Ã � �� (7.10) 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
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 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: 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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