Violation in Mixing

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168 Analysis of the time-dependent �È -violating asymmetry in � � � � decays time-dependent measurement is therefore expected to be dominated by statistical uncertainty and, ignoring systematic uncertainties and assuming zero asymmetry in the background, the analysis that optimizes the effective Ë� Ô Ë � will also minimize the error on the �È asymmetry. The �È asymmetries, as well as the signal and background yields, are determined simultaneously from a global maximum likelihood fit using both tagged and untagged � � events. There are two �È observables in the time-dependent analysis: �� and ÁÑ�: it would be most convenient to fit for �� and ÁÑ�� , since the latter provides a direct measurement of ×�Ò «�«. However, it was found that this fit produces non-Gaussian pull distributions in detailed toy Monte Carlo studies. Moreover, from Eq. 7.2 it is seen that using �� as a fit parameter implicitly constrains the coefficient of the cosine term to be in the physical region � , while there is no such constraint in the data. So there are also conceptual problems associated with using �� as a fit parameter. In contrast, fitting for Ë�� and �� is found to be very robust and does not bias the fit. The current analysis therefore uses Ë�� and �� as fit parameters. 7.4 Data samples and event selection Results in this analysis are based on a greater luminosity with respect to the one described in Sec 4.1: ¯ Run 1 on-resonance data ( �� fb , �� million �� pairs). ¯ Run 2 1 on-resonance data (�� fb , � million �� pairs). ¯ �� million (�� fb ) ÙÙ, �� and ×× Monte Carlo. ¯ � million (�� fb ) Monte Carlo. ¯ �� million (�� fb ) � � Monte Carlo. ¯ �k each of � � , Ã � , and Ã Ã signal Monte Carlo. Candidate � mesons are reconstructed by combining pairs of charged tracks using four-vector addition, where we assume the pion mass for both tracks. The two-track vertex position is obtained with the standard BABAR vertex algorithm, like the tag-side vertex is obtained with default BABAR algorithm using the charged track and the loose Ã Ëcandidate selection lists as input. For comparison, ¡Ø is calculated with and without the beam constraints. The BABAR tagging algorithm is used to identify the opposite � meson as a � or � . We use all the four standard BABAR tagging categories [4, 69]: lepton, kaon, neural network NT1 and NT2. Except for a tighter background suppression cut and the addition of ¡Ø quality cuts, the selection criteria used in this analysis are identical to those in Chapter 4. The cut on Ó× �Ë that was at �� is tightened at � Ó× �Ë� � ��. The Ñ�Ë and ¡� 2-dimensional side-bands are defined as �¡�� Î and �� Ñ�Ë � �� Î� . The signal band which is the fit region is defined with �¡�� Î and �� Ñ�Ë � �� Î� , while the Ñ�Ë side-band is �¡�� Î and �� Ñ�Ë � �� Î� . The 1 This data-set corresponds to data taken in the first half of year 2001 MARCELLA BONA
7.4 Data samples and event selection 169 ¯ � � ¯ Ã � ¯ Ã Ã standard efficiency �� ¦ � � �� ¦ � � �� ¦ � � PID efficiency �� ¦ � � �� ¦ � � �� ¦ � � ¡Ø Selection ¡Ø �� ¦ � � �� ¦ � �� ¦ � �¡Ø �� ¦ � �� ¦ � �� ¦ � ¡Ø efficiency �� ¦ � � �� ¦ � � �� ¦ � � nominal efficiency � �� ¦ � � � �� ¦ � � � � � ¦ � � tracking correction �� Total Efficiency � �� ¦ � � � �� ¦ � � � � � ¦ � � Table 7-3. Summary of detection efficiencies for � � , Ã � , and Ã Ã as determined in �� signal Monte Carlo samples with �k events. The Run 1 tracking efficiency correction factor is included in the total efficiency. The efficiency of each cut is relative to the previous one and the errors are statistical only. upper limit on Ñ�Ë corresponds to our assumed end-point for the ARGUS function. Events in the fit region are used to extract yields and �È parameters with an unbinned maximum likelihood fit, while events in the side-band region are used to extract various background parameters. The ¡Ø selection using the beam spot constraints is: ¯ �¡Ø� � � Ô× ¯ � ��¡Ø� � Ô×. Table 7-3 summarizes the efficiency of the selection criteria as determined in signal � � � � Monte Carlo samples. The efficiency of each cut is relative to the ones above it and the separate efficiencies for the standard, PID, and ¡Ø criteria are also shown. The tracking efficiency correction factor is the Run 1 estimate. Table 7-4 summarizes the tagging composition of the Run 1 and Run 2 events passing the selection criteria. Figure 7-1 shows the Ñ�Ë distributions in each tagging category and for the the subset of untagged events. We use the same ARGUS shape parameter � for all tag categories. The observed differences between the average � and the values obtained in the Lepton and NT1 do not have a significant effect on the results (Sec. 7.9). 7.4.1 Optimization of the � Ó× � Ë � cut Toy Monte Carlo is used to optimize the cut on � Ó× �Ë� relative to the branching ratio analysis cut (� ��). Given the large correlation between Ó× �Ë and the Fisher discriminant, probability density functions (PDFs) for the latter variable need to be re-parameterized for each cut. In contrast to the �� sample, the signal distribution is pure Gaussian for the �� and �� cuts. For background, the double-Gaussian PDF is a better representation of the data. 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
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 and 172: 7 Analysis of the time-dependent
Page 173: 7.3 Analysis strategy 167 Parameter
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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