Violation in Mixing

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178 Analysis of the time-dependent �È -violating asymmetry in � � � � decays ÆÃ� Æ �Ã� Ã � �Ã� È�� Æ�Ã� �Ã� � Æ �Ã � ��Ã� È�� where: ¯ Æ� � fitted number of events of type � in the entire sample. ¯ � � � fraction of events of type � that are tagged in category . ¯ Æ � È Æ�� . ¯ �� Æ Ã � Æ Ã � �Æ Ã � Æ Ã � , the direct �È -violating asymmetry. ¯ È � � È � Ñ�Ë ¡È � ¡� ¡È � � ¡È � � ¡È � � ¡È � ¡Ø . Untagged events are treated as a fifth category with � � ¡� � . Due to the small number of signal events, we use the transformation of variables Æ � � Æ�� in order to fit for the total yields Æ� rather than the yield in each tagging category. Background tag fractions � come from Table 7-6. For signal we assume � �� Ã� � � ÃÃ and use the result from the Breco data sample (Table 7-8). The extended likelihood Ä for a single category is given by Ä � � Æ Æ Æ Æ� � È�� (7.11) where the Poisson term is the probability of observing Æ events in category when Æ are expected. Including this term allows for the direct fitting of yields rather than fractions. Finally, the total likelihood function is the product over all categories: Ä � The quantity ÐÒ Ä � È ÐÒ Ä is minimized. 7.7.2 Probability Density Functions �� Ä � (7.12) The PDF parameterizations for Ñ�Ë, ¡�, �, and � are described in detail in Sec. 4.6.1. Top plots in Fig. 7-5 shows the Ñ�Ë distributions for signal events for Run 1 and Run 2. We use �Ñ�Ë � �� ¦ � Å�Î� and �Ñ�Ë � ��¦ � Å�Î� for both Run 1 and Run 2. The background Ñ�Ë shape is the usual ARGUS shape but the � parameter is left floating in the fit. Bottom plots in Fig. 7-5 shows the distribution of Ñ�Ë in the region � � �¡�� Î in the side-band region. We find similar shapes in Run 1 and Run 2, so we float common parameters for the entire dataset. Figure 7-6 shows the ¡� distribution for signal events in Run 2 and the combined Run 1 + 2 data. The Run 2 parameters are similar to the Run 1 results so we use a common mean, �¡� � � ¦ �Å�Î, and resolution, �¡� � � � �� Å�Î, for the entire dataset. The mean of Ã�(ÃÃ) events is shifted by approximately �� Å�Î ( � Å�Î) relative to ��, where the shift is momentum dependent due to the boost. The two parameters (three from a second order polynomial minus one of the normalization) of the background ¡� shape are left floating in the fit. Again, we float common parameters for the entire dataset Run 1 and Run 2. MARCELLA BONA �
7.7 The maximum likelihood analysis 179 Events / 0.0022375 GeV/c 2 600 500 400 300 200 100 38.32 / 33 P1 89.69 2.623 P2 1482. 40.70 P3 5.280 0. P4 0.2624E-02 0.6195E-04 0 5.2 5.22 5.24 5.26 5.28 5.3 Energy substituted mass dataset:mes Nent = 11938 400 Mean = 5.24 RMS = 0.02419 350 300 250 200 150 100 50 c = -21.09 ± 1.02 Energy substituted mass (GeV/c 2) 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 Events / 0.0022375 GeV/c 2 250 200 150 100 50 47.27 / 32 P1 21.61 1.292 P2 655.4 26.45 P3 5.280 0. P4 0.2609E-02 0.8669E-04 0 5.2 5.22 5.24 5.26 5.28 5.3 mES pi+ Energy substituted mass dataset:mes Nent = 5963 Mean = 5.24 200 RMS = 0.02426 180 160 140 120 100 80 60 40 20 c = -20.93 ± 1.44 Energy substituted mass (GeV/c 2) 0 5.2 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 Figure 7-5. Top plots: distributions of Ñ�Ë for � � � � decays in Run 1 (left) and Run 2 (right). Bottom plots: distributions of Ñ�Ë for Run 1 (left) and Run 2 (right) on-resonance data in the region � � �¡�� Î. The signal Fisher discriminant distribution is obtained from signal � � Monte Carlo and cross-checked with the � � control sample. After tightening the cut on Ó× �Ë relative to the branching fraction analysis we find that the signal Fisher shape is a pure Gaussian. Top plots in Fig. 7-7 shows the combined Run 1 + 2 sample and the signal Monte Carlo. We use the latter distribution for both Run 1 and Run 2, with the � � sample used to estimate the systematic error. The background Fisher shape is the usual double Gaussian whose parameters are left floating in the fit. Bottom plots in Fig. 7-7 shows the Fisher distribution in the side-band region. For the background common parameters for the entire dataset are floated in the fit. The � ��Ö�Ò�ÓÚ angle pulls for pions and kaons are determined in a high-statistics data sample of � £ � � �, � � Ã� decays, where the same PDFs are used for signal and background. We also use the same parameterization for positive and negative tracks. The pulls are defined as � � �ÜÔ Ó«×�Ø �� , where � �ÜÔ is the expected angle for a pion or kaon with the given momentum (corrected for energy loss) and the offsets and resolutions depend on track polar angle. Left plots in Fig. 7-8 show the offset 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
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 and 182: 7.5 Background characterization 175
Page 183: 7.7 The maximum likelihood analysis
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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