Violation in Mixing

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150 Measurement of Branching Fractions for � � Ã Ë Ã Ë Decays Table 6-1. Summary of Ã Ë Ã Ë selection efficiency. Cut Efficiency reco + tag bit + Ê + Sphericity �� ¦ � � � Ó× �Ë� � �� ¦ � � ØÃË��Ø � � � �� ¦ � ¬ ¬ Å � � Å Ã ¬ Ë � � Å�Î� � �� ¦ � resonance Ñ�Ë side-band in the second case, we estimate the best upper limit we can obtain from each of them in order to establish the best method to use. Before being able to test these techniques, we performed the validation of the variables used in both the global likelihood fit and the counting analysis. 6.2.1 Efficiency Table 6-1 summarizes the efficiency of the Ã Ë Ã Ë selection which corresponds to the usual two-body one (see Sec. 4.2.1). Taking into account a minimal � Ó× �Ë� cut at the value of �� and no Fisher cut, the total efficiency is �� ¦ � . All efficiency estimates are derived in Monte Carlo except for the Ã Ë mass cut efficiency, which was estimated from the � � Ã Ë � control sample to be �� ¦ . Corrections to the efficiency value, accounting for the two Ã Ë reconstruction, are then included (see Sec. 3.3.4). These corrections amount to � �¦ � ×Ø�Ø� ¦ � ×Ý×Ø� for the two Ã Ë. Other systematic effects come from the � Ó× �Ë � cut ( ) and the Ã Ë mass cut ( per Ã Ë candidate). This contribution was estimated from the difference between the MC efficiency and that of the � � � Ã Ë control sample. Another contribution to efficiency systematics is a �� coming from the charged tracks reconstruction uncertainty in Ã Ë reconstruction. The final number for efficiency is �� ¦ �� 6.3 The maximum likelihood analysis We use the same unbinned maximum likelihood fit technique developed to determine from the data: ¯ Æ Ë , the number of � � Ã ÃËÃ ËÃË decays; Ë ¯ Æ � , the number of background Ã ÃËÃ ËÃË candidates; Ë MARCELLA BONA
6.3 The maximum likelihood analysis 151 Events / 1 MeV 1000 800 600 400 200 ID 72182 ALLCHAN 5588. Constant 63.07 / 26 898.8 15.12 Mean 5.280 0.5393E-04 Sigma 0.2460E-02 0.3380E-04 0 5.2 5.22 5.24 5.26 5.28 5.3 m ES (GeV/c 2 ) Figure 6-1. Ñ�Ë distribution in the signal Ã Ë Ã Ë Monte Carlo sample. The likelihood, Ä, for the selected sample is given by the product of the probability density functions (PDFs) for each individual candidate and a Poisson factor. We use Ñ�Ë, ¡� and � to separate signal and background. To be used in the fit, a candidate must pass the preliminary selection, the cut on the ÃËinvariant mass and the cut on ØÃË��Ø (see Sec. 5.2). ÃË 6.3.1 Definition of PDFs The beam energy substituted mass of the � candidate, Ñ�Ë, is parameterized as a Gaussian, with mean and width fixed to �� Î� and ��Å�Î� , respectively, for the signal (Fig. 6-1) and as an ARGUS function for the background. The value of the mean and the width of the signal Ñ�Ë distribution come from the � � � � control sample. The value of the � parameter of the ARGUS function is determined to be �� ¦ �� from a fit to onresonance ¡� side-band data (Fig. 6-2). A similar fit performed on off-resonance grand side-band region gives � � ��¦ � , and we find � � ��¦ �� in continuum Monte Carlo events (Fig. 6-3). All the values obtained from these samples are well compatible with each other and with the on-resonance fit. We use the value � � �� ¦�� in the rest of the likelihood analysis. MEASUREMENT OF BRANCHING FRACTIONS FOR � � Ã Ë Ã Ë 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
Page 105 and 106: 4.2 Event selection 99 channel sele
Page 107 and 108: 4.2 Event selection 101 ÀÐ �
Page 109 and 110: 4.2 Event selection 103 Figure 4-2.
Page 111 and 112: 4.3 Background fighting 105 Figure
Page 113 and 114: 4.4 PID selection 107 In the case o
Page 115 and 116: 4.4 PID selection 109 θ c Cut Effi
Page 117 and 118: 4.5 Tracking Corrections 111 Ë�
Page 119 and 120: 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: 6 Measurement of Branching Fraction
Page 159 and 160: 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 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��
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7.11 Summary 201 �Ã� Ë��
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7.11 Summary 203 Variation �Ã�
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BIBLIOGRAFIA 205 Bibliografia Chapt
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BIBLIOGRAFIA 207 [38] J. Charles, P
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BIBLIOGRAFIA 209 Chapter 7 [67] D.
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