Violation in Mixing

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46 �È Violation in the �� System where Ö � �Ì ��È , one can get: Ê � �� Ã ¦ � § � ¦ � Ö Ó× Ó× Æ Ö � � Ã � ¦ The minimum value of Ê as a function of Ö is obtained when Ö � Ó× Ó× Æ and is given by Ê � Ó× Ó× Æ � ×�Ò Assuming that ×�Ò � we have a constrain in the � � plane: ×�Ò � � � � which can be used to obtain a bound on the CKM angle . 1.5.5 � Decays into Ã Ã Although the decay rate for � � Ã Ã is expected to be small (� � ) in the Standard Model, final state rescattering effects can lead to enhancement of the branching fraction and the possibility of large strong phases, with correspondingly large �È -violating charge asymmetries [35, 36]. Such rescattering effects may also have consequences for constraints on derived from � � Ã� decays [37]. Observation of the Ã Ã decay mode would provide important information about the strength of final state rescattering in charmless � decays. Recent studies [38] have also suggested that it is possible to derive a bound on � « «�« � depending on the Ã Ã branching fraction. This channel is a pure � � � penguin process and in the SU(3) limit, this penguin diagram can be related to the � � penguin. Considering the expression 1.73 for the � � amplitude and defining �È � � �È Ã Ã � from the [38]: one get the bound: � Ê �È � � � � Ô � � � Ó× « «�« Ó× « � � « «�«� ��Ö Ó× Ô � � � Ã Ã � � � where � is related to the time-dependent asymmetry and it is defined in Eqs. 7.2. This bound holds under in the assumptions of SU(3) flavour symmetry of the strong interactions and neglecting the electroweak penguin contributions. MARCELLA BONA � ��
2 The BABAR Experiment 2.1 Physics at � � B Factory operating at the § �Ë resonance 2.1.1 �È asymmetry experimental measure The primary goal of the BABAR experiment is the study of �È -violating asymmetries in the decay of neutral � meson. Secondary goals are precision measurement of decays of bottom and charm mesons and of � leptons, searches for rare processes accessible because of the high luminosity of PEP II B factory. Through equation (1.44), in the previous chapter, a �È asymmetry measurement can be related to a measurement of ¡Ø, the time interval between the � decays: ¡Ø � Ø�È ØØ��. In case the � momenta are known, ¡Ø can be measured by the decay point distance ¡Þ. In a symmetric � � collider operating at the § �Ë resonance, the two � mesons are created almost at rest and the decay point distance can be calculated taking the small phase space left once � masses have been subtracted from the § �Ë mass � § �Ë � �� Î � �� § �Ë �� Î� From the total energy of each �, the kinetic energy is getting: Õ �� Ñ � � Ô � Ñ�¬ � � � ��Î ¬ � � �� ¬ where it has been considered that is almost since the system is non-relativistic. The � decay length is then
Page 1 and 2: ÍÒ�Ú�Ö×�Ø��
Page 3 and 4: Contents Introduction . ...........
Page 5 and 6: 4 Strategy and Tools for Charmless
Page 7 and 8: 7.2 Branching fraction � � �
Page 9 and 10: Introduction The main goal of the B
Page 11 and 12: 1 �È Violation in the �� Sys
Page 13 and 14: 1.2 Neutral � Mesons 7 Note, howe
Page 15 and 16: 1.2 Neutral � Mesons 9 Applying t
Page 17 and 18: 1.2 Neutral � Mesons 11 �È �
Page 19 and 20: 1.2 Neutral � Mesons 13 ��
Page 21 and 22: 1.2 Neutral � Mesons 15 � ¡�
Page 23 and 24: 1.2 Neutral � Mesons 17 and � a
Page 25 and 26: 1.2 Neutral � Mesons 19 given tim
Page 27 and 28: 1.3 The Three Types of �È Violat
Page 33 and 34: 1.4 �È Violation in the Standard
Page 43 and 44: 1.5 Determination of « 37 1.5 Dete
Page 45 and 46: 1.5 Determination of « 39 Assuming
Page 47 and 48: 1.5 Determination of « 41 Figure 1
Page 49 and 50: 1.5 Determination of « 43 b q (a)
Page 51: 1.5 Determination of « 45 � �
Page 55 and 56: 2.1 Physics at � � B Factory op
Page 57 and 58: 2.2 The BABAR detector. 51 Integrat
Page 59 and 60: 2.2 The BABAR detector. 53 The dete
Page 61 and 62: 2.2 The BABAR detector. 55 two oute
Page 63 and 64: 2.2 The BABAR detector. 57 SVT Effi
Page 65 and 66: 2.2 The BABAR detector. 59 324 1015
Page 67 and 68: Efficiency 2.2 The BABAR detector.
Page 69 and 70: 2.2 The BABAR detector. 63 2.2.4 Th
Page 71 and 72: entries per mrad 2.2 The BABAR dete
Page 73 and 74: 2.2 The BABAR detector. 67 entries
Page 75 and 76: 2.2 The BABAR detector. 69 energies
Page 77 and 78: 2.2 The BABAR detector. 71 The main
Page 79 and 80: Efficiency 2.2 The BABAR detector.
Page 81 and 82: 2.2 The BABAR detector. 75 Table 2-
Page 83 and 84: 3 Ã Ë reconstruction and efficien
Page 85 and 86: 3.3 Studies on data 79 19.5° BINS
Page 87 and 88: 3.3 Studies on data 81 ¯ off-reson
Page 89 and 90: 3.3 Studies on data 83 0.504 0.502
Page 91 and 92: 3.3 Studies on data 85 0.03 0.025 0
Page 95 and 96: 3.3 Studies on data 89 N(π + π -
Page 99 and 100: 3.3 Studies on data 93 Figure 3-13.
Page 103 and 104:
4 Strategy and Tools for Charmless
Page 105 and 106:
4.2 Event selection 99 channel sele
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4.2 Event selection 101 ÀÐ �
Page 109 and 110:
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
Page 117 and 118:
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
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5.4 Background Suppression and PDF
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5.5 Maximum likelihood analysis 133
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Page 149 and 150:
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5.6 Counting analysis 145 Table 5-1
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5.7 Determination of branching frac
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6 Measurement of Branching Fraction
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6.3 The maximum likelihood analysis
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Page 161 and 162:
Page 163 and 164:
6.4 Counting analysis 157 120 100 8
Page 165 and 166:
6.5 Analysis choice 159 6.5 Analysi
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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
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7.4 Data samples and event selectio
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7.4 Data samples and event selectio
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7.5 Background characterization 173
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7.5 Background characterization 175
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Page 185 and 186:
Page 187 and 188:
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7.8 Validation studies 185 Figure 7
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7.8 Validation studies 187 100 75 5
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7.8 Validation studies 189 Figure 7
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7.8 Validation studies 191 Paramete
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7.9 Results 193 Parameter Fit Resul
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7.9 Results 195 Events/2 MeV/c 2 Ev
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7.10 Systematic studies 197 Categor
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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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