Violation in Mixing

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40 �È Violation in the �� System Table 1-2. Isospin decomposition for � � ��,� � �Ã in terms of the isospin amplitudes � ¡Á�Á�, where ¡Á and Á� are the isospin change of the transition and the final-state isospin, respectively. Channel Decay Amplitudes Ô �� Ô �� Ô � � � Õ Õ � � � � � � � � � � Ô � � � �� Õ �Ã � � � � Ã � � � � � � � � � � Õ �� Ã � � � � � � � � � � Õ Ô �� Ã � � � � � � � � � � Õ Ô �� Ã � � � � � � � � � � 1.5.3 Hadronic charmless two-body � decays Hadronic decays resulting from � � Ù transitions are highly suppressed due to the factor �ÎÙ�� . Decays such as � � �� and � � Ã� can proceed either through a � � Ù spectator diagram or through a gluonic penguin. In a gluonic penguin, a � � � or � � × transition occurs through a virtual loop containing a Ï and either a Ø, or Ù quark with the radiation of a gluon. The dominant contribution is expected to arise from the Ø-quark intermediate state, but effects from the -quark are not necessarily negligible [32, 34]. A simple argument gives a rough idea of the possible relative contribution of the tree and penguin amplitudes in � � �� and � � Ã�. Assuming that Ø-quark dominates the loop, the penguin contribution to � � � � is suppressed relative to that for � � Ã � by �ÎØ��ÎØ×� � Ç � in the rate. Furthermore the tree contribution to � � Ã � is suppressed relative to that � � � � by a factor �ÎÙ×�ÎÙ�� in the rate. By itself, all this tells us is that the tree diagram contributes more to �� than to Ã� and the penguin contributes more to Ã� than to ��. Suppose that � � � � � �� Ã � , then � � Ã � must be mainly penguin or else the � � �Ã � ratio would be larger. Even if all of the � � Ã � rate were penguin, the assumed near equality of the branching fractions implies that the penguin contribution to � � � � must be fairly small. The tree process should contribute more to � � � � than to � � Ã � while the penguin process (with intermediate Ø or quarks) should contribute more to � � Ã � than to � � � � . Both the tree and penguin contributions to � � � � are Ç � . In a scenario where � � � � � � � � � Ã � , we would conclude that � � Ã � was predominantly penguin and that � � � � was predominantly a tree process. That is, the upper-left and lower-right diagrams must dominate. For, if the � � Ã � were mainly a tree process (upper-right diagram, Ç � � ), then the � � � � tree contribution (upper-left, Ç � ) would be even larger and we would observed � � � � � � � � � MARCELLA BONA
1.5 Determination of « 41 Figure 1-7. Diagrams for � � � � and � � Ã � : both modes have contributions from tree � � Ù and penguin processes. The figure shows also the dependence of each amplitude on � � ×�Ò � �. Ã � . Similarly, if � � � � were mainly penguin (lower-left,Ç � ), then � � Ã � penguin contribution (lower-right, Ç � ) would be even larger. 1.5.3.1 � � � � From previous section, one can assume that penguins can be present in � � � � channel. Since the weak phase of the penguin diagram is different from that of the tree diagram, penguin pollution can affect the clean extraction of « from this process. As already said, the isospin analysis can be used to eliminate the penguin pollution in this case [25]. Knowing the isospin decomposition of the amplitude from Table 1-2, we can define the single isospin components: � � � � � � � , � � � � � � � and � � � � � � � . Because of Bose statistics the Â � two-pion state produced in � decay has no �È VIOLATION IN THE �� SYSTEM
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: 1.5 Determination of « 39 Assuming
Page 49 and 50: 1.5 Determination of « 43 b q (a)
Page 51 and 52: 1.5 Determination of « 45 � �
Page 53 and 54: 2 The BABAR Experiment 2.1 Physics
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 93 and 94: 3.3 Studies on data 87 0.504 0.502
Page 95 and 96: 3.3 Studies on data 89 N(π + π -
Page 97 and 98:
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
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5.4 Background Suppression and PDF
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5.5 Maximum likelihood analysis 133
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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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6.4 Counting analysis 157 120 100 8
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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
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7 Analysis of the time-dependent
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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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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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