Violation in Mixing

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22 �È Violation in the �� System ¯ �È violation in the interference between mixing and decay: it occurs in decays into final states that are common to � and � . It often occurs in combination with the other two types but there are cases when, to a very good approximation, it is the only effect. 1.3.1 �È Violation in Decay In order to study this type of �È violation, for any final state �, the quantity � � � � is defined since it is �� independent of phase conventions and physically meaningful. There are two types of phases that may appear in the amplitudes: complex parameters in any Lagrangian term that contributes to the amplitude will appear in complex conjugate form in the �È conjugate amplitude. Therefore these phases appear in �� and � with opposite signs. In the Standard Model these phases appear in the �ÃÅ matrix and are � called weak phases. The weak phase of any single term is dependent on the convention, but the difference between the weak phases in two different terms in the amplitudes is convention independent. A second type of phase can appear even when the Lagrangian is real: such phases come from the possible contribution from intermediate on-shell states dominated by strong interactions and so they are called strong phases. Since strong interactions conserve �È these phases appear in �� and �� with the same sign. Again only the relative strong phases of different terms have physical meaning. Contributions to the amplitudes can be factorized as: - the magnitude ��; - the weak phase term � �� ; - the strong phase term � �Æ� . If several amplitudes contribute to � � �, the amplitude �� (see Eq. 1.20) and the �È conjugate amplitude � � are given by: �� Æ� �� Æ� �� (1.35) � where �� and �� are defined in expressions like 1.17: �È �� and �È � � � � � �� (one should consider the complex conjugate of the latter expression � � � �È � � �� ). If � is a �È eigenstate then � �� ¦ being its �È eigenvalue. The convention-independent quantity is then ¬ �� ¬ � ¬ � � �� ¬ ¬ È � �� Æ� �� È � �� Æ� �� ¬ � ¬ � (1.36) �È is conserved in decays when the magnitude of this ratio is , that means the rate of the decay must be equal to the rate of the �È conjugate decay. This can happen only if all weak phases �� are the same phase or if all the strong phases Æ� are the same one. Therefore, from Eq. 1.36 one sees that MARCELLA BONA
1.3 The Three Types of �È Violation in � Decays 23 ¬ �� ¬ � �� ¬ ¬ ¬� � �� ¬ � � Instead �È is violated in decays if both the weak phases �� and the strong ones Æ� are different one from the others. In this case the ratio cannot be reduce to a pure phase: ¬ �� ¬ �� ÈÚ�ÓÐ�Ø�ÓÒ� (1.37) �� ¬ This type of �È violation is here called �È violation in decay. It is often also called direct �È violation. It results from the �È -violating interference among various terms in the decay amplitude. From Eq. 1.36 it can be shown that, in this case, �È violation requires at least two terms that have different weak phases and different strong phases: �� ×�Ò �� ×�Ò Æ� Æ� � Any �È asymmetries in charged � decays are from �È violation in decay. One can redefine: �� from which, in terms of the decay amplitudes, one has: �� The latter expression can be useful for neutral � mesons also: as a matter of fact �È violation in decays can also occur for neutral meson decays, where it competes with the other two types of �È violation effects described below. Since the amplitudes differ from their �È conjugate ones at most for a phase factor, in case only one amplitude contributes to a given decay process, no direct �È violation effect can be observed. 1.3.2 �È Violation in Mixing A quantity which is useful in the study of this type of �È violation is: ¬ ¬ ¬ � ¬ ¬ Õ¬ Ô¬ � ¬ Å £ � £ � Å ¬ � (1.38) �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: 1.3 The Three Types of �È Violat
Page 31 and 32: 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 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
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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
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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
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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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