Violation in Mixing

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20 �È Violation in the �� System The time dependent rate for producing the combined final states � �� (applying trigonometric rules like Werner’s and duplication ones) is then: Ê Ø �Ø �� Ó× ¡Ñ� Ø Ø Ø Ø ×�Ò ¡Ñ� Ø Ø �� Õ ÁÑ Ô �£ � �� Õ �Ê� Ô �£ � � Õ �ÁÑ Ô �£ � � �� Õ Ê� Ô �£ � � � Õ ÁÑ � ÁÑ Ô �£ � � Õ Ô �£ � where an integral over all directions for both �s has been performed, so the angular dependence has been removed from the expressions, and an overall normalization factor � has been introduced. The approximation �Õ�Ô� � has also been used. In order to measure �È asymmetries, one can look for events where one � decays to a final �È eigenstate ��È at time Ø�, while the second decays to a tagging mode, that is a mode which identifies its �-flavor, at time ØØ��. For example, one can consider a tagging mode with � � , � ��Ø��. This identifies the other �-particle as a � at time Ø � ØØ�� at which the tagging decay occurs. This is true even when the tag decay occurs after the �È eigenstate decay: in this case the state of the other � at any time Ø� �ØØ�� must be just that mixture that, if it had not decayed, would have evolved to become a � at time Ø� � ØØ��. The double time expression reduces to the form: where defining Ê Ø��È �ØØ�� ØØ�� Ø� �È Ó× �¡Ñ� Ø��È ØØ�� ℄ ×�Ò �¡Ñ� Ø��È ØØ�� ℄ ��È Ò� ��È � ��È � Õ � Ô and substituting it in the expression 1.30, one obtains: MARCELLA BONA � ��È � ��È� � � Õ ÁÑ Ô�£ �È ��È ��È ��È � ��Ø�� Ø�� Ø�� Ê Ø��È �ØØ�� ØØ�� Ø� ¨ �È ��Ø�� È � ��È� Ó× �¡Ñ� Ø��È ØØ�� ¡ ℄ ��È� ×�Ò �¡Ñ� Ø��È ØØ�� ℄ ÁÑ ��È � � � �Ó � �� (1.30) (1.31) (1.32)
1.3 The Three Types of �È Violation in � Decays 21 In case the tag final state has � � , � ��Ø��, which identifies the second particle as a � at time ØØ��, an expression similar to Eq. 1.32 applies, except that the signs of both the cosine and the sine terms are reversed. The fact that �Õ�Ô� � means that the amplitudes for the two opposite tags are the same. Thus the difference of these rates divided by their sum, which measures the time-dependent �È asymmetry, is given by ��È � Ê � � �� Ø�� Ê � � �Ø�� Ê � � �� Ø�� Ê � ��Ø�� È� ¡ Ó× ¡Ñ�Ø ÁÑ��È ��È� ×�Ò ¡Ñ�Ø (1.33) where Ø � Ø��È ØØ��. The above expressions has lost its dependence from the variable Ø Ø or Ø�È ØØ��: this means that now one can fit the dependence on the variable Ø Ø without having to measure the § decay time. This can be done also from equation 1.32 that can be integrated over the variable Ø Ø , substituting the variables Ì � Ø Ø and Ø � Ø Ø and integrating over Ì which for Ø � and Ø � can take values between �Ø� and infinity. This way, one gets an expression of Ê Ø which is only a function of the time difference Ø�È ØØ�� and not of the § decay time: ¡ ¨ ��È � Ê Ø��È ØØ�� ØØ�� Ø��È � ¡ (1.34) © � ��È � ¡ Ó× �¡Ñ� Ø��È ØØ�� ℄ ×�Ò �¡Ñ� Ø��È ØØ�� ℄ ÁÑ ��È The fact that the variable Ø Ø can be related to the distance between the decay vertices of the two �’s is the main reason for building an energy-asymmetric collider for this kind of measurements (see Sec. 2.1). By integrating also over this variable, all information on the coefficient of ×�Ò ¡Ñ� Ø Ø would be lost and the experiment would be sensitive only to those �È -violating effects that give �� . This is a consequence of the coherent production of the two � states: in a hadronic environment, where the �’s are produced incoherently, time-integrated rates are always integrals from Ø � to infinity so that they retain information about the ×�Ò ¡Ñ�Ø term. 1.3 The Three Types of �È Violation in � Decays �È violation can manifest itself in three different ways: ¯ �È violation in decay: also called direct �È violation, it occurs when a decay and its �È conjugate process have different amplitudes. It can be studied in both charged and neutral decays. ¯ �È violation in mixing: also called indirect �È violation, it occurs when mixing provides interfering amplitudes. In this case, the two neutral mass eigenstates cannot be �È eigenstates too. �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: 1.2 Neutral � Mesons 19 given tim
Page 29 and 30: 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
Page 79 and 80:
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
Page 87 and 88:
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
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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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Page 137 and 138:
Page 139 and 140:
5.5 Maximum likelihood analysis 133
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Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
5.6 Counting analysis 145 Table 5-1
Page 153 and 154:
5.7 Determination of branching frac
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6 Measurement of Branching Fraction
Page 157 and 158:
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
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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
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7.4 Data samples and event selectio
Page 179 and 180:
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:
Page 189 and 190:
Page 191 and 192:
7.8 Validation studies 185 Figure 7
Page 193 and 194:
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��
Page 207 and 208:
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
Page 215 and 216:
BIBLIOGRAFIA 209 Chapter 7 [67] D.
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