Violation in Mixing

More documents

Recommendations

Info

36 �È Violation in the �� System Semileptonic exclusive and inclusive � decays give: � � � �Î �� ¦ � � �ÎÙ�� ¦ � �� (1.55) For both �Î �� e �Î ×� another technique can be used: assuming the unitarity of the �ÃÅ matrix, as required in the Standard Model, the unitarity of the third row and the third column implies (substituting the values in Eq. 1.55): Õ Õ Õ �ÎØ�� ÎØ�� ÎØ×� � �ÎÙ�� Î �� and therefore �ÎØ�� and �ÎØ×� must be both less than about � � that implies: �ÎÙ�� Î �� ÎØ�� ÎÙ×� �Î ×� � �ÎØ×� � � (1.56) In other words, assuming the unitarity, the known very small values of �Î �� and �ÎÙ�� imply that �Î �� e �Î ×� are essentially determined from �ÎÙ��, �ÎÙ×� and equations 1.56. Information on �ÎØ�� and �ÎØ×� can be extracted from � � and � × � × mixing and from � � �× processes: from the � � mixing rate one extracts these values: ¡Ñ�� ¦ � � Ô× Ü� � ¡Ñ�� where ¡Ñ�� Å � (see Eq. 1.6 and Sec. 1.2.5), and thus the condition: �Î £ Ø� ÎØ�� ¦ � � which shows that �ÎØ�� is of the same order as �ÎÙ��. �� ¦ � � Using unitarity constraints, one can narrow some of the above ranges and put constraints on the top mixing �ÎØ��. The full information on the absolute values of the �ÃÅ elements (as given by [14]) from both direct measurements and three generation unitarity is summarized by �Î � � �� The only large uncertainties are in �ÎÙ�� and �ÎØ��: however, the two are related through Eq. 1.50. The measured ranges for the Î��’s give the following 90% CL range for the �È -violating measure �Â�: MARCELLA BONA �Â� � � ¦ � ¢ � ×�Ò Æ� (1.57)
1.5 Determination of « 37 1.5 Determination of « The angle « can be extracted from decays � � �ÙÙ, for example decays with two pions in the final state. The measurement of « is expected to be complicated if the penguin contribution is not negligible. 1.5.1 �È Violation using � decays into non �È eigenstates and Extraction of « ignoring penguins The angle « can be obtained by the measurements of �È -violating asymmetries in decays to final states that can be either �È eigenstates or not. In case of a �È eigenstate, Sec. 1.3 shows the relation between the asymmetry and the CKM elements. If a single weak amplitude contributes to the decay taken into account and if the penguins are negligible, then ��È ��È � � and so: ��È � ÁÑ��È ×�Ò ¡Ñ�Ø � (1.58) Then, ÁÑ� is cleanly related to one of the angle of the unitary triangle. In the particular case of � � ��, ÁÑ�� ×�Ò «. In case the final state is not a �È eigenstate, four separate amplitudes can be defined [30]: � � � � � �� (1.59) Using the expressions in 1.24 and 1.25 for the physical states � Ô�Ý× Ø and � Ô�Ý× Ø together with the expressions of the coefficients � Ø and � Ø , one can evaluate the amplitudes: � ��À��Ô�Ý× Ø � � � Ø� �ÅØ ¡Ñ�Ø ¡Ñ�Ø ��Å Ó× ��À�� ×�Ò � ��À�� À��Ô�Ý× Ø � � � Ø� �ÅØ ¡Ñ�Ø ¡Ñ�Ø ��Å Ó× ��À�� ×�Ò � ��À�� where �Å is the phase of � -� mixing coming from Õ�Ô � � ��Å � ��È � . From these time-dependent amplitude and substituting Eq. 1.59 one can obtain the rates for � Ô�Ý× Ø and � Ô�Ý× Ø decaying into �: where � � �Ô�Ý× Ø � � � � Ø Ò � ¢ Ó Ê Ó× ¡Ñ�Ø � ×�Ò �Å �� ×�Ò ¡Ñ�Ø �Ô�Ý× Ø � � � � Ø � ¢ Ò Ó Ê Ó× ¡Ñ�Ø �×�Ò �Å �� ×�Ò ¡Ñ�Ø � �� Ê � �� (1.60) � (1.61) �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 41: 1.4 �È Violation in the Standard
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.
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
Page 99 and 100:
3.3 Studies on data 93 Figure 3-13.
Page 101 and 102:
3.3 Studies on data 95 0.508 0.506
Page 103 and 104:
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 135 and 136:
Page 137 and 138:
Page 139 and 140:
5.5 Maximum likelihood analysis 133
Page 141 and 142:
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
Page 155 and 156:
6 Measurement of Branching Fraction
Page 157 and 158:
6.3 The maximum likelihood analysis
Page 159 and 160:
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
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 183 and 184:
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
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��
Page 207 and 208:
7.11 Summary 201 �Ã� Ë��
Page 209 and 210:
7.11 Summary 203 Variation �Ã�
Page 211 and 212:
BIBLIOGRAFIA 205 Bibliografia Chapt
Page 213 and 214:
BIBLIOGRAFIA 207 [38] J. Charles, P
Page 215 and 216:
BIBLIOGRAFIA 209 Chapter 7 [67] D.
show all

Violation in Mixing

Create successful ePaper yourself

Delete template?

Save as template?