Violation in Mixing

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162 Measurement of Branching Fractions for � � Ã Ë Ã Ë Decays Other sources of systematics in the branching fraction measurement come from the efficiency, ( ��¦�� ) contributing with a systematic effect, and the number of � decays ( �� ¦ �� ×Ø�Ø� ¦ � �� ×Ý×� ) adding a �� systematic error. 6.6.2 Cross-check: the counting analysis We also performed the counting analysis as a further cross check. A cut on the Fisher discriminant � is used to suppress ÕÕ background. The optimal set of cuts has been chosen with the 2-dimensional optimization described in Section 6.4: from table 6-5 we choose to use the first set of cuts which is giving one of the best upper limits and the � Ó× �Ë� cut at the value of �� is consistent with the one used in the maximum likelihood method analysis. The overall efficiency, including these cuts, is ��¦ � , while the efficiency corrected with all the contributions described in Section 6.2.1 comes out to be �� ¦ � . We estimate a number Æ� of background events of �� ¦ �� in the signal box with �¡�� Î :on Run1 dataset we find events in the signal box. Using the Feldman-Cousins tables [64], we find the upper limit on the yield to be � events. Systematics include the errors on the efficiency (evaluated in Section 6.2.1) and on Æ �� : the Fisher cut variation systematic has to be added in this case. We moved the Fisher cut from � down to �� and up to � and recorded the branching ratio upper limit variations. We get � systematic error from this Fisher cut variation. Taking into account the relative efficiency and the errors, this result from the cut analysis is in good agreement with the nominal results (see Section 6.7). 6.7 Determination of the branching fraction We have found good agreement between the counting analysis and the global likelihood fit signal yields. The branching fraction � is defined as �Ê � � Ã Ã � �Ê Ã Ã � ÃË Ã Ë ¡ �Ê Ã Ë � � � ÆË � (6.1) ¯ ¡ Æ�� where ÆË is the central value from the fit, ¯ is the total Ã Ë Ã Ë selection efficiency, Æ �� ¦ � � ¢ � is the total number of �� pairs in the dataset and �Ê ÃË � � � � �� [14]. We assume the Standard Model prediction that � � Ã Ë Ã Ë proceeds through the Ã Ã intermediate state (as opposed to Ã Ã or Ã Ã ) and use �Ê Ã Ã � Ã Ë Ã Ë � ��. 1 Implicit in Eq. 6.1 is the assumption of equal branching fractions for § �Ë � � � and § �Ë � � � . 1 Since �È violation affects in the neutral Ã system have been measured to be so small (¯ � � ) that they can be neglected, assuming conservation of angular momentum and �ÈÌ invariance, the decay � � Ã Ã � Ã ËÃ Ä is forbidden. MARCELLA BONA
6.7 Determination of the branching fraction 163 Since no significant signal is found in this mode we calculate the � confidence level upper limit yield and the result is increased by the total systematic error. We measure (with systematic uncertainties explained above) � � � Ã Ã �� The resulting upper limit at � confidence level is � � � Ã Ã � �� ¡ �� stat ¦ �� syst ℄ ¡ This result is a significant improvement over the existing upper limit from the CLEO Collaboration [66], and is approaching the upper range of current theoretical estimates. In the counting analysis case, as a cross check, we get � � � Ã Ã �� ¦ �� stat ¦ �� syst ℄ ¡ � . The resulting upper limit at � confidence level is � � � Ã Ã � �� ¡ � . Both these results are compatible with the results from the likelihood fit. � MEASUREMENT OF BRANCHING FRACTIONS FOR � � Ã Ë Ã Ë DECAYS �
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ÍÒ�Ú�Ö×�Ø��
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Contents Introduction . ...........
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4 Strategy and Tools for Charmless
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7.2 Branching fraction � � �
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Introduction The main goal of the B
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1 �È Violation in the �� Sys
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1.2 Neutral � Mesons 7 Note, howe
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1.2 Neutral � Mesons 9 Applying t
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1.2 Neutral � Mesons 11 �È �
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1.2 Neutral � Mesons 13 ��
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1.2 Neutral � Mesons 15 � ¡�
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1.2 Neutral � Mesons 17 and � a
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1.2 Neutral � Mesons 19 given tim
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1.3 The Three Types of �È Violat
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1.4 �È Violation in the Standard
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1.5 Determination of « 37 1.5 Dete
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1.5 Determination of « 39 Assuming
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1.5 Determination of « 41 Figure 1
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1.5 Determination of « 43 b q (a)
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1.5 Determination of « 45 � �
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2 The BABAR Experiment 2.1 Physics
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2.1 Physics at � � B Factory op
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2.2 The BABAR detector. 51 Integrat
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2.2 The BABAR detector. 53 The dete
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2.2 The BABAR detector. 55 two oute
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2.2 The BABAR detector. 57 SVT Effi
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2.2 The BABAR detector. 59 324 1015
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Efficiency 2.2 The BABAR detector.
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2.2 The BABAR detector. 63 2.2.4 Th
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entries per mrad 2.2 The BABAR dete
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2.2 The BABAR detector. 67 entries
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2.2 The BABAR detector. 69 energies
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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
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 139 and 140: 5.5 Maximum likelihood analysis 133
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 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: 6.6 Results on the Run1 data-set 16
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 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.
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Violation in Mixing

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