Violation in Mixing

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134 Measurement of Branching Fractions for � ¦ � Ã � ¦ decays Table 5-4. Linear correlation coefficients between variables used in the Ã Ë � maximum likelihood fit. Results are obtained from Ã Ë � Monte Carlo. Variables correlation Ñ�Ë, ¡� � �� Ñ�Ë, � � Ñ�Ë, � � � ¡�, � � ¡�, � � � �, � � The PDF for each component, in turn, is the product of the PDFs for each of the fit input variables: Including the Poisson factor, the likelihood is: È � � È � Ñ�Ë È� ¡� È� � È� � Ä � � Æ Æ Æ Æ� �� (5.2) È� � (5.3) Note that the factor Æ Æ in the above equation cancels an identical factor in the denominator that arises from equation 5.1. 5.5.1 Correlations between PDFs The PDFs described in the previous section are assumed to be uncorrelated in the maximum likelihood fit. To check this assumption we have calculated the linear correlation coefficient �� between the PDFs for variables � and �. The definition of �� is in Sec. 4.6.6. Table 5-4 summarizes the correlation coefficients obtained from signal Ã Ë � Monte Carlo. 5.5.2 Event yields and asymmetries The fit, performed on the 3623 candidates in the full Run 1 data-set, returns: MARCELLA BONA Æ Ë Ã Ë � Æ Ë Ã Ë Ã � � Ë Ã Ë � � �� ×Ø�Ø ×Ø�Ø � � � � ×Ø�Ø
5.5 Maximum likelihood analysis 135 � Ë Ã Ë Ã Æ � Ã Ë � Æ � Ã Ë Ã � � Ã Ë � � � Ã Ë Ã � ¬Ü�� ×Ø�Ø � �� ×Ø�Ø � � ¦ � � ×Ø�Ø � � ¦ � � ×Ø�Ø where Ã Ë � signal has a significance of �� standard deviations, determined by fixing that component to zero and recording the change in Ä � ÐÓ� Ä: the significance is � � Ô Ä Ä¬Ø [14]. The asymmetry � Ë Ã Ë � has a significance of � standard deviations. Table 5-5. Correlation Matrix between the fitted variables Æ Ë Ã Ë � Ë Æ ÃËÃ �Ë Ã Ë � � Æ ÃË� � Æ ÃËÃ �� Ã Ë � �� Ã Ë Ã Æ Ë Ã Ë � 1.000 -0.003 -0.106 -0.092 -0.005 0.002 0.000 Æ Ë Ã Ë Ã -0.003 1.000 0.001 0.000 -0.005 0.000 0.000 � Ë Ã Ë � -0.106 0.001 1.000 0.022 0.001 -0.092 -0.005 Æ � Ã Ë � -0.092 0.000 0.022 1.000 -0.106 -0.001 0.001 Æ � Ã Ë Ã -0.005 -0.005 0.001 -0.106 1.000 0.001 -0.001 � � Ã Ë � 0.002 0.000 -0.092 -0.001 0.001 1.000 -0.106 � � Ã Ë Ã 0.000 0.000 -0.005 0.001 -0.001 -0.106 1.000 The systematic correlation matrix of the fit parameters is shown in Table 5-5. In order to test the goodness of fit, we ran 1000 toy Monte Carlo pseudo-experiments taking the result of the fit as the mean number of signal and background events produced: we plot ÐÓ� Ä from the fit of each pseudo-experiment in Fig. 5-13. The arrow indicates the value obtained from the fit to the Run1 data-set: from this, we estimate the probability to find a greater value for ÐÓ� Ä to be � . This value can be considered a measurement of the goodness of fit. 5.5.3 Cross-check and systematics Letting also ÆË and �Ë free in the fit, we obtains: ÃËÃ ÃËÃ Æ Ë Ã Ë � Æ Ë Ã Ë Ã � � �� ×Ø�Ø ×Ø�Ø MEASUREMENT OF BRANCHING FRACTIONS FOR � ¦ � Ã � ¦ 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
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 95 and 96: 3.3 Studies on data 89 N(π + π -
Page 99 and 100: 3.3 Studies on data 93 Figure 3-13.
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 139: 5.5 Maximum likelihood analysis 133
Page 143 and 144: 5.5 Maximum likelihood analysis 137
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 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
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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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