Violation in Mixing

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132 Measurement of Branching Fractions for � ¦ � Ã � ¦ decays In the systematic error on the efficiency, we include a Ó× �Ë cut uncertainty of which is the difference between the expected efficiency of �� given from the flat distribution and the efficiency taken from the signal MC. In the case of the lifetime significance cut, we varied the cut from � to � ¦ : the difference from the final result on the branching ratio is �� . Since this systematic error is strongly correlated with the correction on the Ã Ë reconstruction efficiency, which is function of the Ã Ë flight length, we decide to take into account the largest of the two systematic errors. The error included in the efficiency evaluation is therefore the one coming from the Ã Ë reconstruction correction which is . The corrected efficiency is � �� ¦ �� for Ã Ë � channel and � � ¦ �� for Ã Ë Ã . 5.5 Maximum likelihood analysis We use the unbinned maximum likelihood fit technique described in Sec. 4.6 to determine a total of eight parameters from the data: ¯ Æ Ë ÃË� , the number of � � ÃË � decays; ¯ Æ Ë ÃËÃ , the number of � � ÃËÃ decays; ¯ � Ë Ã Ë � , the observed asymmetry between � � Ã Ë � and � � Ã Ë � decays, Æ ÃË � Æ ÃË � � Æ ÃË � Æ Ã Ë � ; ¯ � Ë Ã Ë Ã , the observed asymmetry between � � Ã Ë Ã and � � Ã Ë Ã decays; ¯ Æ � ÃË� , the number of background ÃË � candidates; ¯ Æ � ÃËÃ , the number of background ÃË Ã candidates; ¯ � � Ã Ë � the observed asymmetry between the number of background Ã Ë � and Ã Ë � candidates; ¯ � � Ã Ë Ã the observed asymmetry between the number of background Ã Ë Ã and Ã Ë Ã candidates. The usual four quantities are used in the fit to distinguish between the various components: to summarize ¯ Ñ�Ë, the beam energy substituted mass of the � candidate: it is parameterized as an ARGUS function with � fixed to � for the background and as a Gaussian, with mean and width fixed to �� Î� and ��Å�Î� , respectively, for the signal; ¯ ¡�, the difference between the � candidate’s energy, using the pion mass for the charged particle, and Ô ×� : it is parameterized as a Gaussian for the signal and as a second order polynomial for the background; MARCELLA BONA
5.5 Maximum likelihood analysis 133 Table 5-3. Summary of functional form of PDFs used in the fit and of the sample used to obtain them. The samples in parentheses were used as a cross-check or to provide alternate parameterization to evaluate systematics. Signal Ñ�Ë Gaussian Ã Ë � MC (� � � � ) Bkg Ñ�Ë ARGUS on-res side-band (off-res, cont MC) Signal ¡� Gaussian Ã Ë � MC with � � � � scale factor Bkg ¡� Quadratic cont MC (off-res, on-res side-band) Signal Fisher Double Gaussian Ã Ë � MC (� � � � ) Bkg Fisher Double Gaussian on-res Ñ�Ë side-band (off-res, cont MC) Kaon � Gaussian � £ control sample Pion � Gaussian � £ control sample ¯ �, the value of the Fisher discriminant for the event: it is parameterized as a double Gaussian for both background and signal; ¯ � � �ÜÔ , the difference between the � ��Ö�Ò�ÓÚ angle of the � ¦ , measured by the �ÁÊ�, and the expected � ��Ö�Ò�ÓÚ angle for a particle of that momentum: it is parameterized as a main Gaussian, whose width and mean depend on the polar angle of the track, with a satellite peak parameterized by a second Gaussian with width and mean fixed. Table 5-3 summarizes the functional form of PDFs and the samples used to obtain them. The likelihood, Ä, for the selected sample is given by the product of the PDFs for each individual candidate and a Poisson factor. The quantity Ä � ÐÓ� Ä is minimized, which is equivalent to maximizing Ä itself, with respect to the eight fit parameters. The PDF for a given event � is the sum of signal and background terms: È� Ñ�Ë�� ¡�� Æ Ë Ã Ë � Æ Æ Ë Ã Ë � Æ Æ Ë Ã Ë Ã Æ Æ Ë Ã Ë Ã Æ � � Ë � ÃË� ÃË� È� � � Ë ÃË� �ÃË� È� � � Ë � ÃËÃ ÃËÃ È� � � Ë ÃËÃ �ÃËÃ È� where Æ � È � Æ� and �ÃË� is the charge asymmetry defined as �ÃË� � ÆÃË� ÆÃË� ÆÃË� ÆÃË� Æ � Ã� Æ � Æ � Ã Ë � � Æ Æ � Ã Ë Ã Æ Æ � Ã Ë Ã Æ � � � �ÃË� ÃË� È� � � � �ÃË� �ÃË� È� � � � � �ÃËÃ ÃËÃ È� � � � �ÃËÃ �ÃËÃ È� (5.1) 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
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 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 135 and 136: 5.4 Background Suppression and PDF
Page 137: 5.4 Background Suppression and PDF
Page 141 and 142: 5.5 Maximum likelihood analysis 135
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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7.7 The maximum likelihood analysis
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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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Violation in Mixing

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