Violation in Mixing

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182 Analysis of the time-dependent �È -violating asymmetry in � � � � decays 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1 -0.5 0 0.5 1 Offset (mrad) vs K cosθ 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1 -0.5 0 0.5 1 Offset (mrad) vs π cosθ BaBar Data (2001) 4.5 4 3.5 3 2.5 2 1.5 -1 -0.5 0 0.5 1 Sigma (mrad) vs K cosθ 4.5 4 3.5 3 2.5 2 1.5 -1 -0.5 0 0.5 1 Sigma (mrad) vs π cosθ 250 200 150 100 50 θ-θ exp K (1.75,1.875) BaBar (2001) 0 -0.05 -0.025 0 0.025 0.05 300 250 200 150 100 50 0 -0.05 -0.025 0 0.025 0.05 250 200 150 100 0 -0.05 -0.025 0 0.025 0.05 θ-θ exp K (1.875,2.0) θ-θ exp π (1.75,1.875) θ-θ exp π (1.875,2.0) 50 250 200 150 100 50 0 -0.05 -0.025 0 0.025 0.05 Figure 7-8. Left plots: distributions of � offsets (left) and resolutions (right) in the Run 2 � control sample as functions of track polar angle. Top plots are for kaons, bottom plots are for pions. Right plots: distributions of � � �ÜÔ Ó«×�Ø for kaons (top) and pions (bottom) in the Run 2 � control sample. The left (right) plots correspond to the momentum bin ��– �� Î� ( ��– � ��Î� ). for the coefficients Ë�� and �� of the sine and cosine terms, respectively. Although the Ã Ã final state is a �È eigenstate, we treat this component as a pure lifetime. The functional form for the Ã� component is given by Eq. 7.9. We fix the parameters � and ¡Ñ�� to their PDG values [14] and take the error into account as a systematic uncertainty. The background ¡Ø PDF is given by the triple-Gaussian resolution function Ê��, with the parameters defined in Table 7-7. The ¡Ø parameterization is summarized in Table 7-12, and the final set of free parameters in the maximum likelihood fit are listed in Table 7-13. 7.7.2.1 Correlations between PDF variables An implicit assumption in the construction of the likelihood function is that the PDF dependent variables are uncorrelated. Table 7-14 summarizes the linear correlation coefficients for all pairs of Ñ�Ë, ¡�, �, � , � , ¡Ø, and �¡Ø. Correlations greater than are highlighted. The correlation between Ñ�Ë and ¡� is not thought to have any significant impact on the fit (mostly because the MC correlation is inflated by the better ¡� resolution compared with data). The correlations between the � ��Ö�Ò�ÓÚ angles, and between � and ¡�, inÃ� and ÃÃ events is due to the underlying momentum MARCELLA BONA
7.7 The maximum likelihood analysis 183 Component Function Parameters Signal �� Ø�� or � � Ø�� Ë��, ��; free Ê×��; Table 7-10 ��, ¡�; Table 7-9 ¡Ñ�� Ô× � �� Ô× Signal Ã � � Ñ�Ü�� Ø�� or � ÙÒÑ�Ü� � Ø�� Ê×��, ��, ¡�, �, ¡Ñ�� Signal Ã � � Ñ�Ü� � Ø�� or � ÙÒÑ�Ü�� Ø�� Ê×��, ��, ¡�, �, ¡Ñ�� Signal ÃÃ exp ª res Ê×��; � Background triple Gaussian Ê��; Table 7-7 Æ�� ÆÃ� Table 7-12. Summary of PDFs for ¡Ø. Number of signal �� events Number of signal Ã� events �Ã� charge asymmetry in signal Ã ¦ � § events ÆÃÃ Number of signal ÃÃ events Æ�� Number of background �� events Æ�Ã� Number of background Ã� events ��Ã� charge asymmetry in background Ã ¦ � § events Æ�ÃÃ Number of background ÃÃ events � background Ñ�Ë ARGUS shape parameter ¡�Ô ¡�Ô �� Ë�� background ¡� linear term background ¡� quadratic term background Fisher mean of first Gaussian background Fisher width of first Gaussian background Fisher mean of second Gaussian background Fisher width of second Gaussian background Fisher fraction of first Gaussian coefficient of the sine oscillation in signal �� events coefficient of the cosine oscillation in signal �� events Table 7-13. Summary of free parameters in the �È fit. ANALYSIS OF THE TIME-DEPENDENT �È -VIOLATING ASYMMETRY IN � � � � 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
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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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5.4 Background Suppression and PDF
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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 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 187: 7.7 The maximum likelihood analysis
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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