Violation in Mixing

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100 Strategy and Tools for Charmless Two-body � Decays Analysis 4.2.1 Topological Variables Most of the background can be eliminated by simple kinematic cuts which make use of the differences between �� and continuum events, which are the primary source of background. In the CM frame this background typically exhibits a two-jet structure. In contrast, the low momentum and pseudo-scalar nature of � mesons in the decay § �Ë � �� leads to a more spherically symmetric event. Some topological variables can be used in order to distinguish between signal and background events. First of all, the event sphericity Ë can be defined like [48]: Ë � Ñ�Ò Ë Ò � Ñ�Ò Ò Ò where index � runs over Æ tracks of the event, the versor Ò spans over all the directions, Ô £ � is the component of the momentum that is perpendicular to the versor Ò evaluated in the CM rest-frame of the § �Ë . The versor Ò that satisfies the equation 4.1 is called sphericity axis. This function Ë Ò contains the information on the way momenta are spatially distributed in the event. Another useful discriminating variable is the event thrust, Ì , defined as: where Ô £ � Ì � Ñ�Ü Ì Ò � Ñ�Ü Ò Ò Æ� �� Æ� �� Ô £ �� Ô £ � � � Ò is the component of the momentum that is parallel to the versor Ò and � Ò is the entire set of tracks whose momenta have the component Ô � greater than zero. As before, momenta are evaluated in the CM rest-frame of the § �Ë . The function Ì Ò represents the preferred direction of the momenta of the tracks in the event: this variable contains information on the jet direction. In the � � � ÕÕ production at high energies, the event in the CM rest-frame tends to assume a two-jet-like structure: since all the hadrons in the final state come from hadronization of the high energy ÕÕ state, they have to conserve the four-momentum and thus their flight directions are correlated to the initial ÕÕ line of flight. This is the reason why variables like sphericity or thrust can be used to discriminate between signal and background events. These functions though are optimized in case the events really have a two-jet structure. On the other hand, results from QCD show that more that of the events produced in a � � annihilation in the continuum and at high energies should produce three or more jets in the CM rest-frame. Therefore topological variables that do not depend on one specific event axis can be used to reject also non-two-jet continuum background: an example of such variables are the Fox-Wolfram moments that can be written as [49]: MARCELLA BONA Æ� �� Ô £ � � �Ô £ � � � (4.1) (4.2)
4.2 Event selection 101 ÀÐ � � �� Ô��Ô�� ÈÐ Ó× �� (4.3) �ØÓØ where indices � and � run over all the hadrons produced in the event, �� represents the angle between the particles � and � and ÈÐ Ó× �� is the Legendre polynomial of the Ð-th order. The energy and momentum conservation imposes the conditions À and À � . Thus the already quoted variable Ê is the ratio of the second order Fox-Wolfram moment over the zero order one: Ê � À À Left plot in Fig. 4-1 shows the Ê distribution for Monte Carlo background and signal events: a cut on Ê is useful to reduce the contribution from the �� background events. Figure 4-1. Left plot: Ê distribution for Monte Carlo events. Right plot: � Ó× � Ë� distribution for Monte Carlo events. The first cuts applied are the one in the following multi-hadron selection: ¯ Ê � �� ¯ S � � . They remove the majority of two-prong events and, in particular, the sphericity cut rejects additional �� background. After applying the multi-hadron selection cuts, continuum background suppression is achieved also by requiring ¯ � Ó× �Ë� � �� (4.4) STRATEGY AND TOOLS FOR CHARMLESS TWO-BODY � DECAYS ANALYSIS
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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
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 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: 4.2 Event selection 99 channel sele
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 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
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6.3 The maximum likelihood analysis
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6.4 Counting analysis 157 120 100 8
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6.5 Analysis choice 159 6.5 Analysi
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6.6 Results on the Run1 data-set 16
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6.7 Determination of the branching
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7 Analysis of the time-dependent
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7.3 Analysis strategy 167 Parameter
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7.4 Data samples and event selectio
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7.4 Data samples and event selectio
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7.5 Background characterization 173
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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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