Violation in Mixing

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102 Strategy and Tools for Charmless Two-body � Decays Analysis where �Ë is the angle between the sphericity axis of the � candidate and the one of the rest of the event (using all charged tracks and neutral particle candidates which are not used in the � candidate). Right plot in Fig. 4-1 shows the � Ó× �Ë� distribution for Monte Carlo background and signal events: a cut at �� removes the background peaking at in this variable. All the cuts previously described are called the two-body standard selection. 4.2.2 � candidate selection: kinematic Variables Candidate � mesons are reconstructed by forming all pairs of oppositely charged tracks, or a charged track and a Ã Ë or � candidate, or two Ã Ë or � candidates. The charged tracks used to form a � candidate are selected on the basis of the GoodTracksAccLoose criteria: ¯ Æ ��À hits � ¯ � � �� Ñ, Þ � Ñ ¯ ÔÌ � Å�Î� ¯ �� Ö�� where Æ ��À hits is the number of ��À hits, � is the distance in the Ü� Ý plane of the POCA (Point Of Closest Approach) of the track from the measured beam-spot, Þ is the Þ position of the POCA, ÔÌ is the transverse momentum of the track and � is its polar angle. Instead, the Ã Ë daughters are selected as described in Sec. 3.3. The vertex algorithm is used to estimate the decay vertex of the candidate �. The momentum vectors of the daughter particles are recalculated using this point as their production vertex. Simple four-vector addition, assuming the pion mass for the charged tracks, is then used to form the � candidate four-vector. A loose mass cut of ¦� Å�Î� around the PDG � mass value [14] is applied as part of the preselection cuts. We define the beam energy-substituted mass [50]: Ñ�Ë � Ö × Ô ¡ Ô� �� Ô � � (4.5) where Ô × and � are the total energies of the � � system in the CM and lab frames, respectively; Ô and Ô� are the momentum vectors in the lab frame of the � � system and the � candidate, respectively; and Ô� is the magnitude of the � candidate momentum in the lab frame. Evaluated in the CM frame, this variable looks like: Õ Ô×� Ñ�Ë � Ô £ � which clarifies its physical meaning. The advantage of using the definition in the lab frame with respect to the one computed in the CM frame is that the first does not require assigning mass hypotheses to the charge tracks. The mean value of Ñ�Ë and its Gaussian width � Ñ�Ë are determined from a sample of fully reconstructed � � � � decays (see next section). The values used are Ñ�Ë � �� ¦ � � ��Î� and MARCELLA BONA
4.2 Event selection 103 Figure 4-2. Correlation between Ñ�Ë and ¡� variables for Monte Carlo � � � � signal events. � Ñ�Ë � �� ¦ � Å�Î� . To an excellent approximation, the shapes of the Ñ�Ë distributions for all fully-reconstructed � decays to final states with charged tracks only are identical. The preselection requires �� Ñ�Ë � �� Î� . The energy difference ¡� is defined as ¡� � � £ � Ô ×� � (4.6) where � £ � is the � candidate energy in the CM frame. Signal events are Gaussian distributed in ¡� with a mean near zero, while the continuum background events fall roughly linearly over the region of interest. For those analyses including charged tracks in the final states, since the pion mass is assigned to the charged tracks, the � � Ã � , Ã Ã decays together with the � � �Ã Ë and ÃÃ Ë decays have ¡� shifted from zero by an amount depending on the momenta of the tracks. From Monte Carlo simulation we find average shifts of ��( � ) and � Å�Î for the Ã � (Ã Ë Ã ¦ ) and Ã Ã decays, respectively (this is described in detail in Sec 4.6.1). The resolution on ¡� is is mode dependent and dominated by momentum resolution: the estimate of the width is taken from Monte Carlo simulated signal data and the observed difference in widths between data and Monte Carlo in � � � � decays is used to scale the Monte Carlo value of all the charmless channels to agree with data. This pair of kinematic variables is chosen because it satisfies two criteria: it maximizes the use of the available information and minimizes the correlation between the two variables [51]. The main reason for requiring Ñ�Ë and ¡� not to be correlated is the use of these variables in the maximum likelihood fit. Fig. 4-2 shows the correlation between the two variables. 4.2.2.1 Control Sample � ¦ � � � ¦ In order to study shape variables and mass resolutions, � � � � � � Ã� candidates have been reconstructed in the on-resonance data sample and compared to Monte Carlo simulated data. 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
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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 and 106: 4.2 Event selection 99 channel sele
Page 107: 4.2 Event selection 101 ÀÐ �
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
Page 157 and 158: 6.3 The maximum likelihood analysis
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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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