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The LINAC and the storage rings
PEP-II is made of two storage rings of 2.2 Km of circumference in which the collision takes place. Fig. 4.1 shows an schematic view of the PEP-II collider and the LINAC accelerator. The LINAC (LINear ACcelerator) constitutes the PEP-II injection system. It is 3 Km long and accelerates the particles up to their nominal energies. The LINAC is a facility also used for other purposes, being able to produce beams with energies up to 50 GeV. The electrons and positrons used by PEP-II only use part of the accelerator capabilities. These electrons and positrons produced in the LINAC are accelerated until their nominal energies, and then injected to PEP-II storage rings placed at the end of the linear accelerator. Once there, the electrons and positrons, which circulate in bunches in separate rings, are made to collide at the IP, around which the BABAR detector is located.
Low Energy Ring (LER), delivers positrons with an energy of 3.1 GeV, which upon collision, result in a boost of hβγi ∼ 0.56 along the e− beam direction in the laboratory frame. This boost allows the measurement of the BCP /Btag mesons time difference (cf. Sec. 1.2.2). The parameters for these storage rings are summarized on table 4.1.
The interaction region
The interaction region is instrumented with magnets that focus the beams before collision, direct them so that there is no crossing angle at the IP, and finally separate them before the exiting bunch of particles collides with a bunch from the other beam (cf. Fig. 4.2). The next quadrupole magnets, labelled by QD and QF, are located outside the BABAR detector. They focus the high and low energy beams. The bunches are brought together, collide head-on, and are separated magnetically in the horizontal plane by a pair of dipole magnets (B1), followed by a series of quadrupole magnets (Q1). The B1 dipoles, located at ±21 cm on either side of the IP, and the Q1 quadrupoles are permanent magnets placed inside the BABAR solenoid (cf. Sec. 4.2.6). This close distance from the IP was designed to obtain a small spacing of bunches in the beams (1.26 m), so the beams have to be separated very quickly in order to avoid parasitic collisions. The first unwanted crossing point is located 63 cm away from the IP.
The collision axis is offset from the z-axis of the BABAR detector by about 20 mrad in the horizontal plane to minimize the perturbation on the beams by the solenoidal field. In order to have the highest possible solid angle, the B1 and Q1 components have to be very compact, and in order not to compromise the vertexing resolution, the vertex detector (cf. Sec. 4.2.1) has to be as close to the water-cooled beryllium beam pipe as practical. The beam pipe has an internal radius of 2.6 cm and its inner surface is coated with a 4 μm thin layer of gold to attenuate synchrotron radiation. The SVT and the B1 and Q1 magnets are placed inside a support tube of 4.5 m long and 27.7 cm inner diameter inside the beamline supports. The quasi-vertical dotted lines of Fig. 4.2 represent the acceptance of BABAR.
Monitoring of the beam parameters
The most critical beam parameters for BABAR performance are: luminosity; energies of the two beams; and positions, angles, and size of the luminous region. While PEP-II measures radiative Bhabha scattering events to provide a fast monitoring of the relative luminosity, BABAR derives the absolute luminosity offline from other QED processes, primarily e+e− and μ+μ− pairs. The measured rates are consistent and stable as a function of time. During operation, the mean energies of the two beams are calculated from the total magnetic bending strength and the average deviations of the accelerating frequencies from their central values. The RMS energy spreads of the LER and HER beams are 2.3 MeV and 5.5 MeV, respectively. To ensure that the data is recorded close to the peak Υ(4S) resonance, the observed ratio of the B ¯B enriched events to lepton pair production is monitored online. Near the peak of the resonance, a 2.5% change in the ratio corresponds to a 2 MeV change in the C.M. energy, but this drop does not distinguish between energy settings below or above the Υ(4S) peak. The best monitor and absolute calibration of the C.M. energy is derived from the measured C.M. momentum of fully reconstructed B mesons combined with the known B-meson mass. The beam energies are necessary input for the calculation of two kinematic variables commonly used to separate signal from background in the analysis of exclusive B-meson decays (cf. Sec 5.6.1). The direction of the beams relative to BABAR is measured iteratively run-by-run1 using e+e− → e+e− and e+e− → μ+μ− events. The size and position of the luminous region (see design values in Table 4.1) are critical parameters for the time-dependent analyses. They are determined from the closest approach to the z-axis of two-charged particles events as a function of the azimuth angle, and from the position of the two tracks.
The continuous injection system
At the beginning of BABAR in 1999, the electrons and positrons were injected in the storage rings in bunches of 109 particles with a frequency between (1 − 30)Hz, with a mean time spacing of 4ns. In normal operation the injection was made every (40 − 50) min. These periods of injection (of ∼ 5 min) generated intense backgrounds in BABAR. Also, the injection induced dead time, because it was necessary to ramp down the high voltages of detector systems for protection purposes. Data taking was interrupted regularly. Additionally, beam currents decreased continuously, and the recorded luminosity was not optimal.
A system of continuous injection known as trickle injection was established since 2004. A new injection is only arranged when the instantaneous luminosity falls below a preestablished threshold, and can be made continuously at a low rate. This was first achieved for the LER, resulting in a gain in luminosity of 35%. Later on it was implemented in the HER, giving a additional gain of 12% (cf. Fig. 4.3). The inconvenient of this new method is in the difficulty to limit the backgrounds created by the injection. In successive tests it was shown that these backgrounds could be kept to a manageable level, and the default operation has been this trickle injection since 2004.
Performance of the charged particle tracking system
The main purpose of the BABAR charged particle tracking system, SVT and DCH, is the efficient detection of charged particles and the measurement of their momenta and angles with high precision. These measurements allow for the reconstruction of exclusive B and D mesons decays. Reconstruction of multiple decay vertices of weakly decaying B and D mesons is of primary importance.
The reconstruction of charged tracks relies on data from both tracking systems, the SVT and the DCH. Charged tracks are defined by five parameters (d0, φ0, ω, z0, tan λ) and their associated error matrix. These parameters are measured at the point of closest approach to the z-axis. d0 and z0 are the distances to this point from the origin of the coordinate system in the x−y plane and along the z-axis, respectively. The angle φ0 is the azimuth of the track, λ is the dip angle relative to the transverse plane. Finally, ω = 1/pt is the curvature. d0 and ω are signed variables. Their sign depends on the charge of the track. The procedures for track finding and fitting use the Kalman filter algorithm [90], which takes into account the distribution of material in the detector and the map of the magnetic field. The efficiency for reconstructing tracks in the DCH, with samples of multi-hadrons events, has been measured as a function of transverse momentum, polar and azimuthal angles in events with multiple tracks. The absolute DCH tracking efficiency is the ratio of reconstructed DCH tracks to tracks detected in the SVT. The top and bottom plots on the left in Fig. 4.10 show the results for two voltage settings of the DCH. At the design voltage of 1960 V, the average efficiency is (98 ± 1)% for tracks above 200 MeV/c and with polar angle θ > 500 mrad.
Table of contents :
I Theoretical Introduction
1 Weak interactions, quark mixing and CP violation
1.1 CP Violation in the Standard Model
1.1.1 Elementary constituents
1.1.2 CP violation and the CKM Matrix
1.1.3 CKM matrix properties
1.2 The B Meson System
1.2.1 The quantum mechanics of neutral B mesons
1.2.2 Tagging and t measurement from coherent B0 ¯B 0 production at BABAR
1.2.3 Three types of CP violation
1.2.4 B factories achievements
1.3 Constraints on the CKM Matrix and B factories
2 B0 → K0S π+π− and Charmless 3-body B decays
2.1 Introduction
2.2 Experimental and theoretical status
2.3 b → s¯qq Penguin Dominated Modes and New Physics
2.4 Three-Body Decays and the B0 → K0S π+π− Channel
2.4.1 Particle Decays
2.4.2 The Dalitz Plot
2.4.3 The isobar model
2.4.4 Mass term description
2.4.5 Blatt-Weisskopf Factors
2.4.6 Angular Distribution
2.4.7 The Square Dalitz Plot
2.4.8 Time and DP-Dependent PDF
2.4.9 Physical observables
3 Theory Elements for the B → K∗π and B → ρK Modes
3.1 Introduction
3.2 Isospin Analysis for the B → K∗π modes
3.2.1 Decay Amplitudes
3.2.2 Physical observables
3.2.3 Isospin Relations
3.2.4 Reparameterization Invariance
3.2.5 Parameterizations
3.2.6 The B0 → K∗+π− and B0 → K∗0π0 subsystemand the CPS/GPSZ technique
3.2.7 Hadronic hypothesis
3.2.8 Conclusion
3.3 Isospin Analysis for the B → ρK modes
3.3.1 Introduction
3.3.2 Decay Amplitudes
3.3.3 The physical observables
3.3.4 Hadronic hypothesis
3.3.5 Conclusion
3.4 Combining the B → K∗π and B → ρK modes
3.4.1 Introduction
3.4.2 The physical observables
3.4.3 Hadronic hypothesis
3.4.4 Conclusion
3.5 Strategies for a phenomenological analysis
II PEP-II and the BABAR Experiment
4 An Introduction to the BABAR experiment
4.1 e+e− B factories and PEP-II
4.1.1 The LINAC and the storage rings
4.1.2 The interaction region
4.1.3 Monitoring of the beam parameters
4.1.4 Machine backgrounds
4.1.5 The continuous injection system
4.1.6 Types of data delivered
4.1.7 Performance
4.2 The BABAR Detector
4.2.1 The Silicon Vertex Tracker (SVT)
4.2.2 The Drift Chamber (DCH)
4.2.3 Performance of the charged particle tracking system
4.2.4 The Detector of Internally Reflected Cerenkov Light (DIRC)
4.2.5 The Electromagnetic Calorimeter (EMC)
4.2.6 The Superconducting Solenoid Magnet
4.2.7 The Instrumented Flux Return (IFR)
4.2.8 The Trigger
4.2.9 The Data Acquisition System (DAQ)
4.2.10 Online Prompt Reconstruction (OPR)
III Analysis of the B0 → K0S π+π− mode
5 Data Sample, Reconstruction and Selection
5.1 The Data Sample
5.1.1 The On-peak and Off-peak data samples
5.1.2 Monte Carlo Samples
5.2 Reconstruction
5.2.1 Tracking algorithms
5.2.2 Calorimeter algorithms
5.2.3 Particle identification (PID)
5.2.4 Vertexing
5.3 The flavor tagging
5.3.1 The BABAR flavor tagging algorithm
5.4 t measurement
5.4.1 z Measurement
5.4.2 t Calculation
5.4.3 t resolution Model
5.5 Event Kinematics and Shape
5.5.1 Kinematics
5.5.2 Event topology
5.6 Main discriminant Variables
5.6.1 Kinematic Variables
5.6.2 Shape Variables and the neural network
5.7 Event Selection
5.7.1 Multiple candidates
5.7.2 Misreconstructed signal and migration over the DP
5.8 B-background
5.8.1 Neutral B background
5.8.2 Charged B background
5.8.3 Summary on B background
6 The Maximum Likelihood Fit
6.1 The likelihood function
6.2 Correlation of fit variables with Dalitz Plot, tag and tagging category
6.3 Parameterization of distributions
6.3.1 E, mES and NN parameterizations
6.3.2 Time and Dalitz Plot PDFs
6.3.3 B background parameterization
6.3.4 Continuum parameterization
6.4 Validation of fit performance with toy studies
6.4.1 Signal-only high statistics toys
6.4.2 Realistic toys with signal, continuum and B background components
6.5 Likelihood vs. 2βeff (f0(980)K0S ) Scans
6.5.1 High statistics, signal-only likelihood scans
6.6 Studies using fully simulated MC samples
6.6.1 Dalitz plot model for embedded fits
6.6.2 Embedded fits
6.7 Extraction of confidence intervals on the physical parameters
6.7.1 The statistical likelihood scans
6.7.2 Convolution with systematic uncertainties
6.8 The Nominal Signal Model
7 Results
7.1 Goodness of Fit and Likelihood Projections
7.1.1 Discriminant Variables
7.1.2 Dalitz Spectra
7.1.3 Time-dependent Asymmetries
7.2 Results on Physical Parameters
7.2.1 Measurement of sin 2(βeff) in penguin dominated modes
7.2.2 The measurement of the CPS/GPSZ phase difference
7.2.3 Results on direct CP asymmetries
7.2.4 Fit fractions and significance of small components
7.2.5 Results on other phase differences
7.2.6 Summary on results
7.2.7 Average signal efficiency and branching fractions
7.3 Systematics uncertainties
7.3.1 Reconstruction and SCF model
7.3.2 KS reconstruction and tracking efficiencies, PID and luminosity
7.3.3 Fixed parameters in the likelihood
7.3.4 Tag-Side Interference Effects
7.3.5 Continuum PDF
7.3.6 B-background PDF
7.3.7 Signal Model Systematics
7.3.8 Total Systematics
7.4 Conclusion
IV Results Interpretation
8 Interpretation of experimental results of the B → K∗π and B → ρK Modes
8.1 The Rfit approach
8.2 Experimental Measurements
8.3 Isospin analysis of the B → K∗π modes
8.3.1 Constraints on unmeasured experimental measurements
8.3.2 Constraints on the ratio of QCD amplitudes
8.3.3 Constraints on the (¯ρ, ¯η) plane
8.4 Isospin analysis of the B → Kρ system
8.5 Isospin analysis of the combined B → K∗π and B → ρK modes
8.5.1 Constraints on unavailable experimental measurements
8.5.2 Constraints on the ratio of QCD amplitudes
8.5.3 Constraints on the φ3/2 observable
8.5.4 Extrapolation to 2015
8.6 Summary
9 Conclusion
9.1 Time-dependent amplitude analysis of the charmless decay mode B0 → K0S π+π−
9.2 Phenomenological Interpretation of the B → K∗π and B → Kρ modes
V Appendix
A Probability density distributions of fit variables
A.1 Signal and Continuum background
A.1.1 The kinematic variables, mES and E
A.2 The Neural Network
A.3 PDFs for B Backgrounds
A.3.1 B0 → D−(→ K0S π−)π+
A.3.2 B0 → J/ (→ ℓ+ℓ+)K0S
A.3.3 Other B backgrounds
B Probing the Signal DP Model
B.1 Addition of other components to the minimal model
B.2 Probing for a non-resonant component
B.3 Probing the signal around mππ ∼ 1.5 GeV/c2
B.4 Probing the mKSπ spectrum above ∼ 1.5 GeV/c2
B.5 Summary
C List of Fixed Parameters in the Nominal Fit
