Flavor physics and CP violation in the Standard Model 

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The LINAC and the storage ring

PEP-II is made of two storage rings of 2.2 Km of circumference in which the collision takes place. Fig 3.1 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 50GeV. 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.
The High Energy Ring (HER) produces electron beams with 9.0GeV of energy, while the Low Energy Ring (LER), delivers positrons with an energy of 3.1GeV, which upon collision, result in a boost of βγ ∼ 0.56 along the e− beam direction in the laboratory frame. This boost allows the measurement of the Brec/Btag mesons time difference (see Sec. 7.1.2). The parameters for these storage rings are summarized on Tab. 3.1.

The interaction region

The Interaction Region is heavily instrumented with magnets that focus the beams before the collision, directs them so that there is no crossing angle between them, and finally separates them before a given bunch of particles collides with a second bunch from the other beam (see Figure 3.2). The quadrupole magnets labelled QD and QF, situated outside the BABAR detector, focus the high and low energy beams. The dipoles labelled B1 are responsible for bringing the beams together and separating them immediately afterwards. This is the reason why they need to be close to the interaction point; in fact, within the detector volume.

The injection system

In 1999, when BABAR started, the electrons and positrons were injected in the storage rings in bunches of 109 particles with a frequency between (1 − 30)Hz and a mean time spacing of 4 ns. In a 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, as it was necessary to ramp down the high voltages of detector systems for protection purposes. The result was that data taking was periodically suspended. Moreover, not only the recorded luminosity was not optimal, but the beam currents continuously decreased.
From 2004 a system of continuous injection was settled, the trickle injection, where a new injection is just performed if the instantaneous luminosity falls below a pre-established threshold, and can be made continuously at a low rate. At first this was obtained for the LER, with a gain in luminosity of 35% and afterwards applied in the HER, resulting in an extra gain of 12%. The main disagreement of this new method consists in it’s difficulty to limit the backgrounds created by the injection. But it was demonstrated through various tests that these backgrounds could be kept to a manageable level and thus the trickle injection has since it’s implementation become the default operation.

The Detector of Internally Reflected ˇCerenkov Light (DIRC)

As the BABARphysics program consists of measuring CP violating asymmetries in a variety of channels, identifying particles is crucial. In neutral modes, it is necessary to define the flavour of the other B in the event in order to measure these asymmetries. This definition is obtained by correlating the charges of certain particles with the flavour of the parent meson. Since these correlations are conditioned by the particle species, these must be identified (see Sec. 7.1.1). Also, as similar channels, like B0 → K+π− and B0 → π+π−, have different asymmetries it is essential to avoid contamination in the isolation of final states.
More specifically, above 700MeV/c, the drift chamber is no longer able to distinguish kaons from pions, which the DIRC aims to separate at 4σ significance up to a momentum of 4.2GeV/c. For the muons, the DIRC must complement the IFR, whose effectiveness falls for momenta below 750MeV/c.
Finally, the DIRC must be small, not only due to it’s location – between the drift chamber and inside the calorimeter – but also in order to minimize the size of this latter one (as the calorimeter is the most expensive part of the detector), amounting to only a fraction of the radiation length (see below).
When a particle travels faster than the speed of light in the medium that surrounds it, v/c = β ≥ 1/n, it emits ˇCerenkov photons at an angle cos θC = 1/nβ with the direction of the particle. Hence, provided that its trajectory is known accurately enough, a measurement of the direction of these photons establishes the speed of the particle. Given the space constraints sketched above, the instrumentation to detect them must lie outside the main body of the detector. Internal reflection on a plane surface is used to preserve the angle of these photons while directing them towards the photomultiplier tubes (see Fig. 4.5). Forward moving photons are reflected in a mirror, allowing the DIRC instrumentation to occupy only the less populated backward end of the detector.
The photons are confined by bars of quartz (n = 1.474) of 17mm thick and 35mm wide but reaching 4.9m long. In a normally incident particle, they totalize 17% of a radiation length.In the backward end of the detector, the photons go through a wedge-shaped quartz piece and then into a water filled expansion region, known as the standoff box, after which they meet the photomultiplier tubes. The role of the wedge is to reflect photons arriving at large angles, thereby reducing the area of the standoff box that needs to be instrumented at the cost of introducing ambiguities in the angle. There are 10752 photomultiplier tubes, surrounded by ”light catchers” that amplify the detection area. Finally, the standoff box is magnetically shielded to avoid disturbances in the tubes.


The Electromagnetic Calorimeter (EMC)

A number of CP eigenstates within BABAR’s physics goals contain π0’s in the final state. Many others involve η particles or photons directly, such as b → sγ, in which the spectrum is quite hard. Some QED processes, such as e+e− → e+e−γ or e+e− → γγ are also important for calibration or luminosity measurement purposes. Therefore, BABAR must be able to reconstruct photons over a wide range of energies, from 20MeV up to 4GeV.
The EMC is the only system being able to supply precise information on particle identification and must thus identify electrons accurately, as they are relevant in flavour tagging and semi-leptonic B decays.

The Instrumented Flux Return (IFR)

The golden mode, J/ψK0 S, involves muons, as the J/ψ is reconstructed in the channels e+e− and μ+μ−. Their detection is also essential for semi-leptonic physics and for the tagging algorithms. Particle identification information on muons is desirable for momenta from about 1GeV/c.
Muons are heavier than electrons, making bremsstrahlung a far less effective energy loss mechanism for them. Since they have relatively long lifetimes and do not participate in nuclear interactions either, they are very penetrating particles. Therefore, the best choice is to place a dedicated subdetector outside the rest of the instruments.
In BABAR, the outer part of the detector plays the role of the flux return for the solenoid, at the same time as it provides a support structure. Interleaved between the steel plates of the flux return, instruments can be placed to turn it into a muon detector and a primitive hadron calorimeter, in charge of detecting neutral hadrons, mainly K0 L. These feature in a number of modes of interest, due to them having an opposite CP eigenvalue to the best experimentally suited modes containing a K0 S.

Table of contents :

I Theoretical overview and brief experimental status 
1 Flavor physics and CP violation in the Standard Model 
1.1 Weak interactions in the flavor sector
1.2 Quark mixing and the CKM matrix
1.3 Mixing and CP violation in the B meson system
1.3.1 Mixing of neutral B mesons
1.3.2 CP violation in the B mesons
1.4 Trees and Penguins
2 The photon polarization in radiative B decays and the K1(1270) resonance 
2.1 The photon polarization
2.2 Physical observables and experimental status
2.2.1 Mixing-induced CP asymmetry
2.2.2 Other methods
2.3 Status of the K1(1270) resonance description
2.3.1 Axial-vector K1 resonances
2.3.2 The Kπ S-wave in K1(1270) decays
2.3.3 Width of the K1(1270)
3 An asymmetric e+e− collider: PEP-II 
3.1 The LINAC and the storage ring
3.2 The interaction region
3.3 Machine backgrounds
3.4 The injection system
3.5 Performance
4 The BABAR Detector 
4.1 The Silicon Vertex Tracker (SVT)
4.2 The Drift Chamber (DCH)
4.3 The Detector of Internally Reflected ˇCerenkov Light (DIRC)
4.4 The Electromagnetic Calorimeter (EMC)
4.5 The Instrumented Flux Return (IFR)
4.6 The Trigger system
4.7 Data acquisition
4.8 Online prompt reconstruction
III Analysis 
5 Data samples and analysis techniques 
5.1 Monte Carlo and data samples
5.1.1 Monte Carlo samples
5.1.2 On-Peak and Off-Peak data samples
5.2 Reconstruction
5.2.1 Tracking algorithms
5.2.2 Calorimeter algorithms
5.2.3 Particle identification
5.2.4 Vertexing
5.3 Discriminating variables
5.3.1 Kinematic variables
5.3.2 Event-shape variables
5.3.3 Fisher discriminant
5.4 The maximum likelihood fit
5.4.1 Extended maximum likelihood fit
5.4.2 Error estimations
5.4.3 Toy Monte Carlo
5.4.4 The sPlot technique
6 Analysis of B+ → K+π−π+γ decays: study of the Kππ resonant structure 
6.1 Signal Monte Carlo cocktail
6.2 Event Selection
6.2.1 Skim
6.2.2 Selection cuts
6.2.3 Cut Optimization
6.2.4 Multiple candidate selection
6.2.5 Efficiency
6.3 Signal study
6.3.1 Truth matching
6.3.2 Expected yields
6.4 Backgrounds study
6.4.1 B backgrounds
6.4.2 Continuum background
6.4.3 Expected background yields
6.5 Fit to mES, E and Fisher
6.5.1 Signal PDFs
6.5.2 Background PDFs
6.5.3 Fitting functions
6.5.4 Validation tests
6.5.5 Fit yields and projections
6.6 Fit to the mKππ spectrum
6.6.1 Fit model
6.6.2 Fit results
6.7 Fit to the mKπ spectrum
6.7.1 Efficiency correction
6.7.2 Fit model
6.7.3 Fit results
6.7.4 Study of the model consistency
6.7.5 Angular moments and results interpretation
6.8 The dilution factor
6.8.1 Analytical expression of the dilution factor
6.8.2 Extraction of the dilution factor
6.9 Systematics
6.9.1 Fit to the mKππ spectrum
6.9.2 Fit to the mKπ spectrum
7 Time Dependent Analysis of B0 → K0 Sπ+π−γ decays: probing the photon helicity 
7.1 Time-dependent model
7.1.1 Flavor tagging
7.1.2 t measurement and resolution
7.1.3 Signal t PDF
7.1.4 Background t PDFs
7.2 Signal Monte Carlo cocktail
7.3 Event selection
7.3.1 Selection cuts
7.3.2 Cut Optimization
7.3.3 Efficiency
7.4 Classification of signal events
7.5 Background study
7.5.1 B backgrounds
7.5.2 Continuum background
7.6 Fit to mES, E, the Fisher discriminant and t
7.6.1 Signal PDFs
7.6.2 Background PDFs
7.6.3 Fitting functions
7.6.4 Parameters of the t PDFs
7.6.5 Validation tests
7.6.6 Results
7.7 Time-dependent analysis systematics
Summary, conclusion and perspectives
A Probability Density Function Definitions 
A.1 Gaussian function
A.2 Bifurcated Gaussian function
A.3 Cruijff function
A.4 Crystal Ball function
A.5 Argus function
A.6 Exponential function
A.7 Linear function
B Fragmentation corrective weights 
C Kaonic resonances distortion 
D Parametrization of TM mES-E correlations 
D.1 Study of E Cruijff parameters dependence in mES bins
D.2 Fit projections
D.2.1 mES projections in E bins
D.2.2 E projections in mES bins
E Toy studies for the charged channel analysis 
E.1 Self-cross-feed fraction
E.2 Pure toy studies
E.3 Embedded toy studies
F B+ → K+π−π+γ fit projection study 
F.1 Study of the mES and the Fisher discriminant fit projections
F.2 Study of the E fit projection
G Toy studies for the time-dependent analysis 
G.1 Pure toy studies
G.2 Embedded toy studies


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