Multivariate selection against the combinatorial background (BDTAC)

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The Large Hadron Collider

The Large Hadron Collider is a particle accelerator currently housed in the 27kmlong tunnel at CERN where the LEP (Large Electron-Positron) collider used to be. It has been designed with the aim of accelerating in opposite directions two different proton beams up to an energy of 7 TeV/c2. The beams are made up of bunches containing 1:2 1011 protons each, separated by 25ns (i.e. 40MHz).
They are accelerated by 16 radio frequency (RF) cavities. More than 12 thousand Niobium-Titanium dipole magnets, delivering a magnetic field of 8.3T, are used to keep the protons in the accelerator’s orbit. Another 392 quadrupole magnets are used to focus the beams, which are injected into the LHC after having been brought up to 450GeV/c2 through a series of smaller accelerator rings. The full CERN’s accelerator complex is represented in Fig. 2.1.
During the first run of the LHC (Run1), the protons were made to collide at a center of mass energy of 7 TeV/c2 (2011) and 8 TeV/c2 (2012), with 50 ns of separation between bunches. In 2015, 2016, 2017 and 2018 the LHC has delivered collisions at 40 MHz and at an energy of 13 TeV/c2 (Run2). After a long shutdown in 2019 and 2020, Run3 will resume in 2021 and the LHC will continue to deliver collisions at 40 MHz and at an energy of 13 TeV/c2 up to 2023. The collisions happen at four distinct interaction points (IPs) around the LHC ring. They are recorded by 7 detectors, the main ones being ATLAS, CMS, ALICE and LHCb. ATLAS and CMS are general purpose detectors, situated at opposite points of the collider in order to record interactions between the same pairs of bunches. ALICE and LHCb are specialized detectors, LHCb being the subject of the next section.

The LHCb detector

The LHCb collaboration gathers more than a thousand physicists from all around the world. Its main physics programme consists in studying the properties of b and c hadrons, with an emphasis on CP-violation and the matter-antimatter asymmetry. The search for NP effects in the rare decays of the heavy flavoured hadrons has also risen to occupy a larger share of the collaboration’s efforts over the years. Electroweak measurements in the forward region, complementary to those of the general purpose detectors, are also performed. The LHCb detector [46] [47] (shown in Fig. 2.2) is a forward spectrometer spanning for about 20 meters from the IP and covering the region between 2 and 5 in pseudorapidity, where b hadrons are relatively abundant, as pictured in Fig. 2.3.
The yearly integrated luminosity gathered insofar by the detector can be seen in Fig. 3.1. In the context of LHCb, a right-handed coordinate system is defined with z along the beam axis into the detector, y vertical and x horizontal. Cylindrical polar coordinates (r, , z) are also used when appropriate.
Among the main ingredients for achieving the physics goals of the collaboration, there is a good resolution on the interaction vertices. This is due to the fact thatb and c hadrons travel several millimiters before decaying and this gives a handle on signal-background separation.

The magnet and the tracking system

A non superconductive dipole magnet [50] composed of two mirror-symmetric coils with an overall bending power of 4Tm allows the tracking system of the LHCb detector to achieve high momentum resolution. The polarity of the magnet can be switched to account for systematics effects and a typical run (i.e. the data taking period) is evenly split in this regard. The subdetectors responsible for the tracking are the Tracker Turicensis (TT) and the tracking stations (T1, T2 and T3). The former sits upstream of the magnet, while the latter is positioned downstream of it. This spatial configuration guarantees a better determination of the charged particles’ momenta.
Both the TT and the T stations are made of four layers perpendicular to the beam axis in the x􀀀u􀀀v􀀀x configuration, where x is the horizontal direction and u and v represent a tilt around the beam direction of 􀀀5o and +5o respectively. The TT and the inner region of the T stations [51] [52] (IT), which is the one with the higher occupancy, are made of silicon strips with a pitch of 200 m. These strips provide a single hit spatial resolution of 50 m. The outer region of the T stations [53] [54] (OT) is made of straw-tubes of 4.9mm in diameter. These are filled with Argon (70%) and CO2 (30%), which allows for a fast drift time of less then 50ns and a drift-coordinate resolution of 200 m. Overall, the relative uncertainty on the momentum of a charged particle varies from 0:5% at low momentum (2 – 60 Gev/c) to 1:0% at 200 GeV/c [52].

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The Cherenkov detectors

Cherenkov detectors exploit the fact that when a charged particle travels through a dielectric material with a speed higher than the phase velocity of light in the medium, it emits photons. This emission happens at a characteristic angle that is related to the refractive constant of the material and the speed of the particle. It is then possible to infer the mass of the particle if its momentum is known. Particle identification (PID) in the context of the LHCb detector is achieved following this procedure.

Real time alignment and calibration

For the Run2 data taking, LHCb has moved to a real time procedure for the alignment and the calibration of the detector. Data collected at the beginning of the fill are used by the alignment tasks, that complete within a few minutes. The calibration constants are also re-evaluated for each run. The HLT2 benefits from the updated calibration and alignment which ensure an offline quality reconstruc-tion for the trigger decisions. The overall flow of this procedure, which is fully automated since 2018, is shown in Fig. 2.8.
The real time alignment and calibration of the detector are one of the crucial components for the next LHCb upgrade. It will be instrumental in making the transition to a fully software based trigger strategy, as detailed in section 3.1.

Table of contents :

Introduction
1 Theoretical overview and motivation 
1.1 The Standard Model of particle physics
1.1.1 Matter content
1.1.2 Gauge bosons and interactions
1.1.3 The Higgs mechanism and the CKM matrix
1.2 Charged Lepton Flavour Violation
1.2.1 Neutrino mixing and the charged lepton sector
1.2.2 Implications of the Lepton Universality tests
2 The LHCb experiment at the LHC 
2.1 The Large Hadron Collider
2.2 The LHCb detector
2.2.1 The Vertex Locator
2.2.2 The magnet and the tracking system
2.2.3 The Cherenkov detectors
2.2.4 The calorimeter system
2.2.5 The muon chambers
2.2.6 The trigger
2.2.7 Real time alignment and calibration
3 Tracking with the SciFi subdetector in the LHCb upgrade 
3.1 The LHCb upgrade
3.1.1 Trigger and readout
3.1.2 Particle identification subdetectors
3.1.3 Tracking subdetectors
3.2 Tracking strategy
3.2.1 Track types
3.2.2 Tracking sequence
3.3 The PrHybridSeeding
3.3.1 Overview of the Hybrid Seeding
3.3.2 The x-z projection step
3.3.3 Stereo step and full track selection
3.4 Additional SciFi layers study
3.4.1 Simulated geometries
3.4.2 Adaptation of the Hybrid Seeding to the additional layers . 
3.4.3 Impact of the layer number on the Seeding
3.4.4 Profiling of the Hybrid Seeding performance
3.5 Alternative seeding algorithms
3.5.1 The projective approach
3.5.2 Layer inefficiencies in the Progressive Seeding
3.5.3 Progressive Seeding refinement and variants
3.5.4 Combined Seeding
4 The B0! K0 analysis 
4.1 Analysis strategy
4.2 Dataset and simulated samples
4.2.1 Dataset description
4.2.2 Monte Carlo samples
4.3 B0 mass reconstruction
4.4 Event selection
4.4.1 Trigger selection
4.4.2 Stripping selection
4.4.3 Fiducial region
4.4.4 Multivariate selection against the combinatorial background (BDTAC)
4.4.5 Multivariate selection for candidates (BDTTAU)
4.4.6 Particle identification selection
4.4.7 Daughters mass cuts
4.4.8 Fisher discriminant on isolation variables and flight distance
4.4.9 Vetos
4.4.10 Multiple candidates
4.5 Efficiencies
4.5.1 PID efficiencies
4.6 Background studies
4.6.1 Background yields estimate: the ABCD method
4.6.2 Monte Carlo background checks
4.7 Control channel
4.7.1 Anti combinatorial BDT (BDTAC)
4.7.2 Overall control channel selection
4.8 Systematic uncertainties
4.8.1 Efficiencies
4.8.2 Normalization channel fit
4.8.3 Background estimate
4.9 Limit setting
A Tracking algorithms for the LHCb upgrade 
A.1 PrPixelTracking
A.2 PrVeloUT
A.3 PrForwardTracking
A.4 PrHybridSeeding
A.5 PrLongLivedTracking
A.6 PrMatchNN
Bibliography 

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