The Large Hadron Collider (LHC) and the ATLAS experiment 

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ATLAS: A Toroidal LHC ApparatuS

The ATLAS detector is one of the two general purpose detectors (along with CMS) that uses the LHC beam to collide Hadrons at the highest energy reached by any accelerator. The detector is described in [58]. The dimensions of the detector are 25 m in height and 44 m in length. The overall weight of the detector is approximately 7000 tonnes. It is used to probe p-p, p-Pb, Pb-Pb and other hadrons collisions. In this thesis, I will only focus on p-p collisions for both performance and physics studies.
One of the main goals of the ATLAS experiment is to prove the existence of a particle compatible with the predictions of the spontaneous symmetry breaking, the Higgs boson (introduced in chapter 1.1.1). This was achieved in 2012 and detailed in this paper [13]. Another goal is to search for new physics signals and test the many BSM models that exist.
The detector is composed of multiple sub-systems to achieve the highest detecting capabilities for various ranges of particle types and physics signals. The three main (and biggest) parts are the inner tracking detector, the electromagnetic and hadronic calorimeter and the muon spectrometer. They are built one on top of the other in a cylindrical onion arrangement. Each system is divided into a central barrel and two end-caps for the two forward regions. The calorimeters have also more forward components. Figure 2.2 shows a cut-away view of the ATLAS detector with a labeling of the different components. Figure 2.3 shows how the detector reconstructs and identifies the different type of particles, like electrons, muons, photons, hadrons . . . Details for each of the main sub-systems of the detector are given in the next sections.

Muon spectrometer

The muon spectrometer (MS) forms the outer part of the ATLAS detector and is designed to reconstruct tracks of charged particles exiting the barrel and end-cap calorimeters, to identify muons and to measure their momentum in the range jj < 2:7. Is is also used to detect punch-through signals: showers inside calorimeters are sometimes not fully contained in the calorimeter and the charged particles that escape it induce hits in the MS. In this case, the energy detected by the MS is used to complement the ones from the calorimeter. The MS is also designed to trigger on muons in the region jj < 2:4. It uses separate instrumentation for the high-precision tracking and trigger chambers. The barrel toroid provides magnetic bending over the range jj < 1:6, whereas end-cap magnets provide it over the range 1:4 < jj < 2:7 where the overlap region is 1:4 < jj < 1:6. The driving performance goal is a stand-alone transverse momentum resolution of approximately 10% for 1 TeV tracks. The  barrel region is divided into eight octants symmetric in . Each octant is subdivided in the azimuthal direction in two sectors, a large and a small one overlap in . This overlap of the chamber boundaries minimizes gaps in detector coverage and also allows for the relative alignment of adjacent sectors using tracks recorded by both a large and a small chambers. The chambers in the barrel are arranged in three concentric cylindrical shells around the beam axis. In the two end-cap regions, muon chambers form large wheels, installed in planes perpendicular to the beam to the z-axis and also arranged in three layers. A view of the muon spectrometer is presented in figure 2.13.

Jet constituents and reconstructions

As already mentioned in section 1.2.3, the most widely algorithm used in high energy physics, and hence ATLAS, is the anti-kt algorithm. The algorithm can form jets using various type of inputs, where the only needed constituent variables are the four-vector momenta. Let us detail some of the
inputs used in ATLAS.
The lateral and longitudinal segmentation of the calorimeters allows for a three-dimensional reconstruction of particle showers. To take advantage of this segmentation, topo-clusters are built from topologically connected calorimeter cells. Topo-clusters are seeded by cells whose signals exceed the expected noise by four times its standard deviation, S > 4noise. Neighboring cells with S > 2noise are then added iteratively. Finally, all cells neighboring the formed topo-cluster are added. Hence, the topo-cluster algorithm separates continuous energy showers rather than energy deposits from different particles. It efficiently suppresses the calorimeter noise which originates from both electronic and pile-up sources.
The cells used are initially calibrated to the electromagnetic scale (EM scale) which correctly measurethe response of electromagnetic shower. The EM scale is derived from test beams measurements and from MC simulations. The jets built from topo-clusters at EM scale are called EMTopo jets.Hadronic showers produce responses that are lower than the EM scale due to the non compensating nature of the ATLAS detector. A second topo-cluster collection tries to correct for the hadronic response by classifying clusters as either electromagnetic or hadronic (primarily based on the energy density and the longitudinal shower depth), and applying local cluster weights accordingly. The LCW clusters are not detailed further more since they are not used in this thesis.

Jet energy scale (JES) calibration

JES calibration consists of multiple correction steps aimed at correcting the energy scale of the jets reconstructed at detector level (reco jets) to that of truth jets at particle-level [66, 67]. Figure 2.25 shows the different steps of the calibration. Regardless of the type of calibration of the jet inputs (EM-scale, PFlow-scale or any other), the calibration steps are the same but are implemented for each different jet reconstruction.
First, the origin correction corrects the jet direction from pointing from the geometrical center of the detector to the hard-scatter primary vertex PV0, but without changing the jet energy. As a result, the jet resolution is improved. Recently, the step of correcting the origin was moved to the jet reconstruction step. Jet constituents entering the jet finding algorithm are now corrected to point to the PV0. Next, the pile-up contribution to the jet energy and momentum is corrected using two components: an area based subtraction and an additional residual correction derived from MC simulation. Then the absolute calibration, based also on MC simulation, is applied which corrects both energy and direction of jets to the ones from truth jets. The global sequential calibration further improves the calibration and minimizes the differences between jet flavors using additional information from the ID, the MS and the calorimeter. At last, to catch any mis-modeling of the detector simulation which makes the correction not perfect for the data, a calibration using in-situ/real events is derived by comparing jets to a well measured reference object. For these corrections, det, the jet pointing from the geometrical center of the detector, is used to remove any ambiguity as to which region of the detector is probed by the jet. Let me detail each of the mentioned steps.

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Pile-up corrections

In-time and out-of-time pile-up contribute to the jet energy measured by the calorimeter. The first correction uses the pile-up energy density to subtract its contribution in jets according to the jet area. Each jet has a defined area, A, measured by the jet finding algorithm using ghost association. Infinitesimal momentum ghost particles are added uniformly in solid angle to the event before jet reconstruction. The ghost particles are then clustered with the real particles into a jet, with their infinitesimal momentum not affecting the clustering output. The jet area is then the number of ghost
particles associated with it divided by their area density. Next, we still need, for the first correction, to measure the pile-up pT density, , and subtract it from the jet pT. To measure , new jets are clustered using kt algorithm with a radius of 0.4 reconstructed only from positive-energy topo-clusters with jj < 2 and with no minimum pT threshold. The kt algorithm is used due to its sensitivity to soft radiation. Only the central region is used due to the higher occupancy of the forward detectors. The pT density of each jet is thus pT/A. is taken as the median of the pT density distribution (the median is used to reduce the bias from hard-scatter jets populating the high tails of the distribution). Figure 2.26 shows the distribution for a given NPV and .

Table of contents :

Introduction
1 Standard Model and Beyond, with a focus on QCD and its predictions 
1.1 The Standard Model (SM)
1.1.1 Lagrangian formulation
1.1.2 Perturbative approach
1.1.3 Renormalization and running coupling
1.2 Deeper into Quantum Chromo-Dynamics (QCD)
1.2.1 Asymptotic freedom
1.2.2 Showering, hadronization and confinement
1.2.3 Jet definition
1.2.4 The contents of the proton: Parton Distribution Functions (PDF)
1.2.5 p-p collision
1.3 Precision predictions
1.3.1 Partonic predictions
1.3.2 Non-perturbative MC simulation
1.3.3 Non-perturbative corrections to partonic predictions
1.3.4 EW corrections to QCD prediction
1.4 Beyond Standard Model (BSM)
1.4.1 Resonant models
1.4.2 Effective field model
2 The Large Hadron Collider (LHC) and the ATLAS experiment 
2.1 LHC
2.2 ATLAS: A Toroidal LHC ApparatuS
2.2.1 Inner Detector
2.2.2 Calorimeter
2.2.3 Muon spectrometer
2.2.4 Forward detectors
2.2.5 Trigge
2.2.6 Object reconstruction
2.3 Jet reconstruction and calibration
2.3.1 Jet constituents and reconstructions
2.3.2 Quality selection
2.3.3 Jet energy scale (JES) calibration
2.3.4 Jet energy resolution (JER)
3 Eta-intercalibration 
3.1 Introduction
3.1.1 Central reference method
3.1.2 Matrix method
3.1.3 Residual correction
3.1.4 Systematic uncertainties
3.1.5 Closure test
3.2 Analytic solution
3.3 Choice of Monte-Carlo generator
3.3.1 pavgT distributions
3.3.2 Truth level relative jet balance
3.3.3 pj T distributions
3.3.4 The dependence of the asymmetry on pj 3T =pavgT
3.3.5 Conclusion
3.4 Dependence of the calibration results on the pile-up profile
3.5 Forward and central triggers efficiencies and combination strategy
3.6 Calibration results
3.6.1 Data selection
3.6.2 binning optimization
3.6.3 Calibration central values
3.6.4 Closure test
3.6.5 Systematic uncertainties
4 Direct search for new phenomena in dijet events 
4.1 Introduction
4.2 Analysis overview
4.2.1 Observable
4.2.2 Background estimation
4.2.3 Systematic uncertainties
4.2.4 Search and Limits setting techniques
4.3 Folding technique
4.3.1 Motivation
4.3.2 Method description
4.3.3 Folding matrices from different MC samples
4.3.4 Tests on the folding procedure
4.3.5 Interpolation tests
4.3.6 Gaussian limits
4.4 Results
4.4.1 Search results
4.4.2 Limits setting results
5 Precision measurement: leading jet cross-section 
5.1 Motivation
5.2 Data selection and quality
5.2.1 Triggers
5.2.2 Cleaning criteria and jet time cut
5.3 Transfer matrix and binning optimization
5.4 Unfolding
5.4.1 The IDS unfolding method
5.4.2 Data-driven closure test and bias estimation
5.4.3 Tuning and results
5.4.4 The effect of jet order flips
5.5 Systematic uncertainties
5.5.1 JES
5.5.2 JER
5.5.3 Luminosity
5.5.4 Jet time cut
5.5.5 Jet cleaning
5.5.6 Total systematic uncertainties
5.6 Theoretical prediction
5.6.1 Fixed order calculations
5.6.2 Fixed order vs truth MC simulation
5.6.3 Theoretical systematic uncertainties
5.6.4 Non-perturbative correction factors
5.7 Results
Conclusion

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