Modeling of the EW backgrounds: corrections and reweightings

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SM Higgs Boson Phenomenology at Hadron Colliders

In Section 2.2 I gave an overview of the foundations of the SM of particle physics, with an additional scalar sector which introduces the Higgs boson as a new particle. I now use this theoretical framework and its predictions to characterize the behavior of the SM Higgs boson particle in the context of a proton-proton hadronic collider such as the LHC, discussing its main modes of production and decay. Particular emphasis is given to the V H associated production mode and the H ! bb decay channel, which are the focus of this research work.
Complete and detailed references for the theoretical calculations for the different Higgs production modes and decay channels are given in [51, 52].

Higgs Production Mechanisms

The main production modes of a SM Higgs boson are categorized depending on the different initial and final states that characterize the process. As shown in Figure 2.5 the production mechanisms, ordered from the highest to the lowest cross section at the LHC, are: gluonfusion (ggH), vector boson fusion (VBF), associated production to vector bosons (V H), associated production to heavy quarks pair (bbH, ttH), associated production to single top quark (tH).
Gluon fusion production mode: ggF The dominant production mechanism for a SM to the Higgs boson, hence at the lowest order the production is mediated by a fermion loop, as illustrated in Figure 2.6, and for this reason it may seem suppressed with respect to other processes at tree level. Nevertheless the gluon density within colliding protons is highly dominant with respect to other partons, as clearly shown by Figure 2.7 where the PDFs for gluon and quarks are shown (the typical range of the average momentum fraction carried by partons in Higgs production at LHC is 0:001 < x > 0:01 ), therefore the Higgs production cross section trough gluon fusion is dominant at hadron colliders. The intermediate fermionic loop has to contain colored particles (to allow coupling with gluons), and because the Higgs coupling is directly proportional to the mass of the interacting particles, the most important contributions come from heavy quark loops (top, bottom) with large Yukawa coupling.

Phenomenology of pp ! V H;H ! bb +leptons processes

The research work documented in this thesis focuses on the search for a Standard Model Higgs boson with mass of 125 GeV, produced in association with a vector boson V (W and Z) and decaying to a pair of bb quarks: pp ! V H;H ! bb.
In this Section I discuss the phenomenological features that characterize this set of processes: most of the aspects treated here are also valid for the BSM search for a CP-odd A boson via pp ! A ! Zh; h ! bb discussed in Chapter 7 (where h is the SM Higgs boson candidate with mh = 125 GeV), however limited to the production in association with Z bosons. Some key aspects of these processes are nonetheless different from the SM Higgs phenomenology, thus they are discussed in detail in Section 2.5.
As described in Section 2.3.2 the bb decay channel is particularly appealing since it allows us to consider more than half of the Higgs total with, with a branching ratio of BR(H ! bb) = 0:5809 with an uncertainty of 0.65% from missing higher order corrections, and parametric uncertainties of O(0:75%) of S, mc, mb and mt, and a partial width of 􀀀H!bb = 2:407 10􀀀3. GeV, for the measured value of mH = 125:09 GeV. In addition this decay channel is a unique probe to study the direct coupling of the Higgs boson to down-type quark.
The main production mechanism at the LHC, gluon fusion Higgs production, cannot be exploited since the SM bb pair production constitutes an irreducible and overwhelming background with cross section several orders of magnitude larger than the gg ! H ! bb one, as can be seen from Figure 2.15. We have to consider other production modes, with lower cross section but cleaner experimental signatures which allow for triggering, identifying and discriminating signal events with more peculiar features. VBF, V H and ttH mechanisms have been studied at the LHC in conjunction with H ! bb decays: the most significant results and the ones considered in this work are obtained from the V H associated production mode, exploiting the leptonic decays of the V boson to achieve good triggering conditions and strong background rejection.

Standard Model Issues and Open Points

In spite of the many features that qualify the SM as a solid and robust theory of elementary particles, there are some critical points that show the limits of its theoretical structure and hint at the fact that new physics may be required in order to describe consistently the known phenomena of particle physics.
Some of this issues come from experimental observations that are not predicted or described by the SM, other rely on theoretical preconceptions about the nature of a fundamental theory of particles: in this Section I give a brief overview of some of these problems.

Higgs/Hierarchy problem

As shown in Section 2.2 it’s possible to generate masses for the electroweak bosons and the fermions thanks to the SM scalar sector and, in detail, the introduction of an elementary Higgs field. For the consistency of the model the Higgs mass cannot be too different from the W boson mass, and the experimental discovery of the Higgs boson at LHC in the last year shows that mH 125 GeV.
However there is a complication: the tree-level Higgs mass receives quadratically divergent radiative corrections from interactions with gauge bosons, fermions and self interactions, as show in Figure 2.20 [73, 74].
In detail we can write the corrections as: m2 H = (m2 H)bare + O(; g2; h2)2 where is the next higher scale of the theory (after electroweak scale). If there were no higher scale could be interpreted simply as an ultraviolet cutoff, assuming that mH is a measured parameter and that (mH)bare is not a physics observable. However the general assumption is that the SM should be embedded in a different theory valid at a larger energy scale, therefore the integral has a cut off at this new higher scale .

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Dark matter and dark energy

The SM can describe the behaviour of ordinary matter, but we already know from cosmological measurements and gravitational effects that this only accounts for 4% of the content of the universe [85, 86]. The remaining part is divided between dark matter (22%) which has no electromagnetic interaction and can be detected only through gravitational force, and dark energy (74%) which appears to be associated with the vacuum in space.
The dark energy is distributed evenly throughout the universe (in space and in time) so it doesn’t have any local gravitational effects and leads to a repulsive force which tends to accelerate the expansion of the universe.
The SM cannot offer any explanation for this different kind of matter, and while some of its extensions (as Supersymmetry) provide good dark matter candidates, these have not yet been observed in experiments.

Matter anti-matter asymmetry

In our universe there is a large predominance of matter over anti-matter: from a cosmological point of view this may cause troubles, since it’s difficult to describe the evolution of the universe from a situation of balance, at the Big Bang, to the very asymmetric condition observed today [85].
The SM provide a source of CP violation that can take into account part of this asymmetry, coming from the presence of a complex phase in the CKM matrix [37] that describe the mixing of different quark flavours, within electroweak interactions. CP violation can break the balance between matter and anti-matter, throughout asymmetry between creation of particles and antiparticles.
Nonetheless the CP violation provided by the CKM matrix of the SM is not enough to justify the observed matter anti-matter asymmetry, therefore there should be other mechanisms which may explain it.

Table of contents :

1 Introduction 
2 The Theoretical Framework 
2.1 The Standard Model of Particle Physics
2.1.1 Fundamental Particles of Matter
2.1.2 Standard Model Lagrangian and Symmetry Group
2.1.3 QCD: SU(3) Lagrangian
2.1.4 Electroweak: SU(2) SU(1) Lagrangian
2.2 Scalar Sector of the Standard Model: Higgs Mechanism
2.2.1 Construction of the Scalar Sector
2.2.2 Scalar Field Potential
2.2.3 Higgs Mechanism
2.2.4 Main Standard Model features involving the Higgs scalar sector .
2.3 SM Higgs Boson Phenomenology at Hadron Colliders
2.3.1 Higgs Production Mechanisms
2.3.2 Higgs Decay Modes
2.3.3 Phenomenology of pp ! V H;H ! bb+leptons processes
2.4 Standard Model Issues and Open Points
2.4.1 Higgs/Hierarchy problem
2.4.2 Gravity problem
2.4.3 Dark matter and dark energy
2.4.4 Matter anti-matter asymmetry
2.4.5 Strong CP problem
2.4.6 Unification of coupling constants
2.4.7 Electromagnetic charge quantization
2.4.8 Hierarchy of fermionic families
2.4.9 Neutrino masses
2.5 Beyond the Standard Model Extensions: Two Higgs Doublet Models
2.5.1 Scalar potential in 2HDM
2.5.2 Flavour Changing Neutral Currents (FCNC) in 2HDM
2.5.3 Relevant phenomenology for Type I and II 2HDM
3 ATLAS and LHC 
3.1 Large Hadron Collider LHC
3.1.1 LHC Experiments
3.2 ATLAS Detector
3.2.1 Detector structure
3.2.2 Magnet System
3.2.3 The Inner Detector
3.2.4 The Calorimeter System
3.2.5 The Muon Spectrometer
3.2.6 The ATLAS Forward Detectors
3.2.7 The ATLAS Trigger and Data Acquisition System
4 Statistical Analysis: The Methodology 
4.1 Physics search as a statistical test
4.2 Treatment of the nuisance parameters in the Likelihood Fit
4.2.1 Smoothing and pruning of systematic uncertainties
4.2.2 Stability of the Likelihood fit: post-fit NPs and rankings
4.2.3 Nuisance parameters correlation
5 Event and Object Reconstruction 
5.1 Physics objects reconstruction
5.1.1 Tracks and vertexes
5.1.2 Leptons
5.1.3 Hadronic Jets
5.1.4 B-Jets
5.1.5 Missing Transverse Energy
5.2 Event reconstruction
5.2.1 Dijet mass resolution: b-jets energy corrections
5.2.2 Kinematic fit
5.2.3 Overlap removal
5.2.4 Truth-tagging
5.3 Objects and event reconstruction in the analysis of p s = 7 TeV data
6 Search for Standard Model V H(bb): Run-1 data 
6.1 Introduction: The Analysis Strategy
6.2 Data and Simulated Samples
6.3 Event selection
6.4 Multivariate Analysis: Boosted Decision Trees
6.4.1 Boosted Decision Trees
6.5 Background Estimate and Modeling
6.5.1 Estimate of the multijet background
6.5.2 Modeling of the EW backgrounds: corrections and reweightings .
6.5.3 Modeling of VH signal: NLO EW differential corrections
6.5.4 Background composition in the V H(bb) analysis
6.6 Systematic Uncertainties
6.6.1 Experimental systematic uncertainties
6.6.2 Uncertainties on the modeling of the multi-jet background
6.6.3 Uncertainties on the MC modeling of signal and backgrounds
6.7 Analysis of the p s = 7 TeV dataset
6.7.1 Main features of the 7 TeV analysis
6.8 Statistical Analysis: the Likelihood fit
6.8.1 The Likelihood function: categories and variables
6.8.2 Nuisance parameters in the Likelihood fit
6.8.3 Combination of p s = 7 TeV and p s = 8 TeV analyses
6.8.4 Measurement of the diboson V Z(bb) signal strength
6.9 Results
6.9.1 Nominal results for the V H(bb) search
6.9.2 Dijet-mass analysis as cross-check of the MVA approach
6.9.3 Diboson V Z(bb) measurement
7 Search for a CP-odd A boson decaying to Zh(bb) with data collected at p s = 13 TeV during the 2015 LHC data-taking 
7.1 Introduction: The Analysis Strategy
7.2 Data and Simulated Samples
7.3 Event selection
7.4 Background Estimate and Modeling
7.5 Systematic Uncertainties
7.5.1 Experimental systematic uncertainties
7.5.2 MC modeling systematic uncertainties
7.6 Statistical Analysis
7.7 Results and Interpretation
8 Search for Standard Model V H(bb): Run-2 data 
8.1 Introduction: The Analysis Strategy
8.2 Data and Simulated Samples
8.3 Event selection
8.4 Multivariate Analysis: Boosted Decision Trees
8.5 Background Estimate and Modeling
8.5.1 Estimate of the multijet background
8.5.2 Modeling of VH signal: NLO EW differential corrections
8.6 Systematic Uncertainties
8.6.1 Experimental systematic uncertainties
8.6.2 Uncertainties on the modeling of the multijet background
8.6.3 Uncertainties on the MC modeling of signal and backgrounds .
8.7 Statistical Analysis: the Likelihood fit
8.8 Results
9 Conclusions and Outlook 

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