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The Prediction of the SM Higgs boson

Gauge symmetries

In the Standard Model, the description of the interactions between elementary parti-cles is derived using symmetry principles. A symmetry is understood as an operation that can be performed on a system leaving it invariant. From Noether’s theorem, every symmetry of nature is associated with the conservation of a physics quantity.
The Standard Model is constructed using the so-called local gauge symmetry, in which the symmetry of the interactions is associated with the conservation of some quantities (charge, color, etc.) locally, i.e. at the point where the interaction occur. A local gauge transformation is one whose parameters depend on the space-time point where it is applied, like:
where is a function of the time and space coordinates.
Consider the Dirac Lagrangian, which describes a spinor eld, associated with an electron like particle with spin 12 and mass m, If the transformation of Equation 1.1 is applied to this Lagrangian, one can see that it is not invariant under this transformation.
In order to make this Lagrangian locally gauge invariant, one is obliged to add some extra terms. One ends up introducing a vector eld AM.
The rst term is the kinetic term of the eld, where F = @ A @ A . It is invariant under the transformation in Equation 1.3, but the second term is not. Thus, the vector eld has to be necessarily massless (mA = 0), to keep the local gauge invariance.
The vector eld A represents the photon eld, and the Lagrangian in fact describes the interactions between Dirac elds and the photon Maxwell elds (quantum elec-trodynamics).
The symmetry considered above is called U(1) gauge invariance. Similarly, a model that describes the strong interactions is obtained with local gauge trans-formations of a group SU(3), and the whole Standard Model is constructed with a symmetry group denoted as SU(3)C SU(2)L U(1)Y . The rules that govern the interactions are extracted by interpreting the Lagrangians after making them satisfying these symmetries.

Spontaneous symmetry-breaking

While the procedure explained above works to describe the strong and electromag-netic interactions, its implementation is not straightforward for the weak interaction. The gauge eld introduced in Equation 1.5 must be massless, otherwise the desired local gauge invariance is broken. But, the W and Z0 vector bosons that mediate the weak interactions are massive; their mass explains the relative weakness of the weak force with respect to the electromagnetic force, and the short range of weak interactions.
The way to introduce the massive vector bosons in the Standard Model keep-ing the local gauge invariance is to use the mechanism proposed by Higgs, Brout, Englert, Guralnik, Hagen and Kibble [4{6], commonly known as Higgs mechanism, in which a phenomenon called spontaneous symmetry-breaking is used. Here, an example is given to show how this mechanism works.
Consider a complex eld that combines two real elds .
As above, some terms need to be added, introducing gauge elds. In fact, there is a procedure to nd the required terms, which consists on replacing the derivative of the Lagrangian by a covariant derivative, which for this example is In order to interpret this Lagrangian, a particular treatment is required because of the form of the potential (in square brackets). The ground state of this potential is in nitely degenerated, as illustrated in Figure 1.1. There are in nite states in the circle of minimum potential, v is called vacuum expectation value. One has to choose one ground state as ref-erence, and develop the Lagrangian re-writing the eld in terms of elds that uctuate around the chosen ground state.
The fact of choosing one ground state among the in nite possibilities and re-formulating the Lagrangian based on it is what is called spontaneous symmetry-breaking, because the symmetry is left with an arbitrary selection to perform the calculation.
The second term corresponds to a massless scalar eld; this type of elds are called Nambu-Goldstone bosons, and are known to appear when there is spontaneous sym-metry breaking. And the third term is a massive gauge vector eld, just as required in the electroweak model; the mass of this gauge vector eld is mA = qv (1.16).

The Higgs mechanism

In the previous section, the required massive vector eld has been introduced; never-theless, the Goldstone boson also introduced is not compatible with the experimental observations, and in addition the term in the third line suggest that the current in-terpretation of the Lagrangian is not correct. This issue is solved in the so-called Higgs mechanism [4{6] by choosing a particular gauge.
The Goldstone boson has disappeared; more precisely, it has been \eaten » by a new A polarization. And the particle associated with is what is called a Higgs particle.

The Prediction of the SM Higgs boson

The SM Higgs boson

In the Standard Model, the Higgs mechanism is used to introduce the mass terms of the W and Z0 vector bosons. In this case, a SU(2) doublet of complex scalar.
This time, the Lagrangian is required to be invariant under local gauge trans-formations of the group SU(2)L U(1)Y , which introduces four gauge vector elds W a, a = 1; 2; 3, and B , for the SU(2) and U(1) symmetry groups respectively. These gauge elds are introduced by replacing the derivative of the Lagrangian by the following covariant derivative.
where g and g0 are coupling strength constants, a are the Pauli matrices, and Y is a hyper-charge associated to the U(1) group.
In order to interpret the Lagrangian, the potential ground state considered is 1 = 2 = 4 = 0; 3 = v; (1.23) and the scalar doublet eld is parametrized around this ground state with four real elds a (with a = 1; 2; 3) and h, 1 0 a = p v + h ei a=v: (1.24) .
After developing the Lagrangian, the three elds a disappear, and h is the only one that remains. The particle associated with h is the predicted Standard Model Higgs boson. Its mass is given by the relationship and are free parameters, and so the Higgs boson mass is also free in the theory.
The physical vector boson elds are linear combinations of the elds W a and B .

Constraints on the Higgs boson mass

Theoretical constraints

There are some theoretical constraints on the mass of the Standard Model Higgs boson mH, correlated with the energy scale beyond which the SM is not anymore valid and from which new phenomena should emerge. Namely, the requirements bringing these constraints are: unitarity of the amplitude for electroweak scatter-ing processes, renormalization and triviality of the electroweak theory, and vacuum stability.
The unitarity requirement constraints the Higgs boson mass to be below 700 GeV; otherwise unitarity is violated, unless there is physics beyond the SM at energies in the TeV range that restores it. This is because the participation of the Higgs boson in some vector boson scattering processes regularizes their cross-sections at high energies, avoiding unitarity violation, but the Higgs boson coupling with the vector bosons depends on its mass.
The renormalization and triviality of the electroweak theory sets an upper limit to the Higgs boson mass that vary with the energy scale , as shown in Figure 1.2 by the red band. From the theory renormalization, the Higgs boson quartic self-coupling depends on the energy scale of the interaction; at high energy, the quartic self-coupling of the Higgs boson grows and eventually becomes in nite. The energy scale point where the coupling becomes in nite, called Landau pole, depends on the Higgs boson mass. Then, from another point of view, for a given energy domain of validity of the Standard Model there is a limit for the Higgs boson mass.
From the theory renormalization a lower limit for mH also results, that also depends on the ; it is known as the vacuum stability bound and is shown by at the TeV scale, the Higgs boson mass is allowed to be in the range 50 GeV < MH < 800 GeV (1.181) while, requiring the SM to be valid up to the Grand Unification scale, ΛGUT ∼ 1016 GeV, the Higgs boson mass should lie in the range
130 GeV < MH < 180 GeV (1.182).

The fine–tuning constraint

the greenFinally, bandlasttheoreticalinFigureconstraint1.2.comes from the fine–tuning problem originating from the radiative corrections to the Higgs boson mass. The Feynman diagrams contributing to the one–loop radiative corrections are depicted in Fig.

Experimental exclusion before the LHC

The experiments at the Large Electron-Positron collider (LEP) have excluded the existence of a Standard Model Higgs boson with mass below 114.4 GeV, with 95% of con dence level. This exclusion has been obtained from data collected in e+e collisions at di erent center-of-mass energies between 91 and 209 GeV. In these collisions the SM Higgs boson was expected to be produced through the so-called Higgs-strahlung process e+e ! Z ! HZ, where the Higgs boson is radiated by a Z vector boson. The plot on the left side of Figure 1.3 shows the nal results on the Higgs boson search at LEP [7]. In this plot, the exclusion limits are expressed as limits on the Higgs boson to Z vector boson coupling.
On top of the LEP results, the Tevatron experiments also set exclusion limits on the SM Higgs boson mass; the right side plot of Figure 1.3 shows the results published by Tevatron in the summer of 2011 [8]. From these results, the SM Higgs boson was excluded in the mass range 156 – 177 GeV, and also in a small range at low mass till 108 GeV, con rming the LEP results. These limits were set based on data collected on proton-antiproton collisions at a center-of-mass energy of ps = 1:96 TeV.

Indirect experimental constraints

In addition to the direct mass range exclusions, information about the possible value of the Higgs boson mass have been obtained through a global t to electroweak pre-cision measurements, and testing the coherence of the Standard Model. This is done exploiting predicted dependency of electroweak processes on the Higgs boson mass.
This t has been performed by several groups: among others the LEP Electroweak Working Group [25] and the G tter group [26]; Figure 1.4 shows as an example the result obtained by G tter for the summer of 2011.
The plot shows the resulting 2 test statistic values as a function of the Higgs boson mass hypothesis mH. Independently of the Higgs boson direct search, if the Standard Model is the right theory, this result indicated that the Higgs boson mass is below 130 GeV with 68% of con dence level, and below 170 GeV with 95% of con dence level. Further details can be found in [27].
At the LHC, the Higgs boson may be produced via several different processes, such as those shown in Fig. 1. These have all been calculated at NLO precision or better and the cross-sections are shown.

The Higgs boson search at the LHC

Higgs boson production at the LHC

In the proton-proton collisions at the LHC, the Higgs boson is expected to be produced through four di erent main processes: gluon fusion, vector boson fusion (VBF), associated production with a vector boson and associated production with a top-antitop quark pair. Figure 1.5 shows Feynman diagram examples for these four processes, and Figure 1.6 shows the Standard Model expected cross-sections for each process as a function of the Higgspboson mass hypothesis, for proton-proton collisions at a center-of-mass energy of s = 8 TeV [28{30].
The gluon fusion (Figure 1.5-a) is the main Higgs boson production mode at the LHC. The gluon fusion is produced through a loop of quarks, mainly top quarks. Its cross-section is computed up to next-to-next-to-leading order (NNLO) in QCD [31{ 36], improved with QCD soft-gluon re-summation calculations up to next-to-next-to-leading logarithmic order (NNLL) [37, 38] and next-to-leading order (NLO) EW corrections [39, 40]. The computed values are compiled in [41{43]. The theoretical uncertainty on the gluon fusion cross-section is about 10%.
The vector boson fusion VBF (Figure 1.5-b) is the second-leading mode in the Higgs boson production at the LHC, contributing to about 10% of the production for a Higgs boson mass of 150 GeV. In this process the Higgs boson is produced by the interaction of two vector bosons radiated by incoming quarks. The VBF has an experimental signature that consists in the presence of two jets (the experimental signature of quarks) in the forward regions of the detector, close to the proton beam axis (details about the experiment geometry are discussed in Chapter 2). This signature allows reducing backgrounds in the Higgs boson search and disentangling VBF events from other production modes. The cross-section for the vector boson fusion is calculated at NLO in QCD, with electroweak (EW) corrections [44{46] and approximate NNLO QCD corrections [47]. The uncertainty on this cross-section is about 3%.
In the associated production with a vector boson (Figure 1.5-c), the Higgs boson is radiated by a vector boson, the so-called Higgs-strahlung mechanism. The pres-ence of the vector boson in the nal state represents an important distinguishing signature for this process. (This process was the main Higgs boson production mode at LEP, and the second leading one at Tevatron, where its signature was exploited by the search channels with the highest sensitivity.) The cross-sections for this process is calculated at NLO [48] and at NNLO [49], and NLO EW radiative corrections [50] are applied. The uncertainty on this cross-section is about 4%.
The associated production with top quarks (Figure 1.5-d) has a low cross-section, two orders of magnitude below the one for the gluon fusion; nevertheless its signa-ture can be exploited in the event selections, for instance for a low mass Higgs boson, when it decays to a b-quark pair (see next section). For the ttH associated production, the cross-section calculations are done at NLO in QCD [51{54].


Higgs boson search channels

The Higgs boson decay branching ratios are shown on the left side of Figure 1.7, and the cross-section times branching ratio for the Higgs boson search channels at the LHC are presented on the right side; both sets of values are shown as a function of the Higgs boson mass hypothesis (MH).
At the very low mass, the Higgs boson decays mainly to a bb pair; nevertheless, at the LHC, due to the high cross-sections for the QCD processes with the same signature, the background for an inclusive bb channel is too high to allow a sensitive search. Additionally, the experimental bb invariant mass resolution is low, which makes the observation of a signal even more di cult in this decay channel. This Higgs boson decay is only considered when the signature of the V H and ttH associ-ated production processes are exploited. For similar reasons the H ! gg, H ! and H ! cc, decays does not provide good sensitivity for a Higgs boson observa-tion. However, the H ! decay is considered exploiting the VBF production mode signature.
Above mH 125 GeV, the H ! W W ( ) ! l l channel becomes the one with highest sensitivity, until mH 200 GeV. Due to the presence of neutrinos in the nal state (which are invisible for the detectors), the full invariant mass can not be reconstructed, but only the transverse invariant mass, which corresponds to the particles’ kinematics in the plane perpendicular to the beam axis. But, the high cross-section and the experimental signature for this channel give a favorable signal-to-background ratio.
For mH & 200 GeV, the H ! ZZ channels are dominant in sensitivity.
The H ! ZZ( ) ! 4l with l = e; is a particularly good channel. It has good invariant mass resolution, it provides high sensitivity to a Higgs boson signal in basically all the mass range (120 – 600 GeV), and the background rate for this channel is quite low; for this reason it is sometimes referred to as the golden channel.
Around twice the top quark mass, mH 350 GeV, the branching ratio for the H ! tt decay increases rapidly. Nevertheless, the high QCD background prevents the Higgs boson search in this channel.
Details on the Higgs boson production at the LHC and the decay processes can be found in [29, 30].

The H ! channel

As mentioned above, the H ! channel is the most sensitive to observe the Higgs boson at the very low mass, below 125 GeV. At the LHC, the search in this channel is performed from 110 GeV, around the exclusion limit set by LEP and Tevatron, up to 150 GeV.
The Higgs boson decays to two photons through loops of W bosons and fermions, mainly top quarks, as shown in Figure 1.8. The branching ratio for this decay in the mentioned mass range is about 0.2%. The calculation of this branching ratio include NLO corrections in QCD and EW [55, 56], and it has an uncertainty of 5%.
This channel is a ected by a large amount of background. The main background source is the QCD diphoton production, called irreducible background. Figure 1.9 shows Feynman diagrams for the three main processes contributing to the photon pair production at the LHC: a) the Born process qq ! , b) the bremsstrahlung process qg ! q , and c) the box process gg ! . The total cross-section for the diphoton production [57] is about three orders of magnitude higher than the one for the signal process pp ! H ! .
The second most important source of background is the associated production of a photon with one quark or gluon, experimentally one jet. The experimental signal of a quark or a gluon in the detector can eventually be wrongly taken as a photon signal (details are discussed in Chapter 3). Feynman diagrams for the main photon-jet production processes are shown in Figure 1.10. At the LHC, the total cross-section for these processes [10, 58] is about six orders of magnitude above the pp ! H ! cross-section. Therefore, a good photon-jet discriminating power is necessary in the experiments, for keeping this background low.
Additional sources of background are the QCD production of multi-jets and the Drell-Yan processes; the Drell-Yan processes are those that yield two electrons in the nal state. They contribute to the background when both objects, both jets or both electrons, are mis-identi ed as photons. Thanks to the photon identi cation capabilities of ATLAS, the background corresponding to these processes represents only a few percent of the diphoton candidate samples.

The Higgs boson search at the LHC

The Large Hadron Collider (LHC) is a proton-proton circular accelerator and collider constructed at CERN, at the Franco-Swiss frontier, near Geneva. It has a circumference of 27 km and is installed underground, about 100 m below the surface. It is placed in a tunnel that was previously occupied by the LEP collider. The LHC has been designed to perform collisions at an unprecedented energy and luminosity1, speci cally a proton-proton center-of-mass energy of ps = 14 TeV and a luminosity of L = 1034 cm 2s 1 (the collisions at the previous most powerful hadron collider, the Tevatron, were performed at ps = 1:96 TeV and L = 4 1032 cm 2s 1 [63]). The LHC can also collide heavy ions, speci cally lead nuclei, with an energy of 2.8 TeV per nucleon and a luminosity of 1027 cm 2s 1.


The LHC allows to perform a large variety of particle physics studies. Here, they are synthesized in three general objectives:
The main objective is the search of new particles, starting with the Standard Model Higgs boson (on which this thesis is reporting about), the particles predicted by supersymmetric theories and others predicted by more exotic models. The beam energy at the LHC will allow exploring up to a few TeV’s in the mass scale.
Studying with high precision the Standard Model (SM) physics processes. The LHC is a large source of b-quarks, top quarks, vector bosons, among other particles and physics processes. It will allow for instance to improve the measurements of the top quark and the W boson masses, and of their production cross-sections. The large amount of B hadrons produced allows studying CP violation and determining with higher precision the CKM matrix parameters. Deviations of these precision measurements from the Standard Model predictions would be indirect evidences of new physics.
Studying the strong interaction in a quark-gluon plasma. The heavy ion colli-sions at the LHC produce a state of matter with extremely high energy density and temperature. At this state, quarks and gluons are expected to be no longer con ned inside hadrons. This state is the so called quark-gluon plasma.

General layout

A set of linear and circular accelerators are used to accelerate protons and heavy ions before their injection into the LHC. Most of these accelerators already existed at CERN before the design of the LHC, and they were upgraded to satisfy the LHC necessities. Figure 2.1 shows a schematic view of the CERN accelerator complex. For protons, the acceleration chain is as follows: protons reach 50 MeV of energy in a linear accelerator (LINAC), then 1.4 GeV in the Synchrotron Booster, 25 GeV in the Proton Synchrotron (PS) and 450 GeV in the Super Proton Synchrotron 1 In particle physics, luminosity, or instantaneous luminosity, is an important quantity to char-acterize the performance of particle colliders because the particle interaction rate depends on this quantity (more details about luminosity are discussed in Section 2.1.5).

Table of contents :

1 The Standard Model Higgs boson 
1.1 The Prediction of the SM Higgs boson
1.1.1 Gauge symmetries
1.1.2 Spontaneous symmetry-breaking
1.1.3 The Higgs mechanism
1.1.4 The SM Higgs boson
1.2 Constraints on the Higgs boson mass
1.2.1 Theoretical constraints
1.2.2 Experimental exclusion before the LHC
1.2.3 Indirect experimental constraints
1.3 The Higgs boson search at the LHC
1.3.1 Higgs boson production at the LHC
1.3.2 Higgs boson search channels
1.3.3 The H ! channel
2 The ATLAS experiment at the LHC
2.1 The Large Hadron Collider
2.1.1 Introduction
2.1.2 Objectives
2.1.3 General layout
2.1.4 The LHC main ring
2.1.5 Performance
2.1.6 Operational history
2.2 The ATLAS experiment
2.2.1 Detector overview
2.2.2 The ATLAS collaboration
2.2.3 Detector requirements
2.2.4 Coordinate system and nomenclature
2.3 Magnet system
2.3.1 Central solenoid
2.3.2 Barrel and end-cap toroids
2.4 Inner detector
2.4.1 Precision silicon sensors
2.4.2 Transition radiation tracker
2.5 Calorimeters
2.5.1 The electromagnetic calorimeter
2.5.2 Hadronic calorimeter
2.5.3 Forward calorimeters
2.6 Muon spectrometer
2.7 Trigger system 54
2.8 Computing framework
2.8.1 Computing facilities
2.8.2 Software
2.8.3 Data processing and formats
2.9 Simulation
3 Identifcation and reconstruction of photons in ATLAS 
3.1 Reconstruction of photon candidates
3.2 Identifcation of electrons, converted and unconverted photons
3.3 Photon energy measurement
3.4 Photon identifcation
3.5 Isolation criteria
4 Statistical analysis procedure 
4.1 General aspects
4.2 Testing the signal-plus-background hypothesis
4.3 Asymptotic approximation for setting exclusion limits
4.4 Testing the background-only hypothesis
4.5 Systematic uncertainties
5 The H ! analysis 
5.1 Introduction
5.2 Samples
5.2.1 Data samples
5.2.2 Monte Carlo samples
5.2.3 Diphoton event selection
5.2.4 Selection of the primary vertex
5.2.5 Diphoton invariant mass
5.3 Expected signal
5.3.1 Signal mass distribution
5.3.2 Uncertainty on the signal peak position
5.3.3 Signal eciency and yields
5.4 Background composition
5.4.1 Decomposition methods
5.4.2 Drell Yan Background
5.4.3 Background composition results
5.5 Event categorization
5.5.1 Categorization according to the photon conversion status and direction
5.5.2 Categorization based on the p Tt discriminant variable
5.5.3 2-jet category
5.5.4 Categorization summary
5.5.5 Systematic uncertainties on the distribution of signal events among the categories
5.6 Data modeling
5.6.1 Signal parametrization
5.6.2 Signal systematic uncertainties
5.6.3 Background parameterization and uncertainties
5.7 Results
5.7.1 Exclusion limits
5.7.2 Excess quantifcation
5.7.3 Excess characterization
6 Overview of recent results of the Higgs boson search 
6.1 Observation of a new particle
6.2 Properties of the new boson


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