Identification of b-jets and investigation of the discovery potential of a Higgs boson in the $WH --> l \nu b \bar{b}$ channel with the ATLAS experiment

The Standard Model of particle physics describes three of the four known fundamental interactions between the elementary particles: the electromagnetic, weak and strong forces.It provides an extremely accurate description of the electroweak interactions up to the energy scales so far explored in high energy physics experiments. The Large Hadron Collider (LHC), which is presently starting to operate, will provide proton-proton collisions with an unprecedented centre-of-mass energy of $\sqrt{s} = 14~{\rm TeV}$ and with instantaneous luminosities of up to $10^{34}~{\rm cm^{-2}s^{-1}}$, and is therefore ideally suited to explore the TeV energy domain. Two multipurpose experiments, ATLAS and CMS, were built to analyse the collisions. The high instantaneous luminosities achievable at the LHC will result in a significant contamination of the signal processes by additional soft proton-proton collisions, usually known as pile-up interactions. In the course of this thesis several algorithms were developed for the ATLAS experiment to reconstruct the position of the primary interaction vertex with improved precision, which rely on adaptive methods to reduce both the influence of pile-up interactions and of secondary interactions. The Kalman filter and mathematical formalism these methods rely on is described in detail and their performance is analysed through the use of Monte Carlo simulations. There is one particle predicted by the Stan dard Model whose existence has not yet been proven: the Higgs boson, which plays the crucial role of giving other particles a mass without breaking the gauge symmetry the model is built upon. All physical properties of this particle are predicted by the theory, except its mass. The most stringent limit on the Higgs boson mass is provided by the direct searches performed at the LEP2 collider, which exclude a Standard Model Higgs boson with a mass below $114.4~{\rm GeV}/c^2$ at 95\% confidence level. Indirect constraints from electroweak precision observables, where the Higgs boson enters through virtual corrections, predict a Higgs boson mass of $87^{+35}_{-26}~{\rm GeV}/c^2$. Under the assumption that the Standard Model is valid, the Higgs boson mass is expected to be found close to the LEP2 limit. In the low mass region, the Higgs boson decays preferentially into a pair of $b$-quarks, which can be observed in the detector as $b$-quark jets. The experimental identification of $b$-jets and the rejection of the copious backgrounds from $u$, $d$, $s$-quarks and gluon jets is made possible by the relatively long lifetime of $b$-hadrons ($\beta\gamma c\tau = O({\rm mm})$), whose decay particles are thus produced at a secondary vertex which is sufficiently displaced with respect to the primary interaction vertex. The most promising $b$-jet identification algorithms are based either on detecting individual charged particle tracks wh ich are displaced with respect to the primary interaction vertex or on the explicit reconstruction of the secondary vertex position. In this thesis a sophisticated secondary vertex reconstruction algorithm is presented, which exploits the topological structure of weak $b$- and $c$-hadron decays inside a $b$-jet and is implemented mathematically as an extension of the Kalman filter formalism for vertex reconstruction. The application to a $b$-jet identification algorithm is discussed in detail and its performance is compared with the standard algorithms available in ATLAS. Even under the hypothesis that an excellent $b$-jet identification performance can be achieved, the search for Higgs bosons decaying to a $b$-quark pair will still suffer from copious irreducible backgrounds with $b$-jets produced by strong interactions. This is the main reason why no Higgs boson search based on the $\bbbar$ decay mode at the LHC is actually considered to yield a significant discovery potential. Searches with the Higgs boson decaying into a pair of photons or taus are typically preferred in the $m_{H}=115$-$130~{\rm GeV}/c^2$ mass region. Recently, a new approach for the search for Higgs bosons decaying to a pair of $b$-quarks was proposed~\cite{Butterworth:2008iy}, which relies on the already well known associated production of a Higgs boson with a $W$ or $Z$ boson, but where only the phase space region where the Higgs and the vector bosons are produced at large transverse momenta is considered. This allows a more efficient rejection of the backgrounds, but, at the same time, poses several new problems to the object identification algorithms. A first detector level study of the $WH \to \ell\nu\bbbar$ Higgs boson search channel, based on a realistic simulation of the ATLAS detector, is presented in this thesis. Special emphasis is put on the implementation of the jet reconstruction algorithm and on the optimisation of the $b$-jet identification performance in this specific scenario. The discovery potential, based on simple event counting, is analysed in terms of statistical significance. A significant degradation of the discovery potential is expected due to the sizable systematic uncertainties affecting the expected amount of background feeding into the signal selection. In order to reduce the impact of these uncertainties, a maximum likelihood based estimator is defined to extract the number of signal and background events directly from the data, based on the expected distributions of a few discriminating variables. Special care is taken to evaluate the effect of experimental systematic uncertainties and the discovery potential is evaluated for Higgs boson masses in the range between $115$ and $130~{\rm GeV}/c^2$.