Use of $B \to h^+ h^{'-}$ as control channels for the measurement of BR$(B^0_s \to \mu^+ \mu^-)$ at LHC$b$

In spite of the impressive success of the Standard Model, some theoretical and experimental facts suggest that it might not be the $final$ theory, and hence that $new$ $physics$ exists. Decays of $B$ meson are an exceptional source of observables where physics beyond the SM could lead to unambiguous effects. Indeed, measurements in this sector provide some of the first possibilities of observing effects from new physics at the LHC. This is the case of the branching ratio of the yet unobserved decay $B^0_s \to \mu^+ \mu^-$. This observable is precisely predicted by the Standard Model and hence it is also very sensitive to new physics. The conception of LHC$b$ as a dedicated experiment for $B$ physics studies puts it is an outstanding position for measuring this branching ratio with respect to other experiments operating at the LHC. The measurement of the branching ratio of $B^0_s \to \mu^+ \mu^-$ at LHC$b$ widely uses methods for both calibrating and normalizing independently of the Monte Carlo simulations, based on control channels. The family of two-body decays of $B$ mesons into charged pions and kaons, referred to as $B \to h^+ h^{'-}$, are particularly interesting due to the very similar kinematical properties with respect to those of $B^0_s \to \mu^+ \mu^-$. The possible uses of such channels within the measurement of the branching ratios of $B^0_s \to \mu^+ \mu^-$, as well as the methods that have been developed in order to correct the differences between $B^0_s \to \mu^+ \mu^-$ and $B \to h^+ h^{'-}$, constitute the subject of this thesis. Chapter 1 justifies the interest of the measurement of the branching ratio of $B^0_s \to \mu^+ \mu^-$, as a test of the Standard Model and its extensions. Chapter 2 discusses the requirements for a $B$ physics experiment at the LHC and describes the LHC$b$ detector. Chapter 3 explains the analysis that has been developed at LHC$b$ for the measurement of the branching ration of $B^0_s \to \mu^+ \mu^-$. The event selection and the definition of discriminant variables are discussed in detail. In addition, the use of $B \to h^+ h^{'-}$ as control channels for this analysis is introduced. Chapter 4 explains the uses of $B \to h^+ h^{'-}$ for calibrating and normalizing the measurement, and shows the similarities and the differences between this family of channels and $B^0_s \to \mu^+ \mu^-$. The common selection of $B^0_s \to \mu^+ \mu^-$ and $B \to h^+ h^{'-}$ and the use of information for particle identification are discussed in detail. Chapter 5 describes methods for correcting the differences between $B^0_s \to \mu^+ \mu^-$ and $B \to h^+ h^{'-}$ caused by track reconstruction, particle identification and trigger. Finally, Chapter 6 presents the current measurement of the upper limit for BR$(B^0_s \to \mu^+ \mu^-)$ set by LHC$b$, and discusses the impact of the studies developed in this document.