Towards the first $B(B^{0}_{(s)} \to \mu^+\mu^−)$ measurements with the LHCb detector

The rare decays $B^{0}_{s} \to \mu^+ \mu^-$ and $B^{0} \to \mu^+ \mu^-$ are benchmark channels to constrain models beyond the Standard Model (BSM) with a larger Higgs sector. In the SM, the branching fraction of these decays is predicted with a good accuracy: $\mathcal{B}(B^{0}_{(s)} \to \mu^+ \mu^-) = (3.2 \pm 0.2) \times 10^{-9}$ and $\mathcal{B}(B^{0} \to \mu^+ \mu^-) = (0.10 \pm 0.01) \times 10^{-10}$. Any deviation from these values can lead to indications of physics BSM. The core of this thesis comprises two main topics: the background rejection and the signal yields extraction. We have optimized a multivariate classifier based on the boosted decision trees technique allowing for a drastic reduction of the $B \to h^+ h'^-$ ($h \equiv \pi, K$) background. After the selection process, about 76$\%$ of the combinatorial background for $B^{0}_{s} \to \mu^+ \mu^-$ is removed, while keeping a signal efficiency of about 92$\%$. A further discrimination between signal and background is accomplished with another multivariate classifier optimized to have a large background rejection in the low signal efficiency region. The work presented in this thesis describes the optimization of a boosted decision trees classifier that suppresses 99.9$\%$ of the background, after the aforementioned selection process, for a signal efficiency of 50$\%$. We have proposed a method to estimate the signal yields present in our data sample using an extended maximum likelihood fit. The validation of the fit using simulation reflects the proper estimation of the statistical uncertainties, and systematic uncertainties have been carefully studied and taken into account in the final results for the 2011 1 fb$^{-1}$ data sample: $\mathcal{B}(B^{0}_{s} \rightarrow \mu^+\mu^-) = (1.4 \left(^{+1.6}_{-1.1} \right)_{(stat)} \left(^{+0.5}_{-0.8} \right)_{(syst)} ) \times 10^{-9}$ and $\mathcal{B}(B^{0} \rightarrow \mu^+\mu^-) = (0.3 \left(^{+0.5}_{-0.4}\right)_{(stat)} \left(^{+0.5}_{-0.3}\right)_{(syst)}) \times 10^{-9}$. Given the lack of signal evidence, upper limits on the branching fractions are computed: $\mathcal{B}(B^{0}_{(s)} \to \mu^+ \mu^-) < 4.5 \times 10^{-9}$ and $\mathcal{B}(B^{0} \to \mu^+ \mu^-) < 1.0 \times 10^{-10}$, which are the most restrictive limits up to date.