Study of $B \to \mu^+\mu^-$ decays with the ATLAS detector

This thesis presents the search for the very rare decays $B_s \to \mu^+\mu^-$ and $B_d \to \mu^+\mu^-$, based on 26.3 $\text{fb}^{-1}$ of $\sqrt s ~=~13$ TeV LHC proton–proton collision data collected in 2015 and 2016 by the ATLAS experiment. $B \to \mu^+\mu^-$ decays are considered one of the pillars of the ATLAS experiment searches for New Phenomena with flavour, thanks to an extremely clean experimental signature, a very small and precisely constrained Standard~Model (SM) amplitude and the potential sizable interference from New Physics phenomena. This work greatly improves past ATLAS results, including a new dataset, improved statistical and systematic extraction techniques, up-to-date muon identification tools and background models. The analysis results in the experiment's most precise measurement to date of the branching fraction ${\mathcal B}(B_s \to \mu^+\mu^-)~=~\left(~3.2^{+1.1}_{-1.0}~\right)~\times~10^{-9}$ and upper limit ${\mathcal B}(B_d \to \mu^+\mu^-)~<~4.3~\times~10^{-10}$ at $95\%$ confidence level. Combining with the ATLAS Run 1 analysis results in ${\mathcal B}(B_s \to \mu^+\mu^-)~=~\left( 2.8^{+0.8}_{-0.7}~\right)~\times~10^{-9}$ and ${\mathcal B}(B_d \to \mu^+\mu^-)~<~2.1~\times~10^{-10}$ at $95\%$ confidence level: the most stringent experimental limit available to this date. All measurements are compatible with the SM prediction. Projections on the future ATLAS sensitivity are also performed.