$B^{0}_{(s)} \to \mu^{+}\mu^{-}$ searches at LHCb

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 (SM) with a larger Higgs sector. In the SM these processes are highly suppressed as they occur through loop processes. Together with an associated helicity suppression renders the branching fraction of these decays to be: $\mathcal{B} (B^{0}_{s} \to \mu^{+}\mu^{-}) = 3.2 \pm 0.2 \times 10^{-9}$ and $\mathcal{B}(B^{0} \to \mu^+ \mu^-) = 0.10 \pm 0.01 \times 10^{-10}$. Any deviation from these well predicted branching fractions can lead to indications of physics beyond the SM. For instance, they can be significantly enhanced within Minimal Supersymmetric extensions of the SM (MSSM) due to contributions from new processes or new heavy particles. In these scenarios, $\mathcal{B}(B^{0}_{s} \to \mu^{+}\mu^{-})$ is proportional to $\tan^6 \beta$, where $\tan \beta$ is the ratio of the vacuum expectation values of the two Higgs fields.