Search for $B^0_s \to \mu^+ \mu^-$ and $B^0 \to \mu^+ \mu^-$ decays in CMS

The rare decays $B^0_s \to \mu^+ \mu^-$ and $B^0 \to \mu^+ \mu^-$ are sensitive to physics beyond the Standard Model as their branching fraction can be highly enhanced or suppressed in new physics models. The CMS experiment at the LHC has reported the studies of these rare decays in $pp$ collisions at $\sqrt{s}=7~$TeV, corresponding to an integrated luminosity of 5~fb$^{-1}$. In both decays, the number of observed events is consistent with the expectation from background plus Standard Model signal prediction. Results of the combination of the exclusion limits for two rare decays in different LHC experiments will also be presented.