Search for $B_s \rightarrow \mu^{+}\mu^{-}$ and $B_d \rightarrow \mu^{+}\mu^{-}$ decays with the full CDF Run II data set

We report on a search for \bsmm\ and \bdmm\ decays using proton-antiproton collision data at $\sqrt{s}=1.96$ TeV corresponding to $10 \fb$ of integrated luminosity collected by the CDF detector at the Fermilab Tevatron collider. The observed number of \bd\ candidates is consistent with background-only expectations and yields an upper limit on the branching fraction of $\brbdmm<4.6\times 10^{-9}$ at 95% confidence level. We observe an excess of \bs\ candidates. The probability that the background processes alone could produce such an excess or larger is 0.94%. The probability that the combination of background and the expected standard model rate of \bsmm\ could produce such an excess or larger is 6.8%. These data are used to determine a branching fraction $\brbsmm = (1.3^{+0.9}_{-0.7}) \times 10^{-8} $ and provide an upper limit of $\brbsmm<3.1\times 10^{-8}$ at 95% confidence level.