We report on a search for $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B^0\to {\mu }^{+}{\mu }^{-}$ decays using proton-antiproton collision data at $\sqrt{s}=1.96\mathrm{TeV}$ corresponding to $10{\mathrm{fb}}^{-1}$ of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. The observed number of $B^0$ candidates is consistent with background-only expectations and yields an upper limit on the branching fraction of $\mathcal{B}(B^0\to {\mu }^{+}{\mu }^{-})<4.6\times {10}^{-9}$ at 95% confidence level. We observe an excess of $B_s^0$ 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 $B_s^0\to {\mu }^{+}{\mu }^{-}$ could produce such an excess or larger is 6.8%. These data are used to determine a branching fraction $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})=({1.3}_{-0.7}^{+0.9})\times {10}^{-8}$ and provide an upper limit of $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})<3.1\times {10}^{-8}$ at 95% confidence level.

• Received 28 January 2013

DOI:https://doi.org/10.1103/PhysRevD.87.072003