Search for $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B_d^0\to {\mu }^{+}{\mu }^{-}$ Decays in $p\overline{p}$ Collisions at $\sqrt{s}=1.96\mathrm{T}\mathrm{e}\mathrm{V}$

We report on a search for $B_s^0\to {\mu }^{+}{\mu }^{-}$ and $B_d^0\to {\mu }^{+}{\mu }^{-}$ decays in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{T}\mathrm{e}\mathrm{V}$ using $171{\mathrm{p}\mathrm{b}}^{-1}$ of data collected by the CDF II experiment at the Fermilab Tevatron Collider. The decay rates of these rare processes are sensitive to contributions from physics beyond the standard model. One event survives all our selection requirements, consistent with the background expectation. We derive branching ratio limits of $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})<5.8\times {10}^{-7}$ and $\mathcal{B}(B_d^0\to {\mu }^{+}{\mu }^{-})<1.5\times {10}^{-7}$ at 90% confidence level.