Search for the flavor-changing neutral current decay $D^0\to {\mu }^{+}{\mu }^{-}$ in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{}\mathrm{TeV}$

We report on a search for the flavor-changing neutral current decay $D^0\to {\mu }^{+}{\mu }^{-}$ in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{}\mathrm{TeV}$ using $65{\mathrm{pb}}^{-1}$ of data collected by the CDF II experiment at the Fermilab Tevatron Collider. A displaced-track trigger selects long-lived $D^0$ candidates in the $D^0\to {\mu }^{+}{\mu }^{-}$ search channel, the kinematically similar $D^0\to {\pi }^{+}{\pi }^{-}$ channel used for normalization, the Cabibbo-favored $D^0\to K^{-}{\pi }^{+}$ channel used to optimize the selection criteria in an unbiased manner, and their charge conjugates. Finding no signal events in the $D^0\to {\mu }^{+}{\mu }^{-}$ search window, we set an upper limit on the branching fraction $\mathcal{B}{(D}^0\to {\mu }^{+}{\mu }^{-})<~2.5\times {10}^{-6}$ $(3.3\mathrm{}\times {10}^{-6})$ at the $90\%$ (95%) confidence level.