Search for the FCNC charmonium decay $J\mathrm{/}\psi \to D^0{\mu }^{+}{\mu }^{-}+\text{c.c.}$

Based on a data sample of $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events taken with the BESIII detector, we search for the flavor-changing neutral current charmonium decay $J\mathrm{/}\psi \to D^0{\mu }^{+}{\mu }^{-}+\text{c.c.}$. No significant signal above the background is observed, and the upper limit on its branching fraction is set to be $\mathcal{B}(J\mathrm{/}\psi \to D^0{\mu }^{+}{\mu }^{-}+\text{c.c.})<1.1\times {10}^{-7}$ at the 90% confidence level. This marks the first search for a flavor-changing neutral current charmonium decay involving muons in the final state.