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Using $(10087\pm44)\times10^{6}$ $J/\psi$ events collected with the BESIIIdetector at the BEPCII $e^+e^-$ storage ring at the center-of-mass energy of$\sqrt{s}=3.097~\rm{GeV}$, we present a search for the rare semi-muoniccharmonium decay $J/\psi\to D^{-}\mu^{+}\nu_{\mu}+c.c.$. Since no significantsignal is observed, we set an upper limit of the branching fraction to be$\mathcal{B}(J/\psi\to D^{-}\mu^{+}\nu_{\mu}+c.c.)<5.6\times10^{-7}$ at $90\%$confidence level. This is the first search for the weak decay of charmoniumwith a muon in the final state.

Search for the semi-muonic charmonium decay $J/\psi\to D^{-}\mu^{+}\nu_{\mu}+c.c.$