We present a search for the lepton flavor violating decay $J/psi o
e^{pm}mu^{mp}$ using $8.998 imes 10^{9} J/psi$ events collected with the
BESIII detector at the BEPCII $e^+e^-$ storage ring. No excess of signal above
background is observed; we therefore set an upper limit on the branching
fraction of $mathcal{B}(J/psi o e^{pm}mu^{mp})<4.5 imes10^{-9}$ at the
$90\%$ confidence level. Improving the previous best result by a factor of more
than 30, this measurement places the most stringent limit to date on lepton
flavor violation in the heavy quarkonium sector.
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