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