Search for the FCNC charmonium decay J/ψ → D⁰μ⁺μ⁻ + c.c.

Based on a data sample of (10087 ± 44) × 10⁶J/ψ events taken with the BESIII detector, we search for the flavor-changing neutral current charmonium decay J/ψ → D⁰μ⁺μ⁻ + c.c. No significant signal above the background is observed, and the upper limit on its branching fraction is set to be ℬ(J/ψ → D⁰μ⁺μ⁻ + c.c.) < 1.1 × 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.