Search for the decay $J/\psi \to \gamma +$ invisible

We search for $J/\psi $ radiative decays into a weakly interacting neutral particle, namely an invisible particle, using the $J/\psi $ produced through the process $\psi \left(3686\right)\to {\pi }^{+}{\pi }^{-}J/\psi $ in a data sample of $\left(448.1±2.9\right)×{10}^{6}\text{}\text{}\psi \left(3686\right)$ decays collected by the BESIII detector at BEPCII. No significant signal is observed. Using a modified frequentist method, upper limits on the branching fractions are set under different assumptions of invisible particle masses up to $1.2\text{}\text{}\mathrm{GeV}/{c}^{2}$. The upper limit corresponding to an invisible particle with zero mass is $7.0×{10}^{-7}$ at the 90% confidence level.