\begin{document}$ J/\psi \to 2\gamma+hadrons $\end{document} was studied, and the main contribution processes, \begin{document}$ J/\psi \to 2\gamma + g g g $\end{document} and \begin{document}$ J/\psi \to 2\gamma + q \bar{q} $\end{document}, were calculated. With the specific conditions at the BESIII, this rare decay process and the main background process \begin{document}$ e^{+} e^{-} \to \gamma \gamma + hadrons (q \bar{q}) $\end{document}were investigated. The results show that the ratio of signal to background can reach 1.24 with optimized selection criteria at the BESIII. In addition, distributions of the signal and background are presented. All the results show that the signal is large enough to be experimentally measured."> Study of the rare decay <inline-formula><tex-math id="M1">\begin{document}${ \boldsymbol J/\boldsymbol\psi \to {\bf 2}{\boldsymbol\gamma}{\boldsymbol{+hadrons}} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/abfa5a07-5841-4f23-8b2d-48e45dc405e7/CPC-2022-0160_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/abfa5a07-5841-4f23-8b2d-48e45dc405e7/CPC-2022-0160_M1.png"/></alternatives></inline-formula> at the BESIII -
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