  Motivated by the experimental study of $J/\psi\to\gamma ~+$ invisible decay
by the CLEO Collaboration, we analyze the process $J/\psi\to \gamma
\nu\bar{\nu}$, as the standard model background for this invisible decay, at
the lowest order. Our investigation shows that Br($J/\psi\to \gamma
\nu\bar{\nu}$) is far below the present experimental upper limit on the
branching ratio of $J/\psi\to\gamma ~+$ invisible, which indicates that some
interesting room for new physics in this channel might be expected. We also
present a similar analysis of the $\eta_c\to \gamma \nu\bar{\nu}$ decay.
