  We study the implication of $J/\psi$ radiative decay into invisible particles
for light sterile neutrino and sub-GeV dark matter (DM). The low-energy
effective field theories (EFTs) are used for the description of general
neutrino interactions and the Dirac fermion DM coupled to charm quark. We
perform the likelihood fits for the individual neutrino and DM operators with
distinct Lorentz structures and photon spectra. The limits on the decay
branching fractions are obtained for different neutrino or DM scenarios and
then converted to the lower bounds on the new energy scales. The most stringent
bounds on the energy scale in neutrino and DM EFTs are 12.8 GeV and 11.6 GeV,
respectively. We also evaluate the limit on the DM-nucleon scattering cross
section converted from BESIII data. The BESIII $J/\psi$ data is sensitive to
the light DM mass range where the DM direct detection experiments cannot probe
yet. The future Super Tau Charm Factory after one year run can push the limits
down by two orders of magnitude.
