Study of charmonium decays at BESIII

Based on the data samples collected at the energies of $J/\psi$, $\psi(3686)$, $\psi(3770)$ and $\psi(4040)$ resonances with the BESIII detector at the BEPCII storage ring, we present charmonium decays in two aspects. One is the search for baryonic decays of $\psi(3770)$ and $\psi(4040)$, including $\Lambda \bar\Lambda\pi^+\pi^-$, $\Lambda\bar\Lambda\pi^0$, $\Lambda \bar\Lambda\eta$, $\Sigma^+ \bar\Sigma^-$, $\Sigma^0 \bar\Sigma^0$, $\Xi^-\bar\Xi^+$ and $\Xi^0\bar\Xi^0$. None are observed, and upper limits are set at the 90% confidence level. The other is the light hadron spectroscopy from charmonium radiative decays, including the spin-parity analysis of the $p\bar p$ mass-threshold enhancement in $J/\psi$ radiative decays and the $\eta\eta$ system in $J/\psi\to\gamma\eta\eta$ radiative decays.