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Study of charmonium decays at BESIII

Based on the data samples collected at the energies of $J/ψ$, $ψ(3686)$, $ψ(3770)$ and $ψ(4040)$ 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 $ψ(3770)$ and $ψ(4040)$, including $Λ\barΛπ^+π^-$, $Λ\barΛπ^0$, $Λ\barΛη$, $Σ^+ \barΣ^-$, $Σ^0 \barΣ^0$, $Ξ^-\barΞ^+$ and $Ξ^0\barΞ^0$. 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 $J/ψ$ radiative decays and the $ηη$ system in $J/ψ\toγηη$ radiative decays.