Studies of Charmonium at BESIII

Based on?ψ(3686)?decays of 106 million, the 1.31 billion J/psi events and a data sample of?ψ(3770)?with?2.9?fb?1?integrated luminosity, many analyses are performed. Exclusively baryonic decays of the?ψ(3770), the radiative transition?ψ(3770)→γηc(2S), the?ψ(3770)?transition to?χcJ, isospin violation decay?χc0,2→π0ηc, the?C?parity violation decays?J/ψ→γγ,γ??are searched for, but no significant signals are observed, and upper limits are set for these decays. The decays of?ψ(3770)→γχc1?and?J/ψ→π0??signals are observed. These measurements provide more information on the charmonium structure, and the isospin and?C-parity violation in the charmonium decays.