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We report the first observation of the Dalitz decay η 0 → γe þ e − , based on a data sample of 1.31 billion J=ψ events collected with the BESIII detector. The η 0 mesons are produced via the J=ψ → γη 0 decay process. The ratio Γðη 0 → γe þ e − Þ=Γðη 0 → γγÞ is measured to be ð2.13 AE 0.09ðstatÞ AE 0.07ðsysÞÞ × 10 −2 . This corresponds to a branching fraction Bðη 0 → γe þ e − Þ ¼ ð4.69 AE 0.20ðstatÞ AE 0.23ðsysÞÞ × 10 −4 . The transition form factor is extracted and different expressions are compared to the measured dependence on the e þ e − invariant mass. The results are consistent with the prediction of the vector meson dominance model.

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Recently, LHCb experiment announced a 3.5σ evidence for direct CP violation in D 0 decay by looking at the difference between ACP (D 0 → K + K − ) and ACP (D 0 → π + π − ). This is the first evidence of CP violation in charm system, which may indicate new physics beyond the Standard Model. Motivated by this measurement, we review rare processes in charmonium decay, especially, the weak decay, C or P violated decay and lepton flavor violated decays. In case the new physics appears in charm sector, these rare decays of charmonium states will provide opportunity to search for significant contributions from physics beyond the Standard Model. With huge J/ψ and ψ(2S) samples in BESIII experiment, the rare decays may be feasible.