Mini-review of rare charmonium decays at BESIII
  Recently, LHCb experiment announced a 3.5$\sigma$ evidence for direct CP violation in $D^0$ decay by looking at the difference between $A_{CP}(D^0\rightarrow K^+K^-)$ and $A_{CP}(D^0\rightarrow \pi^+\pi^-)$. 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 $J/\psi$ and $\psi(2S)$ samples in BESIII experiment, the rare decays may be feasible. 
Hai-Bo Li and SHi-Hai Zhu
hep-ex hep-ph