Prediction of a missing higher charmonium around 4.26 GeV in

Inspired by the similarity between the mass gaps of the $$J/\psi $$ and $$\Upsilon $$ families, the prediction of a missing higher charmonium with mass 4,263 MeV and very narrow width is made. In addition, the properties of two charmonium-like states, $$X(3940)$$ and $$X(4160)$$, and charmonium $$\psi (4415)$$ are discussed, where our calculation shows that $$X(3940)$$ as $$\eta _c(3S)$$ is established, while the explanation of $$X(4160)$$ to be $$\eta _c(4S)$$ is fully excluded and that $$\eta _c(4S)$$ is typically a very narrow state. These predictions might be accessible at BESIII, Belle, and BelleII in near future