Prediction of a missing higher charmonium around 4.26 GeV in $J/\psi$ family

Abstract

Inspired by the similarity of mass gaps of $J/\psi$ and ${\rm Y}$ families, the prediction of missing higher charmonium with mass $4263$ 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. Here, $X(3940)$ as ${\eta }_c(3S)$ is established while the explanation of $X(4160)$ to be ${\eta }_c(4S)$ is fully excluded and ${\eta }_c(4S)$ is typically a very narrow state. These predictions can be accessible at BESIII, Belle and BelleII in near future.

Comments: 5 pages, 5 figures and 1 table. More discussions added. Accepted by Eur. Phys. J. C