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

Abstract

Inspired by the similarity of mass gaps of $J/ψ$ and $Υ$ 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 $ψ(4415)$ are discussed. Here, $X(3940)$ as $η_c(3S)$ is established while the explanation of $X(4160)$ to be $η_c(4S)$ is fully excluded and $η_c(4S)$ is typically a very narrow state. These predictions can be accessible at BESIII, Belle and BelleII in near future.

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