We incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of higher charmonium. We calculate the masses, electromagnetic decays, and E1 transitions of charmonium states in the screened potential model, and propose possible assignments for the newly discovered charmonium or charmoniumlike “$X$, $Y$, $Z$” states. We find the masses of higher charmonia with screened potential are considerably lower than those with unscreened potential. The ${\chi }_{c2}(2P)$ mass agrees well with that of the $Z(3930)$, and the mass of $\psi (4415)$ is compatible with $\psi (5S)$ rather than $\psi (4S)$. In particular, the discovered four $Y$ states in the initial state radiation process, i.e., $Y(4008)$, $Y(4260)$, $Y(4320/4360)$, $Y(4660)$ may be assigned as the $\psi (3S)$, $\psi (4S)$, $\psi (3D)$, $\psi (6S)$ states, respectively. The $X(3940)$ and $X(4160)$ found in the double charmonium production in $e^{+}{e}^{-}$ annihilation may be assigned as the ${\eta }_c(3S)$ and ${\chi }_{c0}(3P)$ states. Based on the calculated E1 transition widths for ${\chi }_{c1}(2P)\to \gamma J/\psi$ and ${\chi }_{c1}(2P)\to \gamma \psi (2S)$ and other results, we argue that the $X(3872)$ may be a ${\chi }_{c1}(2P)$ dominated charmonium state with some admixture of the $D^0{\overline{D}}^{*0}$ component. Possible problems encountered in these assignments and comparisons with other interpretations for these $X$, $Y$, $Z$ states are discussed in detail. We emphasize that more theoretical and experimental investigations are urgently needed to clarify these assignments and other interpretations.

• Received 31 March 2009

DOI:https://doi.org/10.1103/PhysRevD.79.094004