Coupled-channel and screening effects in charmonium spectrum

Abstract

Using the same quenched limit as input, we compare the charmonium spectra predicted by two different models, i.e., the coupled-channel model and the screened potential model in the mass region below 4 GeV, in which the contributions from decay channels involving $P$-wave (as well as even higher excited) $D$ mesons can be neglected. We find that the two models have similar global features in describing the charmonium spectrum since they approximately embody the same effect of the vacuum polarization of dynamical light quark pairs. Adopting these models will be helpful to clarify the nature of the newly discovered charmonium or charmoniumlike states; and the coupled-channel model is more adept in investigating the influences of open-charm thresholds on the charmonium spectrum. In particular, we show the $S$-wave decay coupling effect on lowering the ${\ensuremath{\chi}}_{c1}(2P)$ mass toward the $D{\overline{D}}^{*}$ threshold, in support of the assignment of the $X(3872)$ as a ${\ensuremath{\chi}}_{c1}(2P)$-dominated charmonium state.