A new look at $\psi (4160)$ and $\psi (4230)$

Abstract

By simultaneously analyzing the cross section data of $e^{+}{e}^{-}\to D\bar{D},D{\bar{D}}^{\ast },D^{\ast }{\bar{D}}^{\ast },D\bar{D}\pi$ in a coupled-channel scheme with unitarity, we found that, in contrast to the conventional wisdom, the pole of $\psi (2^3{D}_1)$ might be located at about $\sqrt{s}=4222-32i\mathrm{MeV}$. This observation implies a possibility that the two resonances, dubbed the $\psi (4160)$ and $\psi (4230)$ in the PDG table now, might be the same $\psi (2^3{D}_1)$ state. Such a suggestion could provide more insight to our understanding the enigmatic decay properties of $\psi (4160)$ and $\psi (4230)$. Furthermore, this coupled-channel scheme could be applied to study other phenomena with several interfering resonances.

6 pages, 4 figures, 1 table