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

Abstract

By simultaneously analyzing the cross section data of $e^+e^-\rightarrow D\bar D, D\bar D^*, D^*\bar D^*, D\bar D\pi$ in a coupled-channel scheme with unitarity, we found that, in contrast to the conventional wisdom, the pole of $\psi(2^3D_1)$ 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 $\psi(2^3D_1)$ 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.