$Z_c(3900)/Z_c(3885)$ as a virtual state from $\pi J/\psi -{\bar{D}}^{\ast }D$ interaction

Abstract

In this work, we study the $J/\psi \pi$ and ${\bar{D}}^{\ast }D$ invariant mass spectra of the $Y(4260)$ decay to find out the origin of the $Z_c(3900)$ and $Z_c(3885)$ structures. The $J/\psi \pi -{\bar{D}}^{\ast }D$ interaction is studied in a coupled-channel quasipotential Bethe-Saltpeter equation approach, and embedded to the $Y(4260)$ decay process to reproduce both $J/\psi {\pi }^{-}$ and $D^{\ast -}{D}^0$ invariant mass spectra observed at BESIII simultaneously. It is found out that a virtual state at energy about 3870 MeV is produced from the interaction when both invariant mass spectra are comparable with the experiment. The results support that both $Z_c(3900)$ and $Z_c(3885)$ have the same origin, that is, a virtual state from $J/\psi \pi -{\bar{D}}^{\ast }D$ interaction, in which the ${\bar{D}}^{\ast }D$ interaction is more important and the coupling between ${\bar{D}}^{\ast }D$ and $J/\psi \pi$ channels plays a minor role.

Comments: 8 pages, 4 figures, more reference added