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

TL;DR

This study uses a coupled-channel Bethe-Salpeter approach to analyze decay spectra and suggests that the $Z_c(3900)$ and $Z_c(3885)$ are virtual states originating from the $ar{D}^*D$ interaction, with minimal coupling to $J/\psi\pi$.

Contribution

It introduces a coupled-channel quasipotential Bethe-Salpeter method to explain the $Z_c$ structures as virtual states from $ar{D}^*D$ interactions, unifying their origin.

Findings

A virtual state at about 3870 MeV explains the spectra.

Both $Z_c(3900)$ and $Z_c(3885)$ originate from the same virtual state.

The $ar{D}^*D$ interaction dominates over the coupling to $J/\psi\pi$.

Abstract

In this work, we study the $J/\psi\pi$ and $\bar{D}^*D$ invariant mass spectra of the $Y(4260)$ decay to find out the origin of the $Z_c(3900)$ and $Z_c(3885)$ structures. The $J/\psi \pi-\bar{D}^{*}D$ 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 $D^{*-}D^0$ 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 $J/\psi \pi-\bar{D}^*{D}$ interaction, in which the $\bar{D}^*{D}$ interaction is more important and the coupling between $\bar{D}^*{D}$ and $J/\psi\pi$ channels plays a minor role.