$Z_c(3900)$ as a resonance from the $D\bar{D}^*$ interaction

TL;DR

This paper models the $Z_c(3900)$ as a resonance arising from the $Dar{D}^*$ interaction using a Bethe-Salpeter approach, revealing its nature as a threshold resonance consistent with experimental data.

Contribution

It introduces a detailed interaction model and pole analysis that explains the $Z_c(3900)$ as a resonance, connecting it to the $Dar{D}^*$ dynamics and previous states like $X(3872)$.

Findings

Identification of $Z_c(3900)$ as a resonance near the $Dar{D}^*$ threshold.

Prediction of bound states with specific quantum numbers in the isoscalar sector.

Reproduction of BESIII invariant mass spectra with the model.

Abstract

In this paper it is proposed that the charged charmonium-like state $Z_c(3900)$ is a resonance above the threshold from the $D\bar{D}^*$ interaction. The $D\bar{D}^*$ interaction is described by the one-boson exchange model with light meson exchanges plus a short-range $J/\psi$ exchange. The scattering amplitude is calculated within a Bethe-Salpeter equation approach and the poles near the $D\bar{D}^*$ threshold are searched. In the isoscalar sector, two poles found under the $D\bar{D}^*$ threshold, i.e., bound states, have the quantum numbers $I^G(J^{PC})=0^-(1^{+-})$ and $0^+(1^{++})$. The latter can be related to the $X(3872)$. In the isovector sector, a bound state with $I^G(J^P)=1^+(1^+)$ is found with a large cutoff at about 3 GeV. If a cutoff at about 2 GeV is adopted with which a pole carrying the quantum number of the $X(3872)$ is produced at an energy of about 3871 MeV, the pole for the bound state with $1^+(1^+)$ runs across the threshold to a second Rienman sheet and becomes a resonance above the $D\bar{D}^*$ threshold, which can be identified with the $Z_c(3900)$. With such a cutoff, the $D\bar{D}^{*}$ invariant mass spectrum is also investigated and the experimental results found by BESIII can be reproduced.