A Three-Coupled-Channel Analysis of $Z_c(3900)$ Involving $D\bar{D}^*$, $\pi J/\psi$, and $\rho \eta_c $

TL;DR

This paper presents a three-channel coupled analysis of the $Z_c(3900)$ state using a one-boson exchange model, successfully reproducing experimental data and revealing the peaks are mainly due to threshold cusps rather than physical poles.

Contribution

It introduces a minimal-parameter coupled-channel model that explains the $Z_c(3900)$ structure and aligns with lattice QCD results, emphasizing the threshold cusp nature.

Findings

Reproduces experimental line shapes at 4.23 and 4.26 GeV.

Shows $Z_c(3900)$ peaks are caused by threshold cusps.

Identifies a virtual pole far from the threshold.

Abstract

In this work, we conduct a three-coupled-channel analysis of the $Z_c(3900)$ structure, focusing on the $D\bar{D}^*$, $J/\psi \pi$, and $\rho \eta_c$ channels, based on the one-boson exchange model. Drawing from previous study on the exotic state $T_{cc}$, we only utilize one more parameter to construct the interactions between the channels. Our model successfully reproduces the experimental line shapes of the invariant mass distribution at $\sqrt{s} = 4.23$ and $4.26$ GeV for the three channels. Additionally, the finite-volume energy levels in our model show agreement with current LQCD conclusion. Detailed analysis suggests that the $Z_c(3900)$ peaks in the $\pi J/\psi$ and $\rho \eta_c$ distributions primarily arise from the triangle loop involving the $D_1 \bar{D} D^*$ intermediate system. In the $D\bar{D}^*$ distribution, the threshold peak is generated by the cascade decay mechanism enhanced by a triangle diagram. Moreover, we find a virtual pole located far from the threshold, indicating that $Z_c(3900)$ peaks are not associated with physical pole. We conclude that the $Z_c(3900)$ peaks are predominantly caused by the threshold cusp.