Study on the structure of the $Z_{c}(3900)$ state

TL;DR

This study models the $Z_{c}(3900)$ state using effective field theory, constructing interaction Lagrangians and solving the Bethe-Salpeter equation to explain its structure as a mixture of meson-meson and diquark components.

Contribution

It introduces a novel effective field theory framework and coupled-channel analysis to describe the internal structure of the $Z_{c}(3900)$ state.

Findings

The $Z_{c}(3900)$ can be explained as a mixture of meson-meson and diquark components.

The model reproduces the experimental mass and width of $Z_{c}(3900)$.

Effective potentials are derived for coupled channels involving $Dar{D}^*$ and diquark states.

Abstract

In this work, we studied the $Z_{c}(3900)$ state within the framework of effective field theory. We firstly show the construction of the Lagrangian describing meson-meson-meson and meson-diquark-diquark interactions. By using the Feynman rule, we calculate the effective potentials corresponding to the coupled channels of $D\bar{D}^{*}/D^{*}\bar{D}$ and $S_{cq}\bar{A}_{cq}/A_{cq}\bar{S}_{cq}$ with $S_{cq}$ ($A_{cq}$) the scalar (axial vector) diquark composed of $c$ and $q$ quarks. After solving the Bethe-Salpeter equation of the on-shell parametrized form and compare our numerical results with the experimental mass and width of $Z_{c}(3900)$, we find that the $Z_{c}(3900)$ state can be explained as the mixture of $D\bar{D}^{*}/D^{*}\bar{D}$ and $S_{cq}\bar{A}_{cq}/A_{cq}\bar{S}_{cq}$ components.