A unified description of the hidden-charm tetraquark states $Z_{cs}(3985)$, $Z_c(3900)$ and $X(4020)$

TL;DR

This paper develops a unified theoretical framework combining effective range expansion, compositeness, and decay width analysis to study hidden-charm tetraquark states, providing insights into their structure and decay properties.

Contribution

It introduces a comprehensive approach to analyze tetraquark states, integrating multiple theoretical methods to predict their structure and decay behaviors, which aids future experimental investigations.

Findings

Confirmed the molecular nature of $Z_c(3900)$ using decay width ratios.

Predicted decay widths for $J/\psi K^{-}$ and $h_c\pi$ channels.

Provided scattering parameters and compositeness coefficients for the states.

Abstract

The newly observed hidden-charm tetraquark state $Z_{cs}(3985)$, together with $Z_c(3900)$ and $X(4020)$, are studied in the combined theoretical framework of the effective range expansion, compositeness relation and the decay width saturation. The elastic effective-range-expansion approach leads to sensible results for the scattering lengths, effective ranges and the compositeness coefficients, $i.e.$, the probabilities to find the two-charm-meson molecule components in the tetraquark states. The coupled-channel formalism by including the $J/\psi\pi$ and $D\bar{D}^*/\bar{D}D^*$ to fulfill the constraints of the compositeness relation and the decay width, confirms the elastic effective-range-expansion results for the $Z_c(3900)$, by using the experimental inputs for the ratios of the decay widths between $D\bar{D}^*/\bar{D}D^*$ and $J/\psi\pi$. With the results from the elastic effective-range-expansion study as input for the compositeness, we generalize the discussions to the $Z_{cs}(3985)$ by including the $J/\psi K^{-}$ and $D_s^{-}D^{*0}/D_s^{*-}D^{0}$, and predict the partial decay widths of the $J/\psi K^{-}$. Similar calculations are also carried out for the $X(4020)$ by including the $h_c\pi$ and $D^*\bar{D}^*$, and the partial decay widths of the $h_c\pi$ is predicted. Our results can provide useful guidelines for future experimental measurements.