The $Z_{cs}$ states and the mixture of hadronic molecule and diquark-anti-diquark components within effective field theory

TL;DR

This paper develops an effective field theory framework to analyze the internal structure of $Z_{cs}$ states, revealing their mixed molecular and diquark-anti-diquark nature and predicting new states and properties.

Contribution

It introduces a Lagrangian incorporating both molecular and diquark components, providing a novel approach to understanding $Z_{cs}$ states beyond traditional models.

Findings

Explains $Z_{cs}(4000)^+$ as a mixture of different components.

Predicts a new pole at 4208 MeV consistent with $Z_{cs}(4220)^+$.

Forecasts additional states with various spins.

Abstract

In this work, we construct the Lagrangian describing meson-diquark interaction, such that the diquark-anti-diquark component as well as the molecular component is introduced when studying the $Z_{cs}$ states. In this way, the problem is solved that if only considering the $\bar{D}^{(*)}D_s^{(*)}$ components, the potentials are suppressed by OZI rule. Through solving the Bethe-Salpeter equation, we find that the $Z_{cs}(4000)^+$ can be explained as the mixture of $\bar{D}^{*0}D_s^+$ and $\bar{A}_{cs}S_{cu}$ components. Besides, for the $\bar{D}^{*0}D_s^{*+}/\bar{A}_{cs}A_{cu}$ system, the pole of $4208\pm 13i$ MeV on the second Riemann sheet is predicted, whose mass agrees with that of $Z_{cs}(4220)^+$ while the width is much smaller than $Z_{cs}(4220)^+$. Due to the large error of the $Z_{cs}(4220)^+$'s width, further measurements are expected. In addition, several other poles of different spins are predicted.