Zcs states and the mixture of hadronic molecule and diquark-anti-diquark components within effective field theory

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 ${\overline{D}}^{(*)}{D}_{s}^{(*)}$ components, the potentials are suppressed by the OZI rule. Through solving the Bethe-Salpeter equation, we find that the ${Z}_{cs}(4000{)}^{+}$ can be explained as the mixture of ${\overline{D}}^{*0}{D}_{s}^{+}$ and ${\overline{A}}_{cs}{S}_{cu}$ components. Besides, for the ${\overline{D}}^{*0}{D}_{s}^{*+}/{\overline{A}}_{cs}{A}_{cu}$ system, the pole of $4208\ifmmode\pm\else\textpm\fi{}13i\text{ }\text{ }\mathrm{MeV}$ 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.