The $Z_{cs}$ 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 ${\bar{D}}^{(\ast )}{D}_s^{(\ast )}$ 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 ${\bar{D}}^{\ast 0}{D}_s^{+}$ and ${\bar{A}}_{cs}{S}_{cu}$ components. Besides, for the ${\bar{D}}^{\ast 0}{D}_s^{\ast +}/{\bar{A}}_{cs}{A}_{cu}$ 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.

Comments: 6 pages, 1 figure