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

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 $4208\pm 13i\mathrm{MeV}$ 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.

Figure 1

The diagrams of mesons into mesons, mesons into diquark-anti-diquark, and diquark-anti-diquark into diquark-anti-diquark.

Figure 2

The diagrams of the process $A\to BC$, which is chosen to determine the coupling constants. Figures 2 and 2 are the quark level diagrams in the ${}^3{P}_0$ model. Figure 2(c) is the diagram of hadron-diquark level.