$Z_{cs}(3985{)}^{-}$ as the $U$-spin partner of $Z_c(3900{)}^{-}$ and implication of other states in the ${\text{SU(3)}}_F$ symmetry and heavy quark symmetry

Abstract

Recently, for the first time, the BESIII Collaboration reported the strange hidden charm tetraquark states $Z_{cs}(3985{)}^{-}$ in the $K^{+}$ recoil-mass spectrum near the $D_s^{-}{D}^{\ast 0}/D_s^{\ast -}{D}^0$ mass thresholds in the processes of $e^{+}{e}^{-}\to K^{+}(D_s^{-}{D}^{\ast 0}+D_s^{\ast -}{D}^0)$ at $\sqrt{s}=4.681$ GeV. The significance was estimated to be 5.3 $\sigma$. We show that the newly observed $Z_{cs}(3985{)}^{-}$ state is the $U$-spin partner of $Z_c(3900{)}^{-}$ as a resonance within coupled-channel calculation in the ${\text{SU(3)}}_F$ symmetry and heavy quark spin symmetry (HQSS). In the ${\text{SU(3)}}_F$ symmetry, we introduce the $G_{U/V}$ parity to construct the flavor wave functions of the $Z_{cs}$ states. In a unified framework, we consider the $J/\psi \pi (K)$, ${\bar{D}}_{(s)}{D}^{\ast }/{\bar{D}}_{(s)}^{\ast }D$ coupled-channel effect with the contact interaction. With the masses and widths of $Z_c(3900)$ and $Z_c(4020)$, we determine all the unknown coupling constants. We obtain mass and width of $Z_{cs}(3985)$ in good agreement with the experimental results, which strongly supports the $Z_{cs}$ states as the $U/V$-spin partner states of the charged $Z_c(3900)$. We also calculate the ratio of the partial decay widths of $Z_{cs}(3985)$, which implies that the ${\bar{D}}_s{D}^{\ast }/{\bar{D}}_s^{\ast }D$ decay modes are dominant. We also predict the $Z_{cs}^{\prime }$ states with a mass around $4130$ MeV and width around $30$ MeV, which are the $U/V$-spin partner states of the charged $Z_c(4020)$ and HQSS partner states of the $Z_{cs}(3985)$. In the hidden bottom sector, we predict the strange tetraquark states $Z_{bs}$ and $Z_{bs}^{\prime }$ with a mass around 10700 MeV and 10750 MeV, which are the $U/V$-spin partner states of $Z_b(10610{)}^{\pm }$ and $Z_b(10650{)}^{\pm }$, respectively.

Comments: 6 pages, 2 figures