Decay widths of Z _cs(3985/4000) based on rigorous quark-hadron duality*

In this work, we explore the hadronic coupling constants $G_{ZJ/\psi K}$, $G_{Z\eta_c K^*}$, $G_{ZD^* \bar{D}_s}$ of exotic states $Z_{cs}(3985/4000)$ both in pictures tetraquark and molecular with tentative assignments $J^{PC}=1^{+-}$ based on rigorous quark-hadron duality. Then obtain total widths $\Gamma_{Z_{cs}}^T =15.31\pm 2.06\,\rm{MeV}$ $\Gamma_{Z_{cs}}^M=83.51\pm21.09\,\rm{MeV}$, which are consistent experimental data $13.8^{+8.1}_{-5.2}\pm4.9\,\rm{MeV}$ from BESIII collaboration $131 \pm 15 26\,\rm{MeV}$ LHCb collaboration, respectively, support assigning $Z_{cs}(3985)$ $Z_{cs}(4000)$ to be hidden-charm state $J^{PC}=1^{+-}$, respectively.