Aspects of $Z_{cs}(3985)$ and $Z_{cs}(4000)$

In the present work we investigate the $\eta_c K$, $J/\psi K$, $\eta_c K^*$ and $J/\psi K^*$ hidden-charm decay modes for the $c\bar{c}s\bar{u}$ four-quark system in the molecular and compact tetraquark scenarios using the quark-exchange model. Our theoretical results indicate that if the newly observed states $Z_{cs}(3985)$ and $Z_{cs}(4000)$ are two different states, $Z_{cs}(4000)$ may be interpreted as the mixture $\frac{1}{\sqrt{2}}(D^0D_s^{*-}+D^{*0}D_s^{-})$ of which the $J/\psi K$ partial decay width is about $\Gamma\sim2.89$ MeV, while $Z_{cs}(3985)$ may be explained as the mixture $\frac{1}{\sqrt{2}}(-D^0D_s^{*-}+D^{*0}D_s^{-})$ of which the $J/\psi K$ partial decay width is small to zero. Moreover, if the state $Z_{cs}(4000)$ can be explained as the mixed state $\frac{1}{\sqrt{2}}(D^0D_s^{*-}+D^{*0}D_s^{-})$ indeed, the partial decay width ratio between $J/\psi K$ and $\eta_cK^*$ is close to unit, which indicates the decay channel $\eta_cK^*$ may be a ideal channel as well to decode the inner structure of $Z_{cs}(4000)$. In addition, the partial decay width for the tensor molecular state $|D^{*0}D_s^{*-}\rangle_{2^+}$ decaying into $J/\psi K^*$ can reach up to a few MeV, which shows this tensor molecular state has a good potential to be observed in this decay channel.