Is $Z_{cs}(3982)$ a molecular partner of $Z_c(3900)$ and $Z_c(4020)$ states?

Abstract: We perform an effective-field-theory-based coupled-channel analysis of the recent BES III data on the $e<sup>+e<sup>-$ annihilation into the final state $$K<sup>+(D_s<sup>-D<sup>{<em>0}+D_s^{</em>-}D<sup>0)$$ in a wide energy range and extract the poles responsible for the formation of the $Z_{cs}(3982)$. We identify two scenarios which provide a similar description of the experimental mass distributions but result in utterly different predictions for the spin partners of the $Z_{cs}(3982)$: although both scenarios are consistent with the $Z_{cs}$ as a $SU(3)$ partner of the $Z_c(3900)$, the $Z_c(4020)$ appears naturally as a spin partner of these states only in one of them (fit 1) while in the other (fit 2) its nature has to be different. Also, the $Z_{cs}(3982)$ has a $J<sup>{P}=1<sup>+$ spin partner near the $\bar D_s^* D<sup>*$ threshold in fit 1, while no such state exists in fit 2. We predict the $\bar{D}_s<sup><em>D^</em>$ invariant mass distribution in the $J<sup>{P}=1<sup>+$ channel for the reaction $$e^{+e^-\to} K<sup>+D_s<sup>{*-}D<sup>{*0}$$ and argue that this line shape can be used to distinguish between the two scenarios once data in this channel are available.