Can $Z_{cs}(3985)$ be a molecular state of ${\bar{D}}_s^{\ast }D$ and ${\bar{D}}_s{D}^{\ast }$ ?

Abstract

We study the $Z_{cs}(3985)$ state recently observed by the BESIII Collaboration in the one-boson-exchange model, assuming that it is a ${\bar{D}}_s^{(\ast )}{D}^{(\ast )}$ molecule, which has the quark content $c\bar{c}s\bar{q}$ with $q=u$, $d$. It is shown that the one-boson-exchange potential is too weak to generate dynamcally ${\bar{D}}_{s}D$, ${\bar{D}}_s^{\ast }D$, and ${\bar{D}}_s{D}^{\ast }$ states, while for the case of ${\bar{D}}_s^{\ast }{D}^{\ast }$, very loosely bound states are likely, with binding energies of the order of several MeV. We conclude that, the observed $Z_{cs}(3985)$ state, if confirmed by further experiments, cannot be a pure hadronic molecular state of ${\bar{D}}_s{D}^{\ast }$ and ${\bar{D}}_s^{\ast }D$ and could consist of large components of compact nature.

During the numerical calculation, an unfortunate coding error occurred which mis-identified the exchange of $K$ and $K^{\ast }$ mesons, which could not happen. As a result, the OBE potential could not provide a relevant binding mechanism for the ${\bar{D}}_s^{(\ast )}{D}^{(\ast )}$ systems studied in the present work