Prediction of new $T_{cc}$ states of $D^{\ast }{D}^{\ast }$ and $D_s^{\ast }{D}^{\ast }$ molecular nature

Abstract

We extend the theoretical framework used of describe the $T_{cc}$ state as a molecular state of $D^{\ast }D$ and make predictions for the $D^{\ast }{D}^{\ast }$ and $D_s^{\ast }{D}^{\ast }$ systems, finding that they lead to bound states only in the $J^P=1^{+}$ channel. Using input needed to describe the $T_{cc}$ state, basically one parameter to regularize the loops of the Bethe-Salpeter equation, we find bound states with bindings of the order of the MeV and similar widths for $D^{\ast }{D}^{\ast }$ system, while the $D_s^{\ast }{D}^{\ast }$ system develops a strong cusp around threshold.

21 pages,12 figures,1 table. Minor changes made and references added