Decays of a $T_{cc}^+$ heavy-quark-spin molecular partner to $D^{\ast}D\pi$

Abstract

Starting from the hypothesis that the $T_{cc}^+$ discovered at LHCb is a $D^{\ast+} D^0/D^{\ast 0}D^+$ hadronic molecule, we consider the partial width of its heavy quark spin partner, the $T_{cc}^{\ast +}$ as a $D^{\ast +} D^{\ast 0}$ shallow bound state, decaying into the $D^{\ast}D\pi$ final states including the contributions of the $D^{\ast} D$ and $D^{\ast} \pi$ final state interaction by using a nonrelativistic effective field theory. Because of the existence of the $T_{cc}^+$ pole, the $I=0$ $D^{\ast} D$ rescattering contributes at the leading order, the same order as that of the tree diagram, while the $D^{\ast} \pi$ rescattering contribution is one magnitude smaller. The partial widths of $T_{cc}^{\ast +} \to D^{\ast +} D^0 \pi^0$, $D^{\ast 0}D^+\pi^0$, and $D^{\ast 0}D^0\pi^+$ are about 44 keV, 20 keV, and 18 keV, respectively.Comment: 19 pages, 4 figues. Comments are welcom