Study of possible $DN{D}^{\ast }$ bound states

Abstract

We start from a recently favored picture in which the $\hat{I}{›}_c(2940)$ and $\hat{I}{›}_c(2910)$ correspond mostly to $N{D}^{\ast }$ bound states with $J^P=1/2^{-},3/2^{-}$ and then add a $D$ as a third particle, looking for the possible binding of the $DN{D}^{\ast }$ three body system within the framework of the Fixed Center Approximation. We find that the system is bound with respect to the corresponding $\hat{I}{›}_c^{\ast }D$ threshold with a binding of about $60$ MeV and a width of about $90$ MeV. Alternatively we assume a cluster of $ND$ and a $D^{\ast }$ meson interacting with the cluster and we find similar results. The observation of these states of $J^P=1/2^{+},3/2^{+}$ would provide new and valuable information concerning the $DN$ and $D^{\ast }N$ interaction, an issue of current debate.

9 pages, 4 figures