Disclosing $D^{\ast }{\bar{D}}^{\ast }$ molecular states in the $B_c^{-}\to {\pi }^{-}J/\psi \omega$ decay

Abstract

We study the $B_c^{-}\to {\pi }^{-}J/\psi \omega$ and $B_c^{-}\to {\pi }^{-}{D}^{\ast }{\bar{D}}^{\ast }$ reactions and show that they are related by the presence of two resonances, the $X(3940)$ and $X(3930)$, that are of molecular nature and couple most strongly to $D^{\ast }{\bar{D}}^{\ast }$, but also to $J/\psi \omega$. Because of that, in the $J/\psi \omega$ mass distribution we find a cusp with large strength at the $D^{\ast }{\bar{D}}^{\ast }$ threshold and predict the ratio of strengths between the peak of the cusp and the maximum of the $D^{\ast }{\bar{D}}^{\ast }$ distribution close to $D^{\ast }{\bar{D}}^{\ast }$ threshold, which are distinct features of the molecular nature of these two resonances.

Comments: 13 pages, 6 figures