Strong decays of the isovector-scalar $D^{\ast }{\bar{D}}^{\ast }$ hadronic molecule

Abstract

We adopt the effective Lagrangian approach to study the strong decays of the $1^{-}(0^{++})$ $D^{\ast }{\bar{D}}^{\ast }$ molecular state [denoted as $T_{\psi 0}^a(4010)$ according to the LHCb naming convention] through triangle diagrams. The decay channels include the open-charm $D\bar{D}$, and the hidden-charm ${\eta }_c\pi$, $J/\psi \rho$, and ${\chi }_{c1}\pi$. The coupling between the $T_{\psi 0}^a(4010)$ and its constituents $D^{\ast }{\bar{D}}^{\ast }$ is obtained by solving for the residue of the scattering $T$-matrix at the pole. Our calculations yield a total width of few tens MeV for the $T_{\psi 0}^a(4010)$ state using three different form factors, with its main decay channels being ${\eta }_c\pi$ and ${\chi }_{c1}\pi$. The $X(4100)$ and $X(4050)$ have similar masses and widths, with both masses being close to the $D^{\ast }{\bar{D}}^{\ast }$ threshold. Additionally, their decay final states are consistent with those of the $T_{\psi 0}^a(4010)$. Therefore, it is likely that they represent the same state and both potentially correspond to the $T_{\psi 0}^a(4010)$. We suggest that future experiments focus on searching for the $T_{\psi 0}^a(4010)$ signal in the final states ${\eta }_c{\pi }^{-}$, ${\chi }_{c1}{\pi }^{-}$ and $D^0{D}^{-}$ of the $B^0\to {\eta }_c{\pi }^{-}{K}^{+}$, ${\chi }_{c1}{\pi }^{-}{K}^{+}$ and $D^0{D}^{-}{K}^{+}$ processes, respectively, as well as further investigating its resonance parameters with Flatté-like formula.

Comments: 11 pages, 6 figures, and 4 tables