Speaker
Description
In this work, we investigated in detail the widths of the $X_2$ decaying to $J/ \psi V$ ($V = \rho^0\,,\omega$) and to $\eta_cP$ ($P = \pi^0\,,\eta\,,\eta'$) using the effective Lagrangian approach. In calculations, we assume the $X_2$ as a molecular state of the $D^{*0}\bar{D}^{*0} $ and $D^{*+}D^{*-}$ with equal proportion. Moreover, we only consider the contributions from the triangle hadron loops made of the charmed mesons $D^{(*)}$ and $\bar{D}^*$.We found that the processes $X_2\to J/\psi \rho^0$ and $\eta_c\pi^0$ are both isospin breaking, while the processes $X_2\to J/\psi \omega$ and $\eta_c\eta$ ($\eta'$) are of isospin conservation. We also investigated the dependence of the ratios between these widths on the $X_2$ mass and on the $\eta$-$\eta'$ mixing angle, which may be good quantities for experiments. We hope that these calculation results would be checked experimentally in the future.
