Role of $a_0(1710)$ in the $J/\psi\to\rho^+\rho^-\omega$ and $J/\psi\to\gamma\rho^0\omega$ reactions

Abstract

We investigate the strong decay $J/\psi\to\rho^+\rho^-\omega$ and the radiative decay $J/\psi\to\gamma\rho^0\omega$, taking into account the $S$-wave $K^*\bar{K}^*$, $\rho \omega$ and $\rho \phi$ final-state interactions that dynamically generate the scalar meson $a_0(1710)$. Our results demonstrate that a clear peak structure emerges around 1.8~GeV in the $\rho^+\omega$~($\rho^-\omega$) invariant mass distribution of the strong decay, which can be associated with the $a_0(1710)$ resonance. Similarly, a distinct peak is predicted in the $\rho^0\omega$ invariant mass distribution of the radiative decay. Our results show that clear peaks for the $a_0(1710)$ production should be observed in future experimental measurements of these processes by the BESIII and Belle II Collaborations, as well as the planned Super Tau-Charm Facility (STCF), helping to get more precise values of mass and width than presently available.