Unveiling the $a_0(1710)$ nature in the process $J/\ddot{I}ˆ\to {\bar{K}}^0{K}^{+}\ddot{I}{}^{-}$

Abstract

We have investigated the process $J/\ddot{I}ˆ\to {\bar{K}}^0{K}^{+}\ddot{I}{}^{-}$ by taking into account the $S$-wave $K^{\ast }{\bar{K}}^{\ast }$, $\ddot{I}\ddot{I}‰$, and $\ddot{I}\ddot{I}•$ final-state interactions, where the scalar meson $a_0(1710)$ is generated. In addition, we also take into account the contributions from the scalar $a_0(980)(\to {\bar{K}}^0{K}^{+})$ and the intermediate resonances $K_1(1270{)}^{-}(\to {\bar{K}}^0\ddot{I}{}^{-})$ and $K_1(1270{)}^0(\to K^{+}\ddot{I}{}^{-})$. Our results show that, in the ${\bar{K}}^0{K}^{+}$ invariant mass distribution, a clear peak structure around 1.8~GeV appears, which could be associated with the scalar $a_0(1710)$, however, no significant structure of the $a_0(980)$ is observed. On the other hand, one can find clear peaks of the $K_1(1270)$ in the ${\bar{K}}^0\ddot{I}{}^{-}$ and $K^{+}\ddot{I}{}^{-}$ invariant mass distributions. The future precise measurement of this process by the BESIII and Belle II Collaborations and the planned Super Tau-Charm Facility (STCF) in the future could shed light on the nature of $a_0(1710)$.

12 pages, 13 figures, the version for PRD. arXiv admin note: substantial text overlap with arXiv:2306.15964