Unveiling the $a_0(1710)$ nature in the process $J/\psi \to {\bar{K}}^0{K}^{+}{\rho }^{-}$

Abstract

We have investigated the process $J/\psi \to {\bar{K}}^0{K}^{+}{\rho }^{-}$ by taking into account the $S$-wave $K^{\ast }{\bar{K}}^{\ast }$, $\rho \omega$, and $\rho \varphi$ 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 $K_1(1270{)}^{-}(\to {\bar{K}}^0{\rho }^{-})$ and $K_1(1270{)}^0(\to K^{+}{\rho }^{-})$. 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 ${\bar{K}}^0{\rho }^{-}$ and $K^{+}{\rho }^{-}$ 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

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• Theoretical study of the open-flavor tetraquark $T_{c\bar{s}}(2900)$ in the process ${\bar{B}}_s^0\to K^0{D}^0{\pi }^0$
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