Theoretical study of scalar meson $a_0(1710)$ in the $\hat{I}{\cdot }_c\to {\bar{K}}^0{K}^{+}\ddot{I}{€}^{-}$ reaction

Abstract

We investigate the process $\hat{I}{\cdot }_c\to {\bar{K}}^0{K}^{+}\ddot{I}{€}^{-}$ by taking into account the $S$-wave $K^{\ast }{\bar{K}}^{\ast }$ and $\ddot{I}\ddot{I}‰$ interactions within the unitary coupled-channel approach, where the scalar meson $a_0(1710)$ is dynamically generated. In addition, the contributions from the intermediate resonances $K_0^{\ast }(1430{)}^{-}\to {\bar{K}}^0\ddot{I}{€}^{-}$ and $K_0^{\ast }(1430{)}^0\to K^{+}\ddot{I}{€}^{-}$ are also considered. We find a significant dip structure around 1.8~GeV, associated to the $a_0(1710)$, in the ${\bar{K}}^0{K}^{+}$ invariant mass distribution, and the clear peaks of the $K_0^{\ast }(1430)$ in the ${\bar{K}}^0\ddot{I}{€}^{-}$ and $K^{+}\ddot{I}{€}^{-}$ invariant mass distributions, consistent with the {\it BABAR} measurements. We further estimate the branching fractions $\mathcal{B}(\hat{I}{\cdot }_c\to {\bar{K}}^{\ast 0}{K}^{\ast +}\ddot{I}{€}^{-})=5.5\times 10^{-3}$ and $\mathcal{B}(\hat{I}{\cdot }_c\to \ddot{I}‰\ddot{I}{}^{+}\ddot{I}{€}^{-})=7.9\times 10^{-3}$. Our predictions can be tested by the BESIII and BelleII experiments in the future.

9 pages, 9 figures