Further understanding the nature of $a_0(1710)$ in the $D_s^{+}\to \ddot{I}{€}^0{K}^{+}{K}_S^0$ decay

Abstract

Based on our previous work about the role of $a_0(1710)$ in the $D_s^{+}\to \ddot{I}{€}^{+}{K}_S^0{K}_S^0$ decay [Phy. Rev. D 105, 116010 (2022)], we perform a further theoretical study of $a_0(1710{)}^{+}$ in the process $D_s^{+}\to \ddot{I}{€}^0{a}_0(1710{)}^{+}\to \ddot{I}{€}^0{K}^{+}{K}_S^0$. In addition to $a_0(1710)$, the contributions of $K^{\ast }$ and $a_0(980)$ are also taken into account. Firstly, we consider the contributions from the tree diagrams of $K^{\ast +}\to K^{+}\ddot{I}{€}^0$ and ${\bar{K}}^{\ast 0}\to \ddot{I}{€}^0{\bar{K}}^0$. Secondly, we describe the final state interaction of $K\bar{K}$ in the chiral unitary approach to study the contribution of $a_0(980)$, while the $a_0(1710)$ state is dynamically generated from the $K^{\ast }{\bar{K}}^{\ast }$ interaction, and then decays into $K^{+}{\bar{K}}^0$. Since the final $K^{+}{K}_S^0$ state is in pure isospin $I=1$, the $D_s^{+}\to \ddot{I}{€}^0{K}^{+}{K}_s^0$ decay is an ideal process to study the $a_0(1710{)}^{+}$ and $a_0(980{)}^{+}$ resonances. Based on our theoretical calculations, it is found that the recent experimental measurements on the $K^{+}{K}_S^0$, $\ddot{I}{€}^0{K}^{+}$, and $\ddot{I}{€}^0{K}_S^0$ invariant mass distributions can be well reproduced, which supports the molecular $K^{\ast }{\bar{K}}^{\ast }$ nature of the scalar $a_0(1710)$ resonance.

8 pages, 8 figures