Theoretical study of the process $D^+_s \to \pi^+ K^0_S K^0_S$ and the isovector partner of $f_0(1710)$

Abstract

We present a theoretical study of $a_0(1710)$, the isovector partner of $f_0(1710)$, in the process $D^+_s \to \pi^+ K^0_SK^0_S$. The weak interaction part proceeds through the charm quark decay process: $c(\bar{s}) \to (s + \bar{d} + u)(\bar{s})$, while the hadronization part takes place in two mechanisms, differing in how the quarks from the weak decay combines into $\pi K^*$ with a quark-antiquark pair $q\bar{q}$ with the vacuum quantum numbers. In addition to the contribution from the tree diagram of the $K^{*+} \to \pi^+ K^0_S$, we have also considered the $K^*\bar{K}^*$ final-state interactions within the chiral unitary approach to generate the intermediate state $a_0(1710)$, then it decays into the final states $K^0_SK^0_S$. We find that the recent experimental measurements on the $K^0_SK^0_S$ and $\pi^+K^0_S$ invariant mass distributions can be well reproduced, and the proposed mechanism can provide valuable information on the nature of scalar $f_0(1710)$ and its isovector partner $a_0(1710)$.