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

TL;DR

This paper provides a theoretical analysis of the decay process $D^+_s o ext{pi}^+ K^0_S K^0_S$, exploring the nature of the isovector partner of $f_0(1710)$ and matching experimental data with a chiral unitary approach.

Contribution

It introduces a novel theoretical model combining weak decay mechanisms and final-state interactions to study the $a_0(1710)$ resonance in $D^+_s$ decays.

Findings

Reproduces experimental invariant mass distributions accurately.

Supports the molecular nature of $a_0(1710)$ as a $K^*ar{K}^*$ bound state.

Provides insights into the structure of scalar mesons $f_0(1710)$ and $a_0(1710)$.

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 $a_0(1710)$.