Theoretical study of the process $D_s^{+}\to \ddot{I}{€}^{+}{K}_S^0{K}_S^0$ 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 $D_s^{+}\to \ddot{I}{€}^{+}{K}_S^0{K}_S^0$. 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 $\ddot{I}€K^{\ast }$ with a quark-antiquark pair $q\bar{q}$ with the vacuum quantum numbers. In addition to the contribution from the tree diagram of the $K^{\ast +}\to \ddot{I}{€}^{+}{K}_S^0$, we have also considered the $K^{\ast }{\bar{K}}^{\ast }$ final-state interactions within the chiral unitary approach to generate the intermediate state $a_0(1710)$, then it decays into the final states $K_S^0{K}_S^0$. We find that the recent experimental measurements on the $K_S^0{K}_S^0$ and $\ddot{I}{€}^{+}{K}_S^0$ 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 $a_0(1710)$.

9 pages, 9 figures, the version for PRD