The $D_s^+ \to \pi^+ K_s^0 K_s^0 $ reaction \\and the $I=1$ partner of the $f_0(1710)$ state

TL;DR

This paper investigates the decay modes of the $D_s^+$ meson involving vector mesons and predicts branching ratios for unmeasured reactions, providing insights into the nature of the $f_0(1710)$ and $a_0(1710)$ resonances.

Contribution

It introduces a model generating two resonances from vector-vector interactions and predicts branching ratios for specific $D_s^+$ decay channels, linking them to the nature of certain scalar mesons.

Findings

Two resonances associated with $f_0(1710)$ and $a_0(1710)$ were generated.

Predicted branching ratio for $D_s^+ o \pi^0 K^+ K_s^0$ is approximately $(2.0 imes 10^{-3})$.

Results agree with experimental data for the studied decay modes.

Abstract

We have identified the decay modes of the $D_s^+ \to \pi^+ K^+ K^- , \pi^+ K_s^0 K_s^0$ reactions producing two vector mesons and one pseudoscalar. The posterior vector-vector interaction generates two resonances that we associate to the $f_0(1710)$ and the $a_0(1710)$ recently claimed. We find two acceptable scenarios that give results for the ratio of the branching ratios of these two reactions in agreement with experiment. With these two scenarios we make predictions for the branching ratios of the $D_s^+ \to \pi^0 K^+ K_s^0$ reaction, finding values within the range of $(2.0 \pm 0.7)\times 10^{-3}$. Comparison of these predictions with coming experimental results on that latter reaction will be very most useful to deepen our understanding on the nature of these two resonances.