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

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.