The $$D_s^+ \rightarrow \pi ^+ K_S^0 K_S^0 $$ D s + → π + K S 0 K S 0 reaction and the $$I=1$$ I = 1 partner of the $$f_0(1710)$$ f 0 ( 1710 ) state

Abstract

Abstract We have identified the decay modes of the $$D_s^+ \rightarrow \pi ^+ K^{*+} K^{*-} , \pi ^+ K^{*0} \bar{K}^{*0}$$ D s + → π + K ∗ + K ∗ - , π + K ∗ 0 K ¯ ∗ 0 reactions producing a pion and two vector mesons. The posterior vector–vector interaction generates two resonances that we associate to the $$f_0(1710)$$ f 0 ( 1710 ) and the $$a_0(1710)$$ a 0 ( 1710 ) recently claimed, and they decay to the observed $$K^+ K^-$$ K + K - or $$K_S^0 K_S^0$$ K S 0 K S 0 pair, leading to the reactions $$D_s^+ \rightarrow \pi ^+ K^+ K^- , \pi ^+ K_S^0 K_S^0$$ D s + → π + K + K - , π + K S 0 K S 0 . The results depend on two parameters related to external and internal emission. We determine a narrow region of the parameters consistent with the large $$N_c$$ N c limit within uncertainties which gives rise to decay widths in agreement with experiment. With this scenario we make predictions for the branching ratio of the $$a_0(1710)$$ a 0 ( 1710 ) contribution to the $$D_s^+ \rightarrow \pi ^0 K^+ K_S^0$$ D s + → π 0 K + K S 0 reaction, finding values within the range of $$(1.3 \pm 0.4)\times 10^{-3}$$ ( 1.3 ± 0.4 ) × 10 - 3 . Comparison of these predictions with coming experimental results on that latter reaction will be most useful to deepen our understanding on the nature of these two resonances.