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.

15 pages, 4 figures, 2 tables

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Cited by in corpus (17)

• Two dynamical generated $a_0$ resonances by interactions between vector mesons
• Observation of $a_0(1710{)}^{+}\to K_S^0{K}^{+}$ in study of the $D_s^{+}\to K_S^0{K}^{+}{\pi }^0$ decay
• Theoretical study of the process $D_s^{+}\to {\pi }^{+}{K}_S^0{K}_S^0$ and the isovector partner of $f_0(1710)$
• Repercussion of the $a_0(1710)$ [$a_0(1817)$] resonance and future developments
• Role of the scalar $f_0(980)$ in the process $D_s^{+}\to {\pi }^{+}{\pi }^0{\pi }^0$
• Exploring kaon induced reactions for unraveling the nature of the scalar meson $a_0(1817)$
• Method to observe the $J^P=2^{+}$ partner of the $X_0(2866)$ in the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ reaction
• Unveiling the $a_0(1710)$ nature in the process $J/\psi \to {\bar{K}}^0{K}^{+}{\rho }^{-}$
• Theoretical study of scalar meson $a_0(1710)$ in the ${\eta }_c\to {\bar{K}}^0{K}^{+}{\pi }^{-}$ reaction
• Traces of the new $a_0(1780)$ resonance in the $J/\psi \to \varphi K^{+}{K}^{-}(K^0{\bar{K}}^0)$ reaction
• Roles of the scalar $f_0(500)$ and $f_0(980)$ in the process $D^0\to {\pi }^0{\pi }^0{\bar{K}}^0$
• $J/\psi$ decay to $\varphi ,\omega ,K^{\ast 0}$ plus $f_0(1370)$, $f_0(1710)$, $K_0^{\ast }(1430)$, $f_2(1270)$, $f_2^{\prime }(1525)$ and $K_2^{\ast }(1430)$: role of the $D$-wave for tensor production
• The $D_s^{+}\to K^{+}{\pi }^{+}{\pi }^{-}$ reaction and the scalar $f_0(500)$, $f_0(980)$ and $K_0^{\ast }(700)$ resonances
• Strong decays of $a_0$, $f_0$, $f_2$, and $K_2^{\ast }$ resonances as dynamically generated states of two vector mesons
• Dynamically generated states from the $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$, and $K{K}^{\ast }{\bar{K}}^{\ast }$ systems within the fixed-center approximation
• Role of $a_0(1710)$ in the $J/\psi \to {\rho }^{+}{\rho }^{-}\omega$ and $J/\psi \to \gamma {\rho }^0\omega$ reactions
• Roles of $a_0(980)$ and $a_0(1710)$ in Cabibbo-suppressed process $D^{+}\to {\pi }^0{\pi }^{+}\eta$