Dynamical generation of the scalar $f_0(500)$, $f_0(980)$ and $K^*_0 (700)$ resonances in the $D^+_s \to K^+ \pi^+ \pi^-$ reaction

In this talk, we present the recent work for the Cabibbo-suppressed $D^+_s \to K^+ \pi^+ \pi^-$ decay, which was recently measured by the BESIII collaboration. We investigate the dynamical generation of the scalar $f_0(500)$, $f_0(980)$ and $K^*_0 (700)$ resonances in which three mass distributions of pairs of mesons in this reaction are shown. The largest contributions to the process come from the $D^+_s \to K^+ \rho^0$ and $D^+_s \to K^{*0} \pi^+$ decay modes, but the $D^+_s \to K^*_0(1430) \pi^+$ and $D^+_s \to K^+ f_0(1370)$ modes also play a moderate role and all of them are introduced empirically. Instead, the contribution of the $f_0(500)$, $f_0(980)$ and $K^*_0(700)$ resonances is introduced dynamically by looking at the decay modes at the quark level, hadronizing $q \bar{q}$ pairs to give two mesons, and allowing these mesons to interact, for which we follow the chiral unitary approach, to finally produce the $K^+ \pi^+ \pi^-$ final state. While the general features of the mass distributions are fairly obtained, we pay special attention to the specific effects created by the light scalar resonances, which are visible in the low mass region of the $\pi^+ \pi^- (f_0(500))$ and $K^+ \pi^-(K^*_0(700))$ mass distributions and a narrow peak for $\pi^+ \pi^- $ distribution corresponding to $f_0(980)$ excitation. The contribution of these three resonances is generated by only one parameter. We see the agreement found in these regions as further support for the nature of the light scalar states as dynamically generated from the interaction of pseudoscalar mesons.