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

We develop a model to reproduce the mass distributions of pairs of mesons in the Cabibbo-suppressed $D^+_s \to K^+ \pi^+ \pi^-$ decay. The largest contributions to the process comes 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 to finally produce the $K^+ \pi^+ \pi^-$ final state. These last three modes are correlated by means of only one parameter. We obtain a fair reproduction of the experimental data for the three mass distributions as well as the relative weight of the three light scalar mesons, which we see as further support for the nature of these states as dynamically generated from the interaction of pseudoscalar mesons.