$f_0(980)$ production in $D_s^+ \rightarrow \pi^+ \, \pi^+ \, \pi^-$ and $D_s^+ \rightarrow \pi^+ \, K^+ \, K^-$ decays

Abstract

We study the $D_s^+ \rightarrow \pi^+ \, \pi^+ \, \pi^-$ and $D_s^+ \rightarrow \pi^+ \, K^+ \, K^-$ decays adopting a mechanism in which the $D_s^+$ meson decays weakly into a $\pi^+$ and a $q\bar{q}$ component, which hadronizes into two pseudoscalar mesons. The final state interaction between these two pseudoscalar mesons is taken into account by using the Chiral Unitary approach in coupled channels, which gives rise to the $f_0(980)$ resonance. Hence, we obtain the invariant mass distributions of the pairs $\pi^+ \pi^-$ and $K^+ K^-$ after the decay of that resonance and compare our theoretical amplitudes with those available from the experimental data. Our results are in a fair agreement with these data, and a $f_0(980)$ signal is seen in both the $\pi^+\pi^-$ and $K^+K^-$ distributions.