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

TL;DR

This paper models the production of the $f_0(980)$ resonance in specific $D_s^+$ decays using a chiral unitary approach, successfully reproducing experimental invariant mass distributions and confirming the resonance's presence.

Contribution

It introduces a theoretical framework combining weak decay mechanisms with chiral unitary methods to describe $f_0(980)$ production in $D_s^+$ decays, aligning well with experimental data.

Findings

The $f_0(980)$ resonance appears in both $ o \, ext{pi}^+ ext{pi}^-$ and $ o \, ext{K}^+ ext{K}^-$ channels.

Theoretical invariant mass distributions agree with experimental data.

The model confirms the role of final state interactions in resonance formation.

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.