$\bar K$ induced formation of the $f_0(980)$ and $a_0(980)$ resonances on proton targets

We perform a calculation of the cross section for nine reactions induced by $\bar K$ scattering on protons. The reactions studied are $K^-p \to \Lambda \pi^+ \pi^-$, $K^-p \to \Sigma^0 \pi^+ \pi^-$, $K^-p \to \Lambda \pi^0 \eta$, $K^-p \to \Sigma^0 \pi^0 \eta$, $K^-p \to \Sigma^+ \pi^- \eta$, $\bar K^0 p \to \Lambda \pi^+ \eta$, $\bar K^0 p \to \Sigma^0 \pi^+ \eta$, $\bar K^0 p \to \Sigma^+ \pi^+ \pi^-$, $\bar K^0 p \to \Sigma^+ \pi^0 \eta$. We find that in the reactions producing $\pi^+ \pi^-$ a clear peak for the $f_0(980)$ resonance is found, while no trace of $f_0(500)$ appears. Similarly, in the cases of $\pi \eta$ production a strong peak is found for the $a_0(980)$ resonance, with th…