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

Abstract

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 the characteristic strong cusp shape. Cross sections and invariant mass distributions are evaluated which should serve, comparing with future data, to test the dynamics of the chiral unitary approach used for the evaluations and the nature of these resonances.