Meson-baryon reactions with strangeness−1within a chiral framework

Abstract

We study meson-baryon scattering with strangeness -1 in unitary chiral perturbation theory. Ten coupled channels are considered in our work, namely $\pi^0 \Lambda$, $\pi^0 \Sigma^0$, $\pi^- \Sigma^+$, $\pi^+ \Sigma^-$, $K^- p$, $\bar{K}^0 n$, $\eta \Lambda$, $\eta \Sigma^0$, $K^0 \Xi^0$ and $K^+ \Xi^-$. A large amount of experimental data are analyzed, including the recent precise measurement by the SIDDHARTA Collaboration of the energy shift and width of the $1s$ state of kaonic hydrogen. This leads to a strong constraint on the free parameters in our theory and of the resulting meson-baryon scattering amplitudes. We also analyze the uncertainty that stems by using several different strategies to perform the fits to data. It is found that large uncertainties in the subthreshold extrapolation of the $K^-p$ scattering amplitude arise by employing either only one common weak pseudoscalar decay constant or distinguishing between $f_\pi$, $f_K$ and $f_\eta$. However, in both cases a good reproduction of experimental data is obtained. We also discuss the pole content of the resulting $S$-wave amplitudes, particularly in connection with the two-pole structure of the $\Lambda(1405)$ resonance.