On the isospin 0 and 1 resonances from $\pi \Sigma$ photoproduction data

Recently we presented a successful strategy to extract the position of the two $\Lambda(1405)$ poles from experimental photoproduction data on the $\gamma p \to K^+ \pi^0 \Sigma^0$ reaction at Jefferson Lab. Following a similar strategy, we extend the previous method to incorporate also the isospin 1 component which allows us to consider in addition the experimental data on $\gamma p \to K^+ \pi^\pm \Sigma^\mp$. The idea is based on considering a production mechanism as model independent as possible and implementing the final state interaction of the final meson-baryon pair based on small modifications of the unitary chiral perturbation theory amplitudes. Good fits to the data are obtained with this procedure, by means of which we can also predict the cross sections for the $K^- p \to \bar K N$, $\pi \Sigma$, $\pi\Lambda$ reactions for the different charge channels. Besides the two poles found for the $\Lambda(1405)$ resonance, we discuss the possible existence of an isospin 1 resonance in the vicinity of the $\bar K N$ threshold.