Chiral approach to the two pion decay of the Roper

Abstract

The analysis of Manley and collaborators [1] of the decay of the Roper into two pions requires the introduction of an effective scalar-isosclar ϵ or σ meson in order to describe the s-wave ππ interaction. Here we try to understand at a more fundamental level the origin of this effective channel. In our model the two pions are produced in single pion-baryon-baryon vertices and their re-scattering in the L=0, I=0 channel is explicitly evaluated. For that purpose we use unitarized chiral perturbation theory to obtain the Bethe-Salpeter amplitude for the two pion re-scattering in the appropriate channel. Our model produces invariant mass distributions in agreement with the ones obtained in Manley's approach.