Analytic proof of the Weinberg theorem for off mass shell and composite pions

Abstract

The Weinberg theorem for the pion-pion scattering is proved analytically in full detail for quark models in the ladder truncation. The proof is displayed with Feynman diagrams. The axial and vector Ward identities, for the quark propagator and for the ladder, exactly cancel any model dependence. Off mass shell and finite size effects are included in the quark-antiquark pion Bethe Salpeter vertices. This is applied to compute the isospin 0, 1 and 2 scattering matrices off the mass shell .

Poster presented in '' Quark confinement and the hadron spectrum V '', 10-14 September 2002, Gagnano, Italy