Relativistic chiral SU(3) symmetry, large-Nc sum rules and meson–baryon scattering

Abstract The relativistic chiral SU (3) Lagrangian is used to describe kaon–nucleon scattering imposing constraints from the pion–nucleon sector and the axial-vector coupling constants of the baryon octet states. We solve the covariant coupled-channel Bethe–Salpeter equation with the interaction kernel truncated at chiral order Q 3 where we include only those terms which are leading in the large- N c limit of QCD. The baryon decuplet states are an important explicit ingredient in our scheme, because together with the baryon octet states they form the large- N c baryon ground states of QCD. Part of our technical developments is a minimal chiral subtraction scheme within dimensional regularization, which leads to a manifest realization of the covariant chiral counting rules. All SU (3) symmetry-breaking effects are well controlled by the combined chiral and large- N c expansion, but still found to play a crucial role in understanding the empirical data. We achieve an excellent description of the data set typically up to laboratory momenta of p lab ≃500 MeV.