SU(3) × SU(3) symmetry breaking in a simple model

Abstract

A field-theoretical model, due to Lévy, is studied. It contains a triplet of quarks and a pseudoscalar and a scalar meson nonet. The original SU(3) × SU(3) symmetry is broken by terms linear in the scalar meson fields. A renormalization and regularization procedure is defined in order to remove the ultra-violet divergences. The possibility of a spontaneous breakdown of the symmetry is described and the Goldstone theorem is verified in the one-loop approximation.

Moreover, the Ademollo-Gatto theorem is reproduced. The axial vector coupling constants differ in first order of the SU(3) symmetry breaking.