Implications of a new effective chiral meson Lagrangian

Abstract

Based on a recently derived effective chiral meson Lagrangian from the extended SU(2)⊗ SU(2) Nambu–Jona-Lasinio (ENJL) model, in the linear realization of chiral symmetry, we extract to leading order in the 1/ N c expansion all associated relevant three-point functions ρ→ ππ, σ→ ππ, a 1→ ρπ, a 1→ σπ, as well as the amplitude for ππ scattering. We discuss the formal differences of these amplitudes as compared with those derived in the literature and calculate the associated decay widths and scattering parameters. The differences have two origins: 1. new terms, which are proportional to the current quark mass and arise from taking the correct NJL vacuum from the first steps in a proper-time expansion, are present in the Lagrangian; 2. an implemented chiral covariant treatment of the diagonalization in the pseudoscalar–axial-vector sector induces new couplings between three or more mesonic fields. Both effects have been derived from the chiral Ward Takahashi identities, which are fully taken into account at each order of the proper-time expansion.