Chiral Lagrangian for Baryons in the $1/N_c$ Expansion

Abstract

A $1/\N$ expansion of the chiral Lagrangian for baryons is formulated and used to study the low-energy dynamics of baryons interacting with the pion nonet $π$, $K$, $η$ and $η^\prime$ in a combined expansion in chiral symmetry breaking and $1/\N$. Strong $CP$-violation is included. The chiral Lagrangian correctly implements nonet symmetry and contracted spin-flavor symmetry for baryons in the large $\N$ limit. The implications of nonet symmetry for low-energy baryon-pion interactions are described in detail. The procedure for calculating non-analytic pion-loop corrections to baryon amplitudes in the $1/\N$ expansion for finite $\N$ is explained. Flavor-$\bf 27$ baryon mass splittings are calculated at leading order in chiral perturbation theory as an example.