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

Abstract

A $1/\mathbb{N}$ expansion of the chiral Lagrangian for baryons is formulated and used to study the low-energy dynamics of baryons interacting with the pion nonet $\pi$, $K$, $\eta$ and ${\eta }^{\prime }$ in a combined expansion in chiral symmetry breaking and $1/\mathbb{N}$. Strong $CP$-violation is included. The chiral Lagrangian correctly implements nonet symmetry and contracted spin-flavor symmetry for baryons in the large $\mathbb{N}$ 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 $1/\mathbb{N}$ expansion for finite $\mathbb{N}$ is explained. Flavor-$27$ baryon mass splittings are calculated at leading order in chiral perturbation theory as an example.

25 pages, two postscript figures