Chiral Lagrangian for baryons in the1Ncexpansion

Abstract

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