Baryons as solitons in the effective Lagrangian of spontaneously broken chiral symmetry

Abstract

I present the calculation of the effective Lagrangian from the σ quark model based on some reasonable assumptions of the spontaneously broken chiral symmetry, the large-${\mathrm{N}}_{\mathrm{c}}$ limit, and the nature of the effective action expansion. In addition to the Skyrme Lagrangian with a unique coupling constant e=π[2(3/${\mathrm{N}}_{\mathrm{c}}$ ${\left)\right]}^{1/2}$ and the Wess-Zumino term, it contains an extra new term (${\mathrm{N}}_{\mathrm{c}}$/96${\mathrm{\pi }}^2$) Tr (${\mathrm{\partial }}_{\mathrm{\mu }}$ ${\mathrm{L}}^{\mathrm{\mu }}$ ${)}^2$ which must be treated as a perturbative correction. This new term is responsible for the correct pion form factor corresponding to ${\mathrm{m}}_{\mathrm{\rho }}^2$=8${\mathrm{\pi }}^2$ ${\mathrm{f}}_{\mathrm{\pi }}^2$(3/${\mathrm{N}}_{\mathrm{c}}$ ). This model can be used to describe the rich low-energy dynamics of baryons and mesons with the unique mass scale ${\mathrm{f}}_{\mathrm{\pi }}$.