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

Abstract

I present the calculation of the effective Lagrangian from the \ensuremath{\sigma} 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=\ensuremath{\pi}[2(3/${\mathrm{N}}_{\mathrm{c}}$${)]}^{1/2}$ and the Wess-Zumino term, it contains an extra new term (${\mathrm{N}}_{\mathrm{c}}$/96${\mathrm{\ensuremath{\pi}}}^{2}$) Tr (${\mathrm{\ensuremath{\partial}}}_{\mathrm{\ensuremath{\mu}}}$${\mathrm{L}}^{\mathrm{\ensuremath{\mu}}}$${)}^{2}$ which must be treated as a perturbative correction. This new term is responsible for the correct pion form factor corresponding to ${\mathrm{m}}_{\mathrm{\ensuremath{\rho}}}^{2}$=8${\mathrm{\ensuremath{\pi}}}^{2}$${\mathrm{f}}_{\mathrm{\ensuremath{\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 ${\mathrm{f}}_{\mathrm{\ensuremath{\pi}}}$.