Electric and magnetic polarizability of Goldstone pions to subleading O(N_c^-1) in the bosonized Nambu–Jona-Lasinio model

We study the electric and magnetic polarizability coefficients to subleading order in the inverse number of colors N_c^-1 by constructing Compton scattering amplitudes derived from a bosonized version of the Nambu– Jona-Lasinio (NJL) chiral Lagrangian with finite pion size effects included. We confirm the leading in N_c^-1 mean-field results of Bajc et al. [Nucl. Phys. A604, 406 (1996)] to O(m_π²) in the pion mass m_π. The subleading corrections arise from a gauge invariant sum of meson one-loop diagrams which is nonanalytic in m_π², but free of any chiral or ultraviolet divergences. These corrections lead to a ≳30% reduction in the mean-field values for the polarizability coefficients of the charged pion. Use of the sum rule estimate for the NJL quark mass renders these calculations parameter free, and dependent only on the physical observables of the pion.