Effective 1/Ncexpansion in the Nambu–Jona-Lasinio model

Abstract

The 1/${\mathit{N}}_{\mathit{c}}$ expansion is developed for the Nambu--Jona-Lasinio model, a commonly used low-energy model of QCD. The next to leading order in this expansion that represents pion and sigma meson exchange in the gap equation is evaluated perturbatively. These contributions are seen to be differing in sign, a feature that is due to their opposite parities. Physically one can interpret this meson exchange as giving rise to screening (\ensuremath{\pi}) or antiscreening (\ensuremath{\sigma}) of the bare four-point interaction. As a consequence of the higher isospin degeneracy of the pion, the contributions from it are found to dominate. In total, we find that the resulting corrections to the usual Hartree approximation are of the order of 10%, justifying a posteriori the perturbative approach.