Meson loops in the Nambu-Jona-Lasinio model

Abstract

The effects of meson loops in the vacuum sector of the Nambu--Jona-Lasinio model are calculated. Using the effective action formalism we take consistently all next-to-leading-order $\frac{1}{\text{Nc}}$ terms into account. This leads to a symmetry-conserving approach, in which all features of spontaneously broken chiral symmetry, such as the Goldstone theorem, the Gold\-ber\-ger--Treiman and the Gell-Mann--Oakes--Renner relations are preserved. Contributions to $⟨\overline{q}q⟩$ and $F_{\pi }$ are calculated, and are shown to be substantial, at the level of $\sim 30\%$, consistent with the $\frac{1}{\text{Nc}}$ expansion. The leading nonanalytic terms in the chiral expansion of $⟨\overline{q}q⟩$, $F_{\pi }$ and $m_{\pi }$ agree have the same form as the one-loop results of chiral perturbation theory.

Comments: revised version