Chiral perturbation theory and the SU(2) Nambu–Jona-Lasinio model: A comparison

We examine the Nambu–Jona-Lasinio model in its SU(2) form, and compare this with chiral perturbation theory (CPT). We use a consistent Hartree approximation as being the leading term in a 1/${\mathit{N}}_{\mathit{c}}$ expansion for our mean field calculations and we make implicit chiral expansions of all the physical quantities directly from their defining equations. This enables us to extract explicit expressions for the observable scale-independent constants that are used in CPT. We find that this procedure gives reasonable agreement for the scale-independent constants. We compare our results with existing direct calculations in the literature, and point out difficulties in interpretation, especially with regard to l${\mathrm{¯}}_5$ and ${\mathit{l}}_7$. Our results appear to be in line with the agreement obtained via methods of bosonization, although, due to the different approximations made, these methods are not directly comparable.