  We evaluate the next-to-leading order correction to the Nambu-Jona-Lasinio
model starting from quantum chromodynamics. We show that a systematic expansion
exists, starting from a given set of exact classical solutions, so that higher
order corrections could in principle be computed at any order. In this way, we
are able to fix the constants of the Nambu-Jona-Lasinio model from quantum
chromodynamics and analyze the behavior of strong interactions at low energies.
The technique is to expand in powers of currents of the generating functional.
We apply it to a simple Yukawa model with self-interaction showing how this has
a Nambu-Jona-Lasinio model and its higher order corrections as a low-energy
limit. The same is shown to happen for quantum chromodynamics in the chiral
limit with two quarks. We prove stability of the NJL model so obtained. Then,
we prove that the correction term we obtained does not change the critical
temperature of the chiral transition of the Nambu-Jona-Lasinio model at zero
chemical potential.
