Finite temperature corrections to a NLO Nambu-Jona-Lasinio model

We derive the next-to-leading order correction to the Nambu-Jona-Lasinio model starting from quantum chromodynamics. So, 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 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 that a consistent thermodynamic behaviour is obtained as expected for the given parameters.