An innovative approach for sketching the QCD phase diagram within the NJL model using Lagrange Multipliers

We develop a new approach for sketching the quantum chromodynamics phase-diagram within the Nambu--Jona-Lasinio model for arbitrarily large values of the coupling constant, temperature and chemical potential based upon the strategy of Lagrange multipliers that constrains the corresponding gap equation and its mass gradient. Our approach distinguishes continuous from discountinuous phase transitions and thus is capable of locating the position of the Critical End Point from the thermodynamical parameters of the model alone, without direct reference to the chiral susceptibility or any other observable. The approach can be straightforwardly extended to those effective chiral quark models with a momentum independent constituent quark mass.