Abstract
We study the QCD chiral phase transition at finite temperature and finite quark chemical potential within the two flavor Nambu-Jona-Lasinio (NJL) model, where a generalization of the proper-time regularization scheme is motivated and implemented. We find that in the chiral limit the whole transition line in the phase diagram is of second order, whereas for finite quark masses a crossover is observed. Moreover, if we take into account the influence of quark condensate to the coupling strength (which also provides a possible way of how the effective coupling varies with temperature and quark chemical potential), it is found that a CEP may appear. These findings differ substantially from other NJL results which use alternative regularization schemes, some explanation and discussion are given at the end. This indicates that the regularization scheme can have a dramatic impact on the study of the QCD phase transition within the NJL model.