Do we need to use regularization for the thermal part in the NJL model?

The Nambu–Jona-Lasinio(NJL)model is one of the most useful tools for studying non-perturbative strong interactions in matter.Because it is a nonrenormalizable model,the choice of regularization is a subtle issue.In this paper,we discuss one of the general issues regarding regularization in the NJL model,which is whether we need to use regularization for the thermal part by evaluating the quark chiral condensate and thermal properties in the two-flavor NJL model.The calculations in this work include three regularization schemes that contain both gauge covariant and invariant schemes.We found that,regardless of the regularization scheme we choose,it is necessary to use regularization for the thermal part when calculating physical quantities related to the chiral condensate and to not use regularization for the thermal part when calculating physical quantities related to the grand potential.