Abstract
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.
Highlights
The understanding of QCD matter with finite temperature and chemical potential is one of the main topics in theoretical physics
We discuss one of the general things of the regularization in the NJL model, which is whether we need to use the regularization on the thermal part by evaluating the quark chiral condensate and thermal properties in the two-flavor NJL model
We discussed a fundamental question, whether we need to apply the regularization on the thermal part when we evaluate the physics quantities in the NJL model by considering two sets of physics qualities: the chiral condensate and thermodynamical quantities which is basically from the grand potential
Summary
The understanding of QCD matter with finite temperature and chemical potential is one of the main topics in theoretical physics. [3,4,5]), it incorporates the chiral symmetry and its spontaneous breaking, the gluonic degrees of freedom are replaced by a local four-point interaction of color currents The essential of this model is that it keeps the important symmetry in QCD, it is trivial to represent the symmetry breaking in QCD which is very useful for helping us to understand the properties of QCD matter. Regularization should be applied to all parts of the equation to get correct physics quantities under the same energy limit for physics consistency To answer this regularization of the thermal part problem, a systematic study is needed. We will investigate the simple and fundamental question: should we use the regularization on the thermal part when we are using the NJL model to calculate the physics quantities?. The vacuum part of grand potential with using regularizations could be written as ΩHvac
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