The influence of quark anomalous magnetic moment in the Nambu–Jona-Lasinio model with different regularizations

The Nambu–Jona-Lasinio model is known for its simplicity and capacity to reproduce some of the basic characteristics of the quantum chromodynamics phase diagram. However, since it is a nonrenormalizable model, there are regularization issues that should be treated conveniently. This is the case when considering the quark anomalous magnetic moment (AMM) when external constant magnetic fields are present. Regularization procedures based on entangled functions between the magnetic field and the cutoff of the model can predict first-order phase transitions for chiral symmetry restoration at finite values of magnetic fields and inverse magnetic catalysis. The strengths of magnetic fields explored in NJL model and lattice QCD do not show first-order phase transition. In the present work, we show that some of the previous results are regularization-dependent effects and how to handle the divergences using the vacuum magnetic regularization scheme.