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In this work, we consider the effect of a constant anomalous magnetic moment(AMM) of quarks in the SU(2) Nambu--Jona-Lasinio model in the mean fieldapproximation. To this end, we use the Schwinger {\it ansatz}, which representsa linear magnetic field term in the Lagrangian. A regularization methodinspired in the vacuum magnetic regularization (VMR) is adopted to avoidultraviolet divergences. Our results indicate a smooth decrease of thepseudocritical temperature and quark condensates for magnetic fields $B \leq0.1$ GeV$^2$ when a sizable AMM is considered. We found only a small window forInverse Magnetic Catalysis (IMC), in contradiction with NJL predictions made inthe literature. For a low value of AMM, we observe for all ranges of magneticfields considered that the pseudocritical temperature increases with themagnetic field, indicating only Magnetic Catalysis (MC). In our approach, fornonvanishing quark AMM, the chiral symmetry restoration happens always as asmooth crossover and never turns into a first order phase transition.

Effects of the quark anomalous magnetic moment in the chiral symmetry restoration: magnetic catalysis and inverse magnetic catalysis