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We consider a two flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model where theLagrangian includes an interaction term that explicitly breaks the U$_A(1)$anomaly. At finite temperature, the restoration of chiral and axial symmetries,signaled by the behavior of several observables, is investigated. We comparethe effects of two regularizations at finite temperature, one of them, thatallows high momentum quarks states, leading to the full recovery of chiralsymmetry. From the analysis of the behavior of the topological susceptibilityand of the mesonic masses of the axial partners, it is found in the SU(2) modelthat, unlike the SU(3) results, the recovery of the axial symmetry is not aconsequence of the full recovery of the chiral symmetry. Thus, one needs to usean additional idea, by means of a temperature dependence of the anomalycoefficient, that simulates instanton suppression effects.

Interplay between chiral and axial symmetries in a SU(2) Nambu--Jona-Lasinio Model with the Polyakov loop