QCD critical end point under strong magnetic fields

We use the three-flavor Nambu-Jona-Lasinio model, which includes strangeness and quark physical masses in the mean field approximation, to investigate the influence of strong magnetic fields on the QCD phase diagram covering the whole T-mu plane. It is found that the first order segment of the transition line becomes longer as the field strength increases so that a larger coexistence region for hadronic and quark matter should be expected for strong magnetic fields. The location of the critical end point is also affected by the presence of magnetic fields that invariably increase the temperature value at which the first order line terminates. On the other hand, at low temperatures, the critical chemical potential displays an oscillation around the B = 0 value for magnetic fields within the 10(17) - 10(20) G range. These findings may have nontrivial consequences for the physics of magnetars and heavy ion collisions.