Does there arise a significant enhancement of the dynamical quark mass in external magnetic field?

Recently, it was found in QED that the generation of a dynamical electron mass in a strong magnetic field is significantly enhanced by the perturbative electron mass. In the present Letter, the related question of a possible enhancement of the dynamical quark mass in an external magnetic field and with a bare mass term is investigated in the Nambu–Jona-Lasinio model.