Dynamical quark mass generation in a strong external magnetic field

We investigate the effect of a strong magnetic field on dynamical chiral symmetry breaking in quenched and unquenched QCD. To this end we apply the Ritus formalism to the coupled set of (truncated) Dyson-Schwinger equations for the quark and gluon propagator under the presence of an external constant Abelian magnetic field. We work with an approximation that is trustworthy for large fields eH > \Lambda_{QCD}^2 but is not restricted to the lowest Landau level. We confirm the linear rise of the quark condensate with large external field previously found in other studies and observe the transition to the asymptotic power law at extremely large fields. We furthermore quantify the validity of the lowest Landau level approximation and find substantial quantitative differences to the full calculation even at very large fields. We discuss unquenching effects in the strong field propagators, condensate and the magnetic polarization of the vacuum. We find a significant weakening of magnetic catalysis caused by the back reaction of quarks on the Yang-Mills sector. Our results support explanations of the inverse magnetic catalysis found in recent lattice studies due to unquenching effects.