The quark mass gap in a magnetic field

A magnetic field and the resulting Landau degeneracy enhance the infrared contributions to the quark mass gap. The gap does not grow arbitrarily, however, for models of asymptotic free interactions. For B→∞, the magnetic field decouples from the dimensionally reduced self-consistent equations, so that the gap behaves as ∼ΛQCD (or less), instead of ∼|eB|. On the other hand, the number of participants to the chiral condensate keeps increasing as ∼|eB| so that |〈ψ¯ψ〉|∼|eB|ΛQCD. After the mass gap stops developing, nothing tempers the growth of screening effects as B→∞. These features are utilized to interpret the reduction of critical temperatures for the chiral and deconfinement phase transitions at finite B, recently found on the lattice. The structures of mesons are analyzed and light mesons are identified. Applications for cold, dense quark matter are also briefly discussed.