Quark anomalous magnetic moment in an extreme magnetic background from pQCD

We compute the one-loop QCD correction to the photon-quark-antiquark vertex in an extremely strong magnetic background, i.e., one in which √(eB) is much larger than all other mass scales. We resort to the lowest-Landau level approximation, and consider on-shell fermions. We find that the the total magnetic moment is such that that the anomalous magnetic moment contributes to the electric part ∼ iE_3σ_3, the other contributions to B·σ and iE·σ_⊥ being completely suppressed. We show results for the anomalous magnetic moment of quarks up and down, scaled by their values in the vacuum, as a function of the external magnetic field, considering dressed gluons and a renormalization scale μ_ MS=√(|eB|).