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 total magnetic moment is such that the anomalous magnetic moment contributes to the electric part ~ iE₃σ₃, 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 μMS̄=√|eB|.
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Fraga et al. (2024) studied this question.
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