QCD corrections to QED vacuum polarization

We compute QCD corrections to QED calculations for vacuum polarization in background magnetic fields. Formally, the diagram for virtual eē loops is identical to the one for virtual qq̄ loops. However, due to confinement, or to the growth of α_s as p² decreases, a direct calculation of the diagram is not allowed. At large p² we consider the virtual qq̄ diagram, in the intermediate region we discuss the role of the contribution of quark condensates 〈qq̄〉 and at the low-energy limit we consider the π⁰, as well as charged pion π⁺π^- loops. Although these effects seem to be out of the measurement accuracy of photon–photon laboratory experiments, they may be relevant for γ-ray burst propagation. In particular, for emissions from the center of the galaxy (8.5 kpc), we show that mixing between the neutral pseudo-scalar pion π₀ and photons renders a deviation from the power-law spectrum in the TeV range. For scalar quark condensates 〈qq̄〉 and virtual qq̄ loops are relevant only for very high radiation density ∼300 MeV/fm³ and very strong magnetic fields of order ∼10¹4 T. PACS 12.20.Ds; 14.40.-n; 12.38.Aw; 14.65.Bt