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 e anti e loops is identical to the one for virtual q anti q loops. However, due to confinement, or to the growth of αs as p2 decreases, a direct calculation of the diagram is not allowed. At large p2 we consider the virtual q anti q diagram, in the intermediate region we discuss the role of the contribution of quark condensates left angle q anti q right angle 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 left angle q anti q right angle and virtual q anti q loops are relevant only for very high radiation density ∝300 MeV/fm3 and very strong magnetic fields of order ∝1014 T. (orig.)