QCD Corrections to QED Vacuum Polarization

TL;DR

This paper calculates QCD corrections to QED vacuum polarization, exploring their implications for high-energy astrophysical phenomena like gamma-ray bursts and the effects of quark condensates and meson loops at different energy scales.

Contribution

It introduces a comprehensive analysis of QCD effects on QED vacuum polarization across various energy regimes, including the roles of quark condensates and meson loops, with potential astrophysical implications.

Findings

QCD corrections affect photon propagation in strong magnetic fields.

Pion mixing causes deviations in gamma-ray spectra at TeV energies.

Quark condensates become relevant at extremely high energy densities.

Abstract

We compute QCD corrections to QED calculations for vacuum polarization in background magnetic fields. Formally, the diagram for virtual $e\bar{e}$ loops is identical to the one for virtual $q\bar{q}$ loops. However due to confinement, or to the growth of $\alpha_s$ as $p^2$ decreases, a direct calculation of the diagram is not allowed. At large $p^2$ we consider the virtual $q\bar{q}$ diagram, in the intermediate region we discuss the role of the contribution of quark condensates $\left< q\bar{q}\right>$ and at the low-energy limit we consider the $\pi^0$, as well as charged pion $\pi^+\pi^-$ loops. Although these effects seem to be out of the measurement accuracy of photon-photon laboratory experiments they may be relevant for $\gamma$-ray burst propagation. In particular, for emissions from the center of the galaxy (8.5 kpc), we show that the mixing between the neutral pseudo-scalar pion $\pi_0$ and photons renders a deviation from the power-law spectrum in the $TeV$ range. As for scalar quark condensates $\left< q\bar{q} right>$ and virtual $q\bar{q}$ loops are relevant only for very high radiation density $\sim 300 MeV/fm^3$ and very strong magnetic fields of order $\sim 10^{14} T$.