  We compute the full vacuum polarization tensor in the minimal QED extension.
We find that its low-energy limit is dominated by the radiatively induced
Chern-Simons-like term and the high-energy limit is dominated by the c-type
coefficients. We investigate the implications of the high-energy limit for the
QED and QCD running couplings. In particular, the QCD running offers the
possibility to study Lorentz-violating effects on the parton distribution
functions and observables such as the hadronic R ratio.
