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.
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