Generalizing the Coleman-Hill theorem

Following the work of Khare et al., we show that the generalization to systems with spontaneous symmetry breaking of the Coleman-Hill theorem to one-loop order can be extended to the case including fermions with the most general interactions. Although the correction to the parity-odd part of the vacuum polarization looks complicated in the Higgs phase, it turns out that the correction to the Chern-Simons term is identical to that in the symmetric phase, with the difference coming only from the contribution of the would be Chern-Simons term. We also discuss the implication of our result to non-Abelian systems.