Lorentz violation from the Higgs portal

We study bounds and signatures of models where the Higgs doublet has an inhomogeneous mass or vacuum expectation value, being coupled to a hidden sector that breaks Lorentz invariance. This physics is best described by a low-energy effective Lagrangian in which the Higgs speed-of-light is smaller than c; such effect is naturally small because it is suppressed by four powers of the inhomogeneity scale. The Lorentz violation in the Higgs sector is communicated at tree level to fermions (via Yukawa interactions) and to massive gauge bosons, although the most important effect comes from one-loop diagrams for photons and from two-loop diagrams for fermions. We calculate these effects by deriving the renormalization-group equations for the speed-of-light of the Standard Model particles. An interesting feature is that the strong coupling dynamically makes the speed-of-light equal for all colored particles.