Abstract
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.
Highlights
The sector responsible for the electroweak symmetry breaking still leaves open theoretical questions and is experimentally unknown
Lorentz violation is often phenomenologically studied by considering only non-renormalizable operators leading to corrections to the speed-of-light of the form δc ∼ (E/Λ)p, where p = 1 or 2 and Λ is some high-energy scale, maybe the Planck scale
Once Lorentz symmetry is broken, one expects that the renormalizable terms are strongly affected, such that there are order-unity differences in the speed-of-light of different particles, δc ∼ 1, in dramatic contrast with the experimental bound |δc| < 10−15
Summary
The sector responsible for the electroweak symmetry breaking still leaves open theoretical questions and is experimentally unknown. Being the only superrenormalizable interaction in the Standard Model, this mass term can be viewed as a window open towards the influence of new and unknown high-energy or hidden sectors of the theory. New scalars M (x), neutral under the SM gauge group, can have renormalizable couplings to the Higgs H:. In this paper we consider the possibility that this Higgs portal connects the Standard Model with some hypothetical sector that breaks Lorentz invariance, such that M (x) has a space-time dependent vacuum expectation value (vev) varying on a characteristic small length-scale. Maybe its vev might be ‘foamy’, being non-zero only in some regions, giving rise to a small average vev from a larger fundamental vev In both cases an apparently constant Higgs vev is obtained at low energy, i.e. after averaging over length-scales much bigger than.
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