Lorentz violation in Hořava-Lifshitz-type theories

We show that coupling the standard model to a Lorentz symmetry-violating sector may coexist with viable phenomenology provided that the interaction between the two is mediated by higher-dimensional operators. In particular, if the new sector acquires anisotropic-scaling behavior above a ``Ho {r} {r}{}ava-Lifshitz'' energy scale ΛHL and couples to the standard model through interactions suppressed by Mₚₗ, the transmission of the Lorentz violation into the standard model is protected by the ratio ΛHL²/Mₚₗ². A wide-scale separation ΛHLMₚₗ can then make Lorentz-violating terms in the standard model sector within experimental bounds without fine-tuning. We first illustrate our point with a toy example of Lifshitz-type neutral fermion coupled to photon via the magnetic moment operator, and then implement similar proposal for the Ho {r} {r}{}ava-Lifshitz gravity coupled to conventional Lorentz-symmetric matter fields. We find that most radiatively induced Lorentz violation can be controlled by a large-scale separation, but the existence of instantaneously propagating non-Lifshitz modes in gravity can cause a certain class of diagrams to remain quadratically divergent above ΛHL. Such problematic quadratic divergence however can be removed by extending the action with terms of higher Lifshitz-dimension, resulting in a completely consistent setup that can cope with the stringent tests of Lorentz invariance.