On Lorentz violation in Horava-Lifshitz type theories

Abstract

We show that coupling the Standard Model to a Lorentz symmetry violating sector may co-exist 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 "Horava-Lifshitz" energy scale L_HL and couples to the Standard Model through interactions suppressed by M_P, the transmission of the Lorentz violation into the Standard Model is protected by the ratio L_HL^2/M_P^2. A wide scale separation, L_HL<<M_P, 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\v{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 L_HL. 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.