TY - JOUR
T1 - Lorentz violation in Hořava-Lifshitz-type theories
AU - Pospelov, Maxim
AU - Shang, Yanwen
PY - 2012/5/3
Y1 - 2012/5/3
N2 - 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 "Hořava-Lifshitz" energy scale Λ HL and couples to the standard model through interactions suppressed by M pl, the transmission of the Lorentz violation into the standard model is protected by the ratio ΛHL2/Mpl2. A wide-scale separation Λ HL≪ M pl 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 Hořava-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 Λ 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.
AB - 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 "Hořava-Lifshitz" energy scale Λ HL and couples to the standard model through interactions suppressed by M pl, the transmission of the Lorentz violation into the standard model is protected by the ratio ΛHL2/Mpl2. A wide-scale separation Λ HL≪ M pl 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 Hořava-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 Λ 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.
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U2 - 10.1103/PhysRevD.85.105001
DO - 10.1103/PhysRevD.85.105001
M3 - Article
AN - SCOPUS:84860745756
SN - 1550-7998
VL - 85
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 10
M1 - 105001
ER -