Abstract

Violation of CPT and Lorentz symmetry in the photon sector is described within the minimal Standard-Model Extension by a dimension-3 Chern–Simons-like operator parametrized by a four-vector parameter k A F that has been very tightly bounded by astrophysical observations. On the other hand, in the context of the S U ( 2 ) × U ( 1 ) electroweak gauge sector of the Standard-Model Extension, CPT and Lorentz violation is described similarly, by dimension-3 operators parametrized by four-vector parameters k 1 and k 2 . In this work, we investigate in detail the effects of the resulting CPT and Lorentz violation in the photon and Z-boson sectors upon electroweak-symmetry breaking. In particular, we show that, for the photon sector, the relevant Lorentz-violating effects are described at the lowest order by the k A F term, but that there are higher-order momentum-dependent effects due to photon-Z boson mixing. As bounds on CPT and Lorentz violation in the Z sector are relatively weak, these effects could be important phenomenologically. We investigate these effects in detail in this work.

Highlights

  • The main motivation to search for departures of relativity is that various candidate theories of gravity may allow for spontaneous Lorentz violation [1,2,3,4,5,6]

  • While the Standard-Model Extension (SME), being an effective field theory, consists of terms of arbitrary mass dimension, we will consider in this work the superficially renormalizable part of the SME, called the minimal SME

  • Electroweak symmetry breaking will induce mixing between these initial parameters, which leads to physical effects that depend on the energy scale

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Summary

Introduction

The main motivation to search for departures of relativity is that various candidate theories of gravity may allow for spontaneous Lorentz violation [1,2,3,4,5,6]. The effect of such a term has been studied long ago in [12], where an the effect on the photon sector is to provide a Chern–Simons term with a coefficient k AF that is a certain extremely strong bound on k AF was derived from astrophysical observations. Perturbative argument to show how the mixing process arises at low energy for the photon sector We consider both the photon and Z-boson sectors together, and derive the polarization vectors.

CPT and Lorentz-violation at low energy
A October k AF
66 There at quadratic
Polarization Vectors
Analysis of the Dispersion Relation
Branch-Selection Function
Group Velocity
Extended Hamiltonian Formalism
Discussion
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