Lorentz-Violating Extension of the Standard Model

TL;DR

This work develops a general Lorentz-violating extension of the Standard Model arising from spontaneous Lorentz breaking, preserving gauge invariance, energy-momentum conservation, and observer Lorentz symmetry while permitting particle-frame violations. The authors extract an extended QED and a detailed pure-photon sector, deriving modified Maxwell equations with two propagating photon modes that induce vacuum birefringence, and they connect these effects to cosmological and terrestrial bounds. Radiative-correction analyses show that CPT-odd contributions to k_AF vanish at one loop under anomaly cancellation, while CPT-even k_F receives divergent corrections tied to fermion-sector coefficients c_{μν}, implying a bare k_F is required for renormalizability. The work demonstrates that Planck-scale Lorentz violation can yield observable, Planck-suppressed signals in cosmology and precision QED experiments, and outlines key theoretical and experimental avenues for constraining the theory.

Abstract

In the context of conventional quantum field theory, we present a general Lorentz-violating extension of the minimal SU(3) x SU(2) x U(1) standard model including CPT-even and CPT-odd terms. It can be viewed as the low-energy limit of a physically relevant fundamental theory with Lorentz-covariant dynamics in which spontaneous Lorentz violation occurs. The extension has gauge invariance, energy-momentum conservation, and covariance under observer rotations and boosts, while covariance under particle rotations and boosts is broken. The quantized theory is hermitian and power-counting renormalizable, and other desirable features such as microcausality, positivity of the energy, and the usual anomaly cancellation are expected. Spontaneous symmetry breaking to the electromagnetic U(1) is maintained, although the Higgs expectation is shifted by a small amount relative to its usual value and the $Z^0$ field acquires a small expectation. A general Lorentz-breaking extension of quantum electrodynamics is extracted from the theory, and some experimental tests are considered. In particular, we study modifications to photon behavior. One possible effect is vacuum birefringence, which could be bounded from cosmological observations by experiments using existing techniques. Radiative corrections to the photon propagator are examined. They are compatible with spontaneous Lorentz and CPT violation in the fermion sector at levels suggested by Planck-scale physics and accessible to other terrestrial laboratory experiments.