The Lorentz-Violating Extension of the Standard Model

Abstract

Abstract. Quantum-gravity effects are expected to be suppressed by the Planck mass. For experimental progress it is therefore important to identify potential signatures from Planck-scale physics that are amenable to ultrahigh-precision tests. It is argued that minuscule violations of Lorentz and CPT symmetry are candidate signals. In addition, theoretical and experimental aspects of the Standard-Model Extension, which describes the emergent low-energy effects, are discussed. MotivationAn important open question in our understanding of nature at its fundamental level concerns a unified quantum description of all fundamental interactions including gravity. Such a theory is likely to become dominant only as the Planck scale is approached, so that quantum-gravity effects are expected to be minuscule at presently attainable energies. Moreover, the absence of a fully realistic and viable candidate underlying theory provides a major obstacle for the identification of concrete quantum-gravity signatures that can be searched for in present-day or near-future experiments.A possible approach to overcome this phenomenological issue is to determine exact relations in the currently accepted laws of physics that may be violated in prospective fundamental theories and that can be tested with ultrahighprecision. Symmetries typically satisfy these criteria. For example, Lorentz and CPT invariance are cornerstones of our present understanding of nature at the fundamental level, and a variety of Lorentz and CPT tests belong to the most sensitive null experiments available. Lorentz and CPT violation is also a key feature of certain approaches to underlying physics.For example, couplings varying on cosmological scales are one possible source of Lorentz and CPT violation [1]. This fact does not come as a surprise: parameters dependent on spacetime break translational invariance, and translations, rotations, and boosts are linked in the Poincaré group. Thus, violations of translation symmetry can also affect Lorentz invariance. This can be understood intuitively as follows. The equations of motion typically contain the gradient of the coupling, which selects a preferred direction in spacetime leading to apparent Lorentz violation.In this talk, we discuss some theoretical and experimental aspects of the Standard-Model Extension (SME) [2][3][4][5][6][7], which is the low-energy framework for Lorentz-breaking effects. The SME is a dynamical model constructed to contain all Lorentz-and CPT-violating lagrangian terms consistent with coordinate