ar X iv : h ep - p h / 05 11 26 2 v 1 22 N ov 2 00 5 Tests of Lorentz Symmetry with Penning Traps and Antihydrogen

Possibilities for testing Lorentz symmetry using precision experiments with antiprotons in Penning traps and with antihydrogen spectroscopy are reviewed. Estimates of bounds on relevant coefficients for Lorentz violation in the Standard-Model Extension (SME) are considered. THE STANDARD-MODEL EXTENSION Einstein’s General Relativity and the Standard Model of particle physics provide an excellent description of nature. They are expected to merge into a single theory at energies near the Planck scale of 1019 GeV. Experiments cannot access these energies, but one can at least hope to see suppressed effects of Planck-scale physics in suitable high-precision experiments. One possible signal of an underlying unified quantum gravity theory is the violation of Lorentz symmetry. In this proceedings of the 2005 International Conference on Low-Energy Antiproton Physics (LEAP 05), some possibilities for detecting Lorentz and CPT violation in experiments with low-energy antiprotons will be reviewed. Most of the results summarized here are presented in more detail in the published literature, and a few speculative ideas are discussed. Any effects of Lorentz violation can be described using effective field theory [1]. To be realistic, both General Relativity and the Standard Model must be included together with coordinate-independent Lorentz violation. These components make up the effective field theory called the Standard-Model Extension (SME). It provides a general description of all possible realistic Lorentz violations in nature. The Minkowski limit of this theory has been studied for more than a decade [2, 3], and recent work [4] has clarified the key ideas in curved spacetime. Among the underlying ideas are string-theory concepts and various types of symmetry breaking [5]. For some other perspectives on Lorentz violation presented at LEAP ’05, see [6]. The focus in this article is primarily on theoretical and experimental studies of Lorentz tests investigating the SME with Penning traps [7, 8, 9] and with spectroscopy of hydrogen (H) and antihydrogen (H) [10, 11]. A wide range of recent results investigating the SME exists and continues to grow. This includes studies of neutrinos [12], electromagnetism [13, 14], electromagnetic cavities [15], clock-comparison experiments [16], 1 Proceedings for invited talk at Eighth International Conference on Low Energy Antiproton Physics (LEAP ’05), Bonn, Germany, 16-22 May 2005. satellites [17], hydrogen molecules [18], neutral-meson oscillations [19], muons [20], baryogenesis [21], the torsion pendulum [22], spacetime varying couplings [23], the Higgs sector [24], and noncommutative coordinates [25].