$CPT$ and Lorentz tests in Penning traps

Abstract

A theoretical analysis is performed of Penning-trap experiments testing CPT and Lorentz symmetry through measurements of anomalous magnetic moments and charge-to-mass ratios. Possible CPT and Lorentz violations arising from spontaneous symmetry breaking at a fundamental level are treated in the context of a general extension of the SU(3) × SU(2) × U(1) standard model and its restriction to quantum electrodynamics. We describe signals that might appear in principle, introduce suitable figures of merit, and estimate CPT and Lorentz bounds attainable in present and future Penning-trap experiments. Experiments measuring anomaly frequencies are found to provide the sharpest tests of CPT symmetry. Bounds are attainable of approximately 10−20 in the electron-positron case and of 10−23 for a suggested experiment with protons and antiprotons. Searches for diurnal frequency variations in these experiments could also limit certain types of Lorentz violation to the level of 10−18 in the electron-positron system and others at the level of 10−21 in the proton-antiproton system. In contrast, measurements comparing cyclotron frequencies are sensitive within the present theoretical framework to different kinds of Lorentz violation that preserve CPT. Constraints could be obtained on one figure of merit in the electron-positron system at the level of 10−16, on another in the proton-antiproton system at 10−24, and on a third at 10−25 using comparisons of H− ions with antiprotons.