Testing $CPT$ with anomalous magnetic moments

A theoretical framework is introduced that describes possible $CPT$-violating effects in the context of quantum electrodynamics. Experiments comparing the anomalous magnetic moments of the electron and the positron can place tight limits on $CPT$ violation. The conventional figure of merit adopted in these experiments, involving the difference between the corresponding $g$ factors, is shown to provide a misleading measure of the precision of $CPT$ limits. We introduce an alternative figure of merit, comparable to one commonly used in $CPT$ tests with neutral mesons. To measure it, a straightforward extension of current experimental procedures is proposed. With current technology, a $CPT$ bound better than about 1 part in $10^{20}$ is attainable