Constraint from Lamb Shift and Anomalous Magnetic Moment on Radiatively Induced Lorentz and CPT Violation in Quantum Electrodynamics

We investigate the precisely measured anomalous magnetic moment and Lamb shift as tests for the possible existence of the radiatively induced Lorentz and CPT violation effects in quantum electrodynamics. To this end we calculate the one-loop vacuum polarization tensor and vertex radiative correction in dimensional reduction and on-shell renormalization scheme. We explicitly show how the Lorentz and CPT violation sector affects the anomalous magnetic moment and Lamb shift. Remarkably, we find infrared divergences coming from Lorentz and CPT violating term that do not cancel in physical cross sections. This result appears to place stringent constraints on the type of Lorentz/CPT violating terms that can be added to the QED Lagrangian.