We have studied the effects of the standard-model extension (SME) on hydrogen as a realization of new physics effects that incorporate Lorentz and $CPT$ violation. Specifically, we calculated the SME-induced energy level shifts at order ${\alpha }^2$ times the SME parameters. We obtained contributions at this order both from the nonrelativistic effective Hamiltonian for motion of a spin-$1/2$ particle in the presence of SME interactions and also from SME corrections to the propagator for exchange photons. We applied our result to the $2S-1S$ transition in hydrogen, which has been measured with extremely high precision. The results obtained in this work give the leading SME corrections for this transition.

• Received 12 July 2012

DOI:https://doi.org/10.1103/PhysRevD.86.116005