Abstract
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 ${\ensuremath{\alpha}}^{2}$ 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 $2S\ensuremath{-}1S$ 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.
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