Higher order corrections to the hydrogen spectrum from the   Standard-Model Extension
  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 non-relativistic 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. 
Theodore J. Yoder and Gregory S. Adkins
hep-ph