Higher order corrections to the hydrogen spectrum from the Standard-Model Extension

TL;DR

This paper calculates higher-order Lorentz and CPT violating effects on hydrogen energy levels within the Standard-Model Extension, providing precise corrections to the highly measured 2S-1S transition.

Contribution

It introduces the first calculation of order α^2 SME-induced energy shifts in hydrogen, combining effective Hamiltonian and photon propagator corrections.

Findings

Derived SME corrections for the 2S-1S transition in hydrogen.

Provided leading SME correction estimates for high-precision measurements.

Enhanced understanding of Lorentz and CPT violation effects in atomic spectra.

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 $\alpha^2$ 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.