Lorentz-violating corrections on the hydrogen spectrum induced by a non-minimal coupling

TL;DR

This paper investigates how Lorentz-violating background fields, introduced via a non-minimal coupling, affect the hydrogen spectrum, revealing energy shifts and setting bounds on the model's parameters.

Contribution

It introduces a non-minimal coupling framework to analyze Lorentz violation effects on hydrogen, including energy shifts and Zeeman-like effects, with experimental bounds.

Findings

Energy shifts modify hydrogen's fine structure.

No first-order correction without external field for torsion-like coupling.

External magnetic field induces secondary Zeeman effect.

Abstract

The influence of a Lorentz-violating fixed background on fermions is considered by means of a torsion-free non-minimal coupling. The non-relativistic regime is assessed and the Lorentz-violating Hamiltonian is determined. The effect of this Hamiltonian on the hydrogen spectrum is determined to first-order evaluation (in the absence of external magnetic field), revealing that there appear some energy shifts that modify the fine structure of the spectrum. In the case the non-minimal coupling is torsion-like, no first order correction shows up in the absence of an external field; in the presence of an external field, a secondary Zeeman effect is implied. Such effects are then used to set up stringent bounds on the parameters of the model.