Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions III -- rovibrational spectrum and the non-minimal SME

TL;DR

This paper derives the rovibrational spectrum of hydrogen and antihydrogen molecular ions within the SME framework, enabling high-precision tests of Lorentz and CPT symmetry through spectroscopy.

Contribution

It provides a comprehensive derivation of the rovibrational spectrum in the SME, including non-minimal couplings and detailed quantum number analysis for experimental tests.

Findings

Extended the spectrum analysis to non-minimal SME couplings.

Analyzed sidereal and annual variations in transition frequencies.

Enhanced sensitivity to SME couplings via quantum number dependence.

Abstract

Rovibrational transitions in the hydrogen and antihydrogen molecular ions $H_2^+$ and $\overline{H}_2^-$ offer the possibility of testing Lorentz and CPT symmetry to extremely high precision, in principle attaining $O(10^{-17})$. In this paper, the third in a series, we give a comprehensive derivation of the rovibrational spectrum of $H_2^+$ and $\overline{H}_2^-$ in the SME, an effective quantum field theory incorporating Lorentz and CPT violation. New developments described here include a complete analysis of the molecular dynamics from first principles in terms of the spherical tensor representation of the SME couplings, the systematic extension of our previous results to the non-minimal SME, a full description of the quantum number dependence of the rovibrational energy levels in the spherical tensor formalism with both high and low background magnetic fields, and an extended discussion of sidereal and annual variations of transition frequencies arising from both rotations and Lorentz boosts. The resulting sensitivity of the rovibrational spectrum to an extended range of SME couplings, together with the ability to isolate their individual effects using the quantum number dependence of the transition frequencies, enhances the opportunities to detect Lorentz and CPT symmetry breaking through rovibrational spectroscopy of $H_2^+$ and $\overline{H}_2^-$.