Lorentz and CPT violation and the hydrogen and antihydrogen molecular ions I -- rovibrational states

TL;DR

This paper analyzes the rovibrational spectrum of hydrogen molecular ions to explore their potential for high-precision tests of Lorentz and CPT symmetry violations, highlighting enhanced sensitivity over atomic transitions.

Contribution

It provides a detailed theoretical analysis of rovibrational states in (anti-)hydrogen molecular ions within a Lorentz and CPT violation framework, emphasizing their experimental relevance.

Findings

Rovibrational transitions could improve bounds on Lorentz and CPT violation by up to a factor of 10^17.

Enhanced sensitivity to proton sector violations compared to atomic transitions.

Potential for high-precision symmetry tests using molecular ions.

Abstract

The extremely narrow natural linewidths of rovibrational energy levels in the molecular hydrogen ion $\textrm{H}_2^{\,+}$, and the prospect of synthesising its antimatter counterpart $\overline{\textrm{H}}_2^{\,-}$, make it a promising candidate for high-precision tests of fundamental symmetries such as Lorentz and CPT invariance. In this paper, we present a detailed analysis of the rovibrational spectrum of the (anti-)hydrogen molecular ion in a low-energy effective theory incorporating Lorentz and CPT violation. The focus is on the spin-independent couplings in this theory, for which the best current bounds come from measurements of the 1S-2S transition in atomic hydrogen and antihydrogen. We show that in addition to the improvement in these bounds from the increased precision of the transition frequencies, potentially reaching 1 part in $10^{17}$, rovibrational transitions have an enhanced sensitivity to Lorentz and CPT violation of $O(m_p/m_e)$ in the proton (hadron) sector compared to atomic transitions.