Ro-vibrational spin-averaged transitions in the hydrogen molecular ions

TL;DR

This paper improves the theoretical calculation of rovibrational transition frequencies in hydrogen molecular ions by including previously neglected effects and higher-order QED corrections, achieving better agreement with experiments and refining fundamental mass ratios.

Contribution

It introduces a more comprehensive calculation of transition frequencies in hydrogen molecular ions, incorporating additional effects and higher-order corrections not considered before.

Findings

Theoretical transition frequencies now align closely with recent high-precision measurements.

New values for the proton-to-electron and deuteron-to-proton mass ratios are provided.

Enhanced accuracy in fundamental constants derived from molecular ion spectroscopy.

Abstract

We reconsider the calculation of rovibrational transition frequencies in hydrogen molecular ions. Some previously neglected contributions, such as the deuteron polarizability, are included into consideration in comparison with our previous work. In particular, one-loop and two-loop QED corrections at $m\alpha^7$ and $m\alpha^8$ orders are recalculated in the framework of the adiabatic approximation, with systematic inclusion of corrections associated with vibrational motion. Improved theoretical transitions frequencies are obtained and found to be in very good agreement with recent high-precision spectroscopy experiments in HD$^+$. New values for the $m_p/m_e$ and $m_d/m_p$ mass ratios are determined.