Hydrogen molecular ions for improved determination of fundamental constants

TL;DR

This paper explores how high-resolution spectroscopy of hydrogen molecular ions can improve the measurement of fundamental constants, potentially resolving the proton size puzzle and enhancing the precision of key physical ratios.

Contribution

It demonstrates that rovibrational spectroscopy of H2+ and HD+ can determine fundamental constants with unprecedented accuracy, addressing current discrepancies and providing new insights.

Findings

Spectroscopy can reach accuracy of 10^-12 levels.

Measurements can shed light on the proton size puzzle.

New precise values for mass ratios and the Rydberg constant.

Abstract

The possible use of high-resolution rovibrational spectroscopy of the hydrogen molecular ions H + 2 and HD + for an independent determination of several fundamental constants is analyzed. While these molecules had been proposed for metrology of nuclear-to-electron mass ratios, we show that they are also sensitive to the radii of the proton and deuteron and to the Rydberg constant at the level of the current discrepancies colloquially known as the proton size puzzle. The required level of accuracy, in the 10 --12 range, can be reached both by experiments, using Doppler-free two-photon spectroscopy schemes, and by theoretical predictions. It is shown how the measurement of several well-chosen rovibrational transitions may shed new light on the proton-radius puzzle, provide an alternative accurate determination of the Rydberg constant, and yield new values of the proton-to-electron and deuteron-to-proton mass ratios with one order of magnitude higher precision.