Determination of a set of fundamental constants from molecular hydrogen ion spectroscopy: a modeling study

TL;DR

This modeling study explores how ultra-high-accuracy spectroscopy of molecular hydrogen ions can significantly improve the precision of fundamental constants, including mass ratios and charge radii, using ab initio quantum electrodynamics calculations.

Contribution

It demonstrates that future spectroscopy data can drastically reduce uncertainties in key fundamental constants through advanced modeling and analysis.

Findings

Mass ratios of proton, deuteron, and triton can be measured with over hundred-fold precision.

Proton and deuteron charge radii can be determined with current-level uncertainties.

Rydberg constant can be accurately obtained solely from electronic system data.

Abstract

The rovibrational transition frequencies of molecular hydrogen ions (MHI) can be accurately computed using ab initio nonrelativistic quantum electrodynamics. A subset of the fundamental constants are required input. We analyze how, once upcoming ultra-high-accuracy spectroscopy data has been obtained, that subset of constants can be determined with greater accuracy. Our analysis shows that under realistic assumptions the uncertainties of the mass ratios of proton, deuteron and triton relative to the electron, and of the triton charge radius can be reduced more than onehundred-fold compared to today (CODATA 2022). Furthermore, the Rydberg constant, as well as the proton and deuteron charge radii can be determined with uncertainties similar to those of today, but solely using data from electronic systems. The implications are discussed.