Higher-order corrections to spin-orbit and spin-spin tensor interactions in hydrogen molecular ions: theory and application to H$_2^+$

TL;DR

This paper calculates higher-order quantum electrodynamics corrections to hyperfine interactions in hydrogen molecular ions, significantly improving theoretical accuracy and comparing results with experimental data.

Contribution

It derives the $m ext{α}^7 ext{ln}( ext{α})$ radiative correction within the NRQED framework and provides complete numerical calculations for H$_2^+$, reducing theoretical uncertainty.

Findings

Uncertainty reduced by over an order of magnitude

Derived the $m ext{α}^7 ext{ln}( ext{α})$ correction

Results agree with rf spectroscopy data

Abstract

We consider higher-order corrections to hyperfine coefficients related to the spin-orbit and spin-spin tensor interactions in hydrogen molecular ions. The $m\alpha^7 \ln(\alpha)$-order radiative correction is derived in the NRQED framework. We present complete numerical calculations, including as well the $m\alpha^6$-order relativistic correction, for the case of H$_2^+$. The theoretical uncertainty is reduced by more than one order of magnitude with respect to the Breit-Pauli level, down to a few ppm. We also compare our results with available rf spectroscopy data.