Hyperfine splitting in ordinary and muonic hydrogen

TL;DR

This paper refines the calculation of hyperfine splitting in hydrogen and muonic hydrogen by accurately evaluating two-photon exchange corrections, reducing proton structure uncertainties using electronic hydrogen data.

Contribution

It introduces a more precise evaluation of two-photon exchange corrections, significantly reducing proton structure uncertainties in hyperfine splitting calculations.

Findings

Reduced proton structure uncertainty in hyperfine splitting calculations.

Improved accuracy in two-photon exchange correction estimates.

Enhanced understanding of hyperfine structure in muonic hydrogen.

Abstract

We provide an accurate evaluation of the two-photon exchange correction to the hyperfine splitting of S energy levels in muonic hydrogen exploiting the corresponding measurements in electronic hydrogen. The proton structure uncertainty in the calculation of $\alpha^5$ contribution is sizably reduced.