Proton structure corrections to hyperfine splitting in muonic hydrogen

TL;DR

This paper derives formulas for proton structure corrections to hyperfine splitting in muonic hydrogen, reconciling previous discrepancies and reducing uncertainties, with implications for proton radius measurements.

Contribution

It provides a consistent set of formulas for proton structure corrections and clarifies the impact of modern form factor fits on hyperfine splitting calculations.

Findings

Reduction of hyperfine splitting by about 46 ppm due to convention corrections

Smaller spread in Zemach radii using modern form factors

Minimal impact on muonic hydrogen Lamb shift and proton radius

Abstract

We present the derivation of the formulas for the proton structure-dependent terms in the hyperfine splitting of muonic hydrogen. We use compatible conventions throughout the calculations to derive a consistent set of formulas that reconcile differences between our results and some specific terms in earlier work. Convention conversion corrections are explicitly presented, which reduce the calculated hyperfine splitting by about 46 ppm. We also note that using only modern fits to the proton elastic form factors gives a smaller than historical spread of Zemach radii and leads to a reduced uncertainty in the hyperfine splitting. Additionally, hyperfine splittings have an impact on the muonic hydrogen Lamb shift/proton radius measurement, however the correction we advocate has a small effect there.