Precision calculation of the recoil--finite-size correction for the hyperfine splitting in muonic and electronic hydrogen

TL;DR

This paper provides a high-precision calculation of the recoil--finite-size correction to hyperfine splitting in muonic and electronic hydrogen, aiding future experimental searches and precise determination of related nuclear properties.

Contribution

It introduces a novel high-precision calculation method for recoil--finite-size corrections using dispersion theory-based nucleon form factors.

Findings

Enhanced accuracy in hyperfine splitting predictions.

Guidance for upcoming muonic hydrogen experiments.

Improved understanding of nuclear structure contributions.

Abstract

We present a high-precision calculation of the recoil--finite-size correction to the hyperfine splitting (HFS) in muonic and electronic hydrogen based on nucleon electromagnetic form factors obtained from dispersion theory. This will help guide the upcoming searches of the HFS transition in muonic hydrogen, and will allow a precise determination of the polarizability and Zemach radius contributions when this transition is found.