Non-perturbative Analysis of the Influence of the Proton Magnetization and Charge Densities on the Hyperfine Splitting of Muonic Hydrogen

TL;DR

This paper examines how the proton's spatial charge and magnetization distributions non-perturbatively affect the hyperfine splitting in muonic hydrogen, revealing significant corrections beyond traditional perturbative methods.

Contribution

It introduces a non-perturbative relativistic Dirac approach to evaluate proton structure effects on hyperfine splitting, showing larger corrections than perturbative estimates.

Findings

Non-perturbative corrections are about 15% of the hyperfine splitting.

Corrections exceed the next-leading order perturbative contributions by an order of magnitude.

The approach provides a more accurate assessment of proton structure effects.

Abstract

We investigate the influence of the spatial extent of the proton magnetization and charge densities on the 2S hyperfine splitting in muonic hydrogen. The use of a non-perturbative relativistic Dirac approach leads to corrections of 15% to values obtained from the perturbative treatment encapsulated by the Zemach radius, which surpass the next-leading order contribution in the perturbation series by an order of magnitude.