Two-photon exchange correction to the hyperfine splitting in muonic hydrogen

TL;DR

This paper recalculates the two-photon exchange correction to hyperfine splitting in muonic hydrogen, providing precise values for the Zemach radius and TPE contribution, highlighting the importance of these corrections for upcoming high-precision measurements.

Contribution

It offers a refined evaluation of the TPE correction and related proton structure constants, improving the theoretical understanding of hyperfine splitting in muonic hydrogen.

Findings

TPE correction uncertainty exceeds 105 ppm

Precise Zemach radius value obtained

Implications for upcoming hyperfine splitting experiments

Abstract

We reevaluate the Zemach, recoil and polarizability corrections to the hyperfine splitting in muonic hydrogen expressing them through the low-energy proton structure constants and obtain the precise values of the Zemach radius and two-photon exchange (TPE) contribution. The uncertainty of TPE correction to S energy levels in muonic hydrogen of 105 ppm exceeds the ppm accuracy level of the forthcoming 1S hyperfine splitting measurements at PSI, J-PARC and RIKEN-RAL.