Recoil corrections to $\mu$H hyperfine splitting

TL;DR

This paper develops a comprehensive theoretical calculation of the muonic hydrogen hyperfine splitting, including quantum electrodynamic, recoil, and proton structure corrections, achieving a precise prediction of 182,626(5) μeV.

Contribution

It provides a complete theory of muonic hydrogen hyperfine splitting with all contributions above 1 ppm, directly calculating QED and recoil effects and estimating proton structure corrections.

Findings

Predicted hyperfine splitting: 182,626(5) μeV

Includes all contributions above 1 ppm

Provides a comprehensive theoretical framework

Abstract

This work attempts to present a complete theory of the $\mu$H hyperfine splitting, including all contributions above 1 ppm. Quantum electrodynamic and recoil corrections are calculated directly, while the proton structure correction is obtained with the help of the H hyperfine splitting. The resulting theoretical prediction for the ground state of $\mu$H is $E_\mathrm{hfs} = 182\,626(5)$ $\mu$eV.