Hyperfine splitting in muonium: Accuracy of the theoretical prediction

Michael I Eides

doi:10.1016/j.physletb.2019.06.011

Abstract

In the last twenty years, the theory of hyperfine splitting in muonium developed without any experimental input. Finally, this situation is changing and a new experiment on measuring hyperfine splitting in muonium is now in progress at J-PARC. The goal of the MuSEUM experiment is to improve by an order of magnitude experimental accuracy of the hyperfine splitting and muon-electron mass ratio. Uncertainty of the theoretical prediction for hyperfine splitting will be crucial for comparison between the forthcoming experimental data and the theory in search of a possible new physics. In the current literature estimates of the error bars of the theoretical prediction differ roughly by a factor of two. We explain the origin of this discrepancy and obtain the theoretical prediction for the muonium hyperfine splitting ΔνHFSth(Mu)=4463302872(515)Hz,δ=1.2×10−7.

Highlights

Calculations of hyperfine splitting (HFS) in one-electron atoms have a long and distinguished history starting with the classic works by Fermi [1] and Breit [2]
We have shown above that the uncertainty of the current theoretical quantum electrodynamic (QED) prediction for the muonium HFS is about 515 Hz, see Eq (8)
The uncertainty of the theoretical prediction for muonium HFS in Eq (8) is roughly two times larger than in the 2014 adjustment (see eq (216) in [5]) and in other 1998-2014 adjustments [9,10,11,12]. All these years the underestimation of the error bars of HFS was not practically important because there were no experimental activity on measuring muonium HFS and the muon-electron mass ratio, and the adjustments produced the value of the muon-electron mass ratio with the correct error bars

Summary

Introduction

Calculations of hyperfine splitting (HFS) in one-electron atoms have a long and distinguished history starting with the classic works by Fermi [1] and Breit [2]. The CODATA adjustments of the fundamental physical constants is a highly respected and reliable source, and the two times lower error bars cited in [5,9,10,11,12] found their way in experimental and theoretical papers on muonium HFS, too numerous to cite them here. We will derive the uncertainty of the current theoretical prediction of the HFS in muonium and slightly improve its estimate in [3,4] This improvement is made possible by the new theoretical contributions and more accurate values of the fundamental physical constants that were obtained after the reviews [3, 4] were published. We trace out the origin of the two times lower error bars in [5,9,10,11,12] and explain why they cannot be used for comparison between theory and experiment

Zeeman splitting and experimental measurements of muonium HFS

Theoretical prediction of muonium HFS and its uncertainty

CODATA estimate of the theoretical uncertainty

Conclusions