Muonium HFS Uncertainty Revisited

TL;DR

The paper scrutinizes the uncertainty of the quantum electrodynamics (QED) prediction for muonium hyperfine splitting (HFS) and how this quantity has been treated in the two most recent CODATA adjustments. It contrasts the traditional, calculated form of the HFS, given by $\\Delta\\nu_{HFS}=\\nu_{F}[1+F(\\alpha,Z\\alpha,\\frac{m_e}{m_\\mu})]+\\Delta\\nu_{weak}+\\Delta\\nu_{hadr}+\\Delta\\nu_{th}$, with CODATA’s so-called “recommended value” approach, arguing that the latter misinterprets the theoretical prediction as the experimental value. The author highlights disagreements in the cited theoretical uncertainties—$51$ Hz versus $271$ Hz or $515$ Hz depending on the source—and stresses that the true uncertainty arises from the experimental mass ratio $(m_\\mu/m_e)_{ex}$ and uncalculated terms rather than the uncalculated terms alone. This misinterpretation is shown to be potentially problematic for the upcoming MuSEUM experiment, which aims to measure weak interaction contributions and probe New Physics, underscoring the need for a clear separation between experimental results, theoretical predictions, and their uncertainties in CODATA adjustments.

Abstract

Uncertainty of the quantum electrodynamics theoretical prediction for the hyperfine splitting in the ground state of muonium is considered. It is compared with the respective discussion in the two most recent CODATA adjustments of the fundamental physical constants.