Hyperfine Splitting in Muonium: Accuracy of the Theoretical Prediction

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 $Δν^{th}_{\scriptscriptstyle HFS}(Mu)=4~463~302~872~(515)~\mbox{Hz},\; δ=1.2\times 10^{-7}$.

9 pages; v.2: Minor improvements and corrections, acknowledgments updated, conclusions unchanged; v.3: minor editorial changes, version published in Phys. Lett. B

References in corpus (2)

• Measurement of the fine-structure constant as a test of the Standard Model
• Two-loop binding corrections to the electron gyromagnetic factor

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