New Evaluation of the QED Running Coupling and of the Muonium Hyperfine Splitting

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We present a new independent evaluation of the hadronic and QCD contributions to the QED running coupling α(MZ) and to the muonium hyperfine splitting ν. We obtain: Δαhad=2770(17)10⁻⁵ and Δνhad=232.5(2.5) Hz. Combined with the QED and Electroweak Standard Model contributions, they lead to: α⁻¹(MZ)=128.926(25) and to the Fermi energy splitting νF=4 459 031 783(229) Hz, where for the latter, we have used, in addition, the precise measurement of the muonium hyperfine splitting νexp. We use νF in order to predict the ratios of masses mμ/mₑ=206.768 276(11) and of the magnetic moments μμ/μᵉB=4.841 970 47(25)10⁻³, which are in excellent agreement with the ones quoted by the Particle Data Group. These remarkable agreements can provide strong constraints on some contributions beyond the Standard Model.