  We present a new independent evaluation of the hadronic and QCD contributions
to the QED running coupling \alpha(M_Z) and to the muonium hyperfine splitting
\nu. We obtain: \Delta\alpha_{had}=2770(17)10^{-5} and
\Delta\nu_{had}=232.5(2.5) Hz. Combined with the QED and Electroweak Standard
Model contributions, they lead to: \alpha^{-1}(M_Z)=128.926(25) and to the
Fermi energy splitting \nu_F=4~459~031~783(229) Hz, where for the latter, we
have used, in addition, the precise measurement of the muonium hyperfine
splitting \nu_{exp}. We use \nu_F in order to predict the ratios of masses
m_{\mu}/m_e=206.768~276(11) and of the magnetic moments
\mu_{\mu}/\mu^e_B=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.

High Energy Physics - Phenomenology;Astrophysics;High Energy Physics - Experiment;High Energy Physics - Theory