  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.
