Refinement of the hadronic contribution to the muon anomalous magnetic moment and to $\mathbf{\alpha(M^2_z)}$

The contribution of the muon anomalous magnetic moment $a_{\mu}({\rm hadr})$ o the vacuum polarization and electro-magnetic coupling constant $\alpha(q^2)$ for $q^2 = M^2_z$ is refined by using a new, more accurate value of the $\rho$-meson width. The values $a_{\mu}({\rm hadr}) = 678(7)\cdot10^{-10}$ and $\delta \alpha_{{\rm hadr}}(M^2_z) = 0.02786 (6)$ were obtained in a QCD model with an infinite number of vector mesons.