Update of the electromagnetic effective coupling constant $\alpha(M^2_Z)$

Abstract

We recalculate the hadronic contribution to the effective electromagnetic coupling constant $\alpha(M^2_Z)$ using quasi-analytical approximations for the cross-section of $e^{+}e^{-} \to hadrons$ proposed earlier by one of the authors(N.V.K.,Mod.Phys.Lett.A9(1994)2825). We find that $\alpha^{-1}(M^2_Z) = 128.98 \pm 0.06$.