Running electromagnetic coupling constant: low energy normalization and   the value at M_Z
  A numerical value for the running electromagnetic coupling constant in the MS scheme is calculated at the low energy normalization scale equal to the tau-lepton mass M_\tau. This low energy boundary value is used for running the electromagnetic coupling constant to larger scales where high precision experimental measurements can be performed. Particular scales of interest are the b-quark mass for studying the \Upsilon-resonance physics and the Z-boson mass M_Z for high precision tests of the standard model and for the Higgs mass determination from radiative corrections. A numerical value for the running electromagnetic coupling constant at M_Z in the on-shell renormalization scheme is also given. 
A.A. Pivovarov