Running Electromagnetic-Coupling Constant: Low-Energy Normalization and the Value at M_Z

摘要

A numerical value for the running electromagnetic-coupling constant in the (MS)~bar scheme is calculated at a low-energy normalization scale equal to the τ-lepton mass M_τ. This low-energy boundary value is used for running the electromagnetic coupling to larger scales, where high-precision experimental measurements can be performed. Particular scales of interest are the b-quark mass for studying Y-resonance physics and the Z-boson mass M_Z for high-precision tests of the Standard Model and of the determination of the Higgs boson mass from radiative corrections. A numerical value of the running electromagnetic-coupling constant at M_Z in the on-shell renormalization scheme is also given.