Measurements of $\alpha_s$ From Scaling Violations and From $R_\tau$ at LEP

Abstract

The results of two methods to extract the strong coupling constant, $\alpha_s$, are reviewed for the LEP experiments. In the first, scaling violations in the scaled momentum distributions of charged particles at LEP and at lower energy experiments are employed. In the second, QCD corrections to $R_\tau$, the ratio of hadronic to leptonic decay rates of the tau lepton, determine $\alpha_s$ and, using moments of the invariant mass distribution in hadronic tau decays, the non-perturbative corrections to $R_\tau$.