The uncertainty in ${\alpha }_s(M_Z^2)$ determined from hadronic tau decay measurements

C. J. Maxwell, D. G. Tonge

We show that QCD Minkowski observables such as the $e^{+}{e}^{-}$ R-ratio and the hadronic tau decay $R_{\tau }$ are completely determined by the effective charge (EC) beta-function, $ρ(x)…