Perturbative QCD prediction for the ratioRτinτ-lepton decays

Using a new corrected value for $R=\frac{\sigma (e^{+}{e}^{-}\to \mathrm{hadrons})}{\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})}$ to order ${\alpha }_s^3$ we calculate $R_{\tau }=\frac{\Gamma (\tau \to \mathrm{hadrons})}{\Gamma (\tau \to e\overline{\nu }\nu )}$ to order ${\alpha }_s^3$. Our result is $R_{\tau }={3.97}_{-0.4\mathrm{}}^{+2.1\mathrm{}}$. The agreement with the experimental value $R_{\tau }=3.65\mathrm{}\left(13\right)\mathrm{}$ is excellent. If we assume agreement between theory and experiment we may obtain an accurate value for the strong-interaction coupling at $M_{\tau }$. Our result is ${\alpha }_s\left(M_{\tau }\right)={0.34}_{-0.02\mathrm{}}^{+0.04\mathrm{}}$.