Determination of the strong coupling constant from the CLEO measurement of the total hadronic cross section in $e^+e^-$ annihilation below 10.56 GeV

Using recent CLEO III results for the cross section for $e^+e^- \to {\rm hadrons}$ at seven centre-of-mass energies between 6.964 and 10.538 GeV, we derive a value for the strong coupling constant $\alpha_s(M_Z^2)=0.110_{-0.012}^{-0.010}{}_{-0.011}^{+0.010}$ where the uncertainties are uncorrelated and correlated, respectively. Our result differs significantly from the one derived by CLEO III, as a consequence of inclusion of quark mass effects and the proper matching between the effective theories with four and five flavours. Combining this new result with an analysis based on earlier cross section measurements in the energy region between 2 and 10.6 GeV, we obtain $\alpha_s(M_Z^2)=0.119^{+0.009}_{-0.011}$, well consistent with the current world average.