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 $e^{+}{e}^{-}\to \mathrm{\text{hadrons}}$ at seven center-of-mass energies between 6.964 and 10.538 GeV, we derive a value for the strong coupling constant ${\alpha }_s(M_Z^2)={0.110}_{-0.012-0.011}^{-0.010+0.010}$ 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 flavors. 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 ${\alpha }_s(M_Z^2)={0.119}_{-0.011}^{+0.009}$, well consistent with the current world average.

Figure 1

$R(s)$ as measured by CLEO in 1998 [34] and 2007 [12]. The error bars represent the uncorrelated and the total uncertainties. The full solid line and the hatched band correspond to the theory prediction where Eq. (2) has been used as input and the renormalization scale, the charm quark mass, and ${\alpha }_s$ have been varied as described in the text. The dashed line represents the theory prediction where the result from Ref. 12, ${\alpha }_s^{(5)}(M_Z)=0.126$, has been used as input.