We directly fit the experimentally measured energy dependence of the average value of $1-\mathrm{thrust}$, $〈1-T〉$, over the $e^{+}{e}^{-}$ center-of-mass energy range $Q=14\mathrm{}–172\mathrm{GeV}$ to the quantum chromodynamics expectation obtained by integrating up the evolution equation for $d〈1-T〉/d\log Q$ in terms of $〈1-T〉$. We fit for ${\Lambda }_{\overline{\mathrm{MS}}}^{\left(5\right)}$, uncalculated $O\left({\alpha }_s^3\right)$ and higher perturbative corrections parametrized by the scheme invariant ${\rho }_2$, and the parameter $\lambda$ which characterizes the magnitude of the leading $1/Q$ power corrections. We find ${\Lambda }_{\overline{\mathrm{MS}}}^{\left(5\right)}{=245\mathrm{}}_{-17\mathrm{}}^{+20\mathrm{}}\mathrm{MeV}$, which is equivalent to ${\alpha }_s\left(M_Z\right)=0.1194\mathrm{}\pm 0.0014$. In this approach, there is no error associated with the choice of the renormalization scale $\mu$.

• Received 6 March 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.1568