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In this paper, we give comprehensive analyses for event shape observables inelectron-positron annihilation by using the Principle of Maximum Conformality(PMC) which is a rigorous scale-setting method to eliminate the renormalizationscheme and scale ambiguities in perturbative QCD predictions. Conventionallythe renormalization scale and theoretical uncertainties in event shapeobservables are often evaluated by setting the scale to the center-of-massenergy $\sqrt{s}$. The event shape distributions using this conventional scalesetting are plagued by the large renormalization scale uncertainty andunderestimate the experimental data. Moreover, since the renormalization scaleis simply fixed to the center-of-mass energy $\sqrt{s}$, only one value of thecoupling $\alpha_s$ at the single scale $\sqrt{s}$ can be extracted. Incontrast, the PMC renormalization scales are determined by absorbing thenonconformal $\beta$ contributions that govern the behavior of the runningcoupling via the Renormalization Group Equation (RGE). The resulting PMC scaleschange with event shape kinematics, reflecting the virtuality of the underlyingquark and gluon subprocess. The PMC scales thus yield the correct physicalbehavior of the scale and the PMC predictions agree with precise event shapedistributions measured at the LEP experiment. More importantly, we canprecisely determine the running of the QCD coupling constant $\alpha_s(Q^2)$over a wide range of $Q^2$ in perturbative domain from event shapedistributions measured at a single center-of-mass energy $\sqrt{s}$.

the journal of high energy physics/the journal of high energy physics

New analyses of event shape observables in electron-positron  annihilation and the determination of $\alpha_s$ running behavior in  perturbative domain