A reanalysis of event shape distributions in electron-positron annihilation

Theoretical calculations for event shape observables are often determined by using the conventional scale setting; i.e. the procedure defined by setting the renormalization scale to the center-of-mass energy μr = s and evaluating theoretical uncertainties by varying the same scale μr in an arbitrary range. Both the event shape distributions and the extracted QCD coupling αs are plagued by the large renormalization scale uncertainties when using the conventional scale setting. The Principle of Maximum Conformality (PMC) provides a rigorous method to eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions. In this paper, we perform a detailed analysis of the event shape observables by applying the PMC method together with the use of the physical V -scheme. The PMC scales are not simple single-valued functions, but depend with continuity on the value of the unintegrated event shape variable. This reflects the virtuality of the underlying quark and gluon subprocess and yields to a physical behavior of the scale all over the entire range of each observable. Moreover, the PMC scales in the V -scheme exhibits a faster increase compared to the MS¯ scheme, and a better convergence in the perturbative series can be obtained. Results obtained by the PMC method for the event shape variables, thrust (T), heavy jet mass ρ=MH2/s, wide jet broadening (BW), total jet broadening (BT), C-sparameter (C), are in agreement with the high precision experimental data, and for the case of the jet transition variable Y3, we obtain a first improvement in the results to some extent compared with the MS¯ scheme.