A reanalysis of event shape distributions in electron-positron annihilation

Abstract

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 ${\mu }_r=\sqrt{s}$ and evaluating theoretical uncertainties by varying the same scale ${\mu }_r$ in an arbitrary range. Both the event shape distributions and the extracted QCD coupling ${\alpha }_s$ 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 $\overline{\mathrm{MS}}$ 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 ($\rho =M_H^2/s$), wide jet broadening ($B_W$), total jet broadening ($B_T$), C-parameter ($C$), are in agreement with the high precision experimental data, and for the case of the jet transition variable $Y_3$, we obtain a first improvement in the results to some extent compared with the $\overline{\mathrm{MS}}$ scheme.

arXiv comment10 pages, 9 figures, published version

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