Measurement of event shape distributions and moments in e+e- -> hadrons at 91-209 GeV and a determination of alpha_s

TL;DR

This study analyzes hadronic final states from e+e- annihilation over 91–209 GeV using OPAL data to measure a broad set of event-shape distributions and their moments. By comparing these observables to state-of-the-art QCD predictions with NLLA+O(αs^2) accuracy and hadronization-model corrections, the authors extract the strong coupling αs and test its energy evolution, finding results consistent with QCD running. The distribution-based αs(MZ) is determined to be 0.1191( stat )( expt )( hadr )( theo ), while the moment-based approach yields 0.1223 with larger theoretical uncertainties; both approaches validate the expected scale dependence. Overall, the measurements favor the distributions-derived value as the more precise and robust determination, and the results align with the world average, reinforcing the predictive power of QCD for event shapes in high-energy e+e- collisions.

Abstract

We have studied hadronic events from e+e- annihilation data at centre-of-mass energies from 91 to 209 GeV. We present distributions of event shape observables and their moments at each energy and compare with QCD Monte Carlo models. From the event shape distributions we extract the strong coupling alpha_s and test its evolution with energy scale. The results are consistent with the running of alpha_s expected from QCD. Combining all data, the value of alpha_s(M_Z) is determined to be alpha_s(M_Z) = 0.1191 +- 0.0005 (stat.) +- 0.0010 (expt.) +- 0.0011 (hadr.) +- 0.0044 (theo.). The energy evolution of the moments is also used to determine a value of alpha_s with slightly larger errors: alpha_s(M_Z) = 0.1223 +- 0.0005 (stat.) +- 0.0014 (expt.) +- 0.0016 (hadr.) +0.0054 -0.0036 (theo.).

Figures (26)

• Figure 1: Distributions of thrust, $(1-T)$, at four c.m. energy points --- 91 GeV, 133 GeV, 161--183 GeV (labelled 177 GeV) and 189--209 GeV (labelled 197 GeV). The latter three have been multiplied by factors 3, 9 and 27 respectively for the sake of clarity. The inner error bars show the statistical errors, while the total errors are indicated by the outer error bars. The predictions of the PYTHIA, HERWIG and ARIADNE Monte Carlo models as described in the text are indicated by curves. The lower panels of the figure show the differences between data and Monte Carlo, divided by the total errors, at 91 and 197 GeV.
• Figure 2: Distributions of heavy jet mass, $M_{\mathrm{H}}$, at four c.m. energy points --- 91 GeV, 133 GeV, 161--183 GeV (labelled 177 GeV) and 189--209 GeV (labelled 197 GeV). The latter three have been multiplied by factors 3, 9 and 27 respectively for the sake of clarity. The inner error bars show the statistical errors, while the total errors are indicated by the outer error bars. The predictions of the PYTHIA, HERWIG and ARIADNE Monte Carlo models as described in the text are indicated by curves. The lower panels of the figure show the differences between data and Monte Carlo, divided by the total errors, at 91 and 197 GeV.
• Figure 3: Distributions of the $C$-parameter at four c.m. energy points --- 91 GeV, 133 GeV, 161--183 GeV (labelled 177 GeV) and 189--209 GeV (labelled 197 GeV). The latter three have been multiplied by factors 3, 9 and 27 respectively for the sake of clarity. The inner error bars show the statistical errors, while the total errors are indicated by the outer error bars. The predictions of the PYTHIA, HERWIG and ARIADNE Monte Carlo models as described in the text are indicated by curves. The lower panels of the figure show the differences between data and Monte Carlo, divided by the total errors, at 91 and 197 GeV.
• Figure 4: Distributions of the total jet broadening, $B_{\mathrm{T}}$, at four c.m. energy points --- 91 GeV, 133 GeV, 161--183 GeV (labelled 177 GeV) and 189--209 GeV (labelled 197 GeV). The latter three have been multiplied by factors 3, 9 and 27 respectively for the sake of clarity. The inner error bars show the statistical errors, while the total errors are indicated by the outer error bars. The predictions of the PYTHIA, HERWIG and ARIADNE Monte Carlo models as described in the text are indicated by curves. The lower panels of the figure show the differences between data and Monte Carlo, divided by the total errors, at 91 and 197 GeV.
• Figure 5: Distributions of the wide jet broadening, $B_{\mathrm{W}}$, at four c.m. energy points --- 91 GeV, 133 GeV, 161--183 GeV (labelled 177 GeV) and 189--209 GeV (labelled 197 GeV). The latter three have been multiplied by factors 3, 9 and 27 respectively for the sake of clarity. The inner error bars show the statistical errors, while the total errors are indicated by the outer error bars. The predictions of the PYTHIA, HERWIG and ARIADNE Monte Carlo models as described in the text are indicated by curves. The lower panels of the figure show the differences between data and Monte Carlo, divided by the total errors, at 91 and 197 GeV.