Measurement of the Strong Coupling alpha s from Four-Jet Observables in e+e- Annihilation

TL;DR

The OPAL collaboration performs a precise extraction of the strong coupling α_s from four-jet observables in e+e− annihilation, using Durham-clustered four-jet rates with matched NLO+NLLA predictions across 91–209 GeV. Complementary analyses of D and thrust minor provide cross-checks with larger theoretical uncertainties due to missing higher-order terms. The combined result from the four-jet rate yields α_s(M_Z) = 0.1182 with a multi-component error budget, in agreement with the world average. The study demonstrates the robustness of four-jet observables for α_s determinations and highlights the dominant role of scale and hadronization uncertainties in event-shape analyses.

Abstract

Data from e+e- annihilation into hadrons at centre-of-mass energies between 91 GeV and 209 GeV collected with the OPAL detector at LEP, are used to study the four-jet rate as a function of the Durham algorithm resolution parameter ycut. The four-jet rate is compared to next-to-leading order calculations that include the resummation of large logarithms. The strong coupling measured from the four-jet rate is alphas(Mz0)= 0.1182+-0.0003(stat.)+-0.0015(exp.)+-0.0011(had.)+-0.0012(scale)+-0.0013(mass) in agreement with the world average. Next-to-leading order fits to the D-parameter and thrust minor event-shape observables are also performed for the first time. We find consistent results, but with significantly larger theoretical uncertainties.

Figures (6)

• Figure 1: The four-jet rate distribution at hadron level as a function of the $y_{\mathrm{cut}}$ resolution parameter obtained with the Durham algorithm. The four-jet rates are shown for the data corrected to the hadron level at four average centre-of-mass energies between 91 and 209 GeV together with predictions based on PYTHIA, HERWIG and ARIADNE Monte Carlo events generated at the averaged energy. The error bars show the statistical (inner error bars) and experimental uncertainties added in quadrature. Error bars not shown are smaller than the point size. The panel in each upper right corner shows the differences between data and Monte Carlo predictions, divided by the sum of the statistical and experimental error. For data points with no data events, the difference is set to zero.
• Figure 2: The hadron-level four-jet rate distributions for energies between 91 GeV and 209 GeV. The error bars show the statistical (inner error bars) and experimental uncertainties added in quadrature. When not shown, the errors are smaller than the point size. The curves show the theory prediction after $\chi^{2}$ minimization within the fit range indicated. The fit range is determined as discussed in Section \ref{['fitprocedure']}. The data points are strongly correlated and an enlarged fit range would lead to only a minor gain in statistical precision.
• Figure 3: The values for $\alpha_\mathrm{S}$ obtained by a fit to the four-jet rate with $x_{\mu}$ set to 1.0 in the four energy intervals. The error bars show the statistical (inner error bars) and the total error. The statistical error at 91 GeV is smaller than the point size. The lines indicate the current world average from alphasbethke with the one standard deviation uncertainty.
• Figure 4: The values of $\alpha_\mathrm{S}$ and $\chi^2/\mathrm{d.o.f.}$ from the fit to the four-jet rate at 91 GeV data as a function of the scale parameter $x_{\mu}$. The arrows indicate the variation $0.5 < x_{\mu} < 2.0$ used to determine the theoretical systematic uncertainty.
• Figure 5: The hadron-level $D$-parameter and $T_{\mathrm{min}}$ distributions for energies of 91 GeV and 197 GeV. The error bars show the statistical (inner error bars) and experimental uncertainties added in quadrature. When not shown, the errors are smaller than the point size. The curves indicate the theory prediction after $\chi^{2}$-minimization with the renormalization scale set to 1.0. The fit range is determined as discussed in Section \ref{['eventshapes']}.