Determination of αS using OPAL hadronic event shapes at sqrt(s) = 91 - 209 GeV and resummed NNLO calculations

TL;DR

This study determines the strong coupling constant $\alpha_{\mathrm{S}}$ from hadronic event-shape distributions in $e^+e^-$ annihilation using OPAL data from $\sqrt{s}=91$–$209$ GeV. It employs state-of-the-art QCD predictions at NNLO and NNLO+NLLA, performing fits to six observables and combining results across 13 energy points to extract $\alpha_{\mathrm{S}}(m_{Z^0})$. The NNLO result yields $\alpha_{\mathrm{S}}(m_{Z^0}) = 0.1201(0.0031)$ and the NNLO+NLLA result yields $\alpha_{\mathrm{S}}(m_{Z^0}) = 0.1189(0.0041)$, with the energy dependence consistent with QCD running and asymptotic freedom. These measurements exemplify the improved theoretical control and precision achievable with higher-order perturbative calculations and align with the current world average.

Abstract

Hadronic event shape distributions from e+e- annihilation measured by the OPAL experiment at centre-of-mass energies between 91 GeV and 209 GeV are used to determine the strong coupling αS. The results are based on QCD predictions complete to the next-to- next-to-leading order (NNLO), and on NNLO calculations matched to the resummed next-to-leading-log-approximation terms (NNLO+NLLA). The combined NNLO result from all variables and centre-of-mass energies is αS(mZ0) = 0.1201 {\pm} 0.0008(stat.) {\pm} 0.0013(exp.) {\pm} 0.0010(had.) {\pm} 0.0024(theo.). while the combined NNLO+NLLA result is αS(mZ0) = 0.1189 {\pm} 0.0008(stat.) {\pm} 0.0016(exp.) {\pm} 0.0010(had.) {\pm} 0.0036(theo.). The completeness of the NNLO and NNLO+NLLA results with respect to missing higher order contributions, studied by varying the renormalization scale, is improved compared to previous results based on NLO or NLO+NLLA predictions only. The observed energy dependence of αS agrees with the QCD prediction of asymptotic freedom and excludes the absence of running.

Figures (7)

• Figure 1: Comparison of NNLO+NLLA calculations for the $1-T$, $M_{\mathrm{H}}$, $B_{\mathrm{T}}$, $B_{\mathrm{W}}$, $C$ and $y_{23}^\mathrm{D}$ variables with the parton level predictions of the Monte Carlo generators PYTHIA 6.1, HERWIG 6.2 and ARIADNE 4.11 at $\sqrt{s}$=91 GeV (see Sect. \ref{['MeasurementsAs']}). The vertically symmetrical band between solid lines shows the maximum deviation of the ratio from one, between the three generators MC$_i$ in the positive and the negative direction. The arrows indicate the respective fit ranges.
• Figure 2: The points show the $1-T$ and $M_{\mathrm{H}}$ distributions at the hadron level for $\sqrt{s}=91.3$ and 206.6 GeV with statistical uncertainty bars. Some uncertainty bars are smaller than the data points. Superimposed as histograms are the NNLO and NNLO+NLLA predictions combined with hadronisation effects using the corresponding fit results for $\alpha_{\mathrm{S}}(\sqrt{s})$ shown in Tabs. \ref{['asresultsnnlo']}, \ref{['asresultsnnlonlla']}. The arrows indicate the fit ranges.
• Figure 3: The points show the $B_{\mathrm{T}}$ and $B_{\mathrm{W}}$ distributions at the hadron level for $\sqrt{s}=91.3$ and 206.6 GeV with statistical uncertainty bars. Some uncertainty bars are smaller than the data points. Superimposed as histograms are the NNLO and NNLO+NLLA predictions combined with hadronisation effects using the corresponding fit results for $\alpha_{\mathrm{S}}(\sqrt{s})$ shown in Tabs. \ref{['asresultsnnlo']}, \ref{['asresultsnnlonlla']}. The arrows indicate the fit ranges.
• Figure 4: The points show the $C$ and $y_{23}^\mathrm{D}$ distributions at the hadron level for $\sqrt{s}=91.3$ and 206.6 GeV with statistical uncertainty bars. Some uncertainty bars are smaller than the data points. Superimposed as histograms are the NNLO and NNLO+NLLA predictions combined with hadronisation effects using the corresponding fit results for $\alpha_{\mathrm{S}}(\sqrt{s})$ shown in Tabs. \ref{['asresultsnnlo']}, \ref{['asresultsnnlonlla']}. The arrows indicate the fit ranges.
• Figure 5: The points show the values of $\alpha_{\mathrm{S}}$ for the OPAL energy ranges. The inner uncertainty bars show the combined statistical and experimental uncertainties and the outer the total uncertainties. The full and dashed lines indicate the $\alpha_{\mathrm{S}}$ result from the NNLO+NLLA analysis that combines all variables and OPAL energy points. The results from the NNLO+NLLA analysis of JADE data jadeNNLO are shown as well.