The measurement of alpha_s from event shapes with the DELPHI detector at the highest LEP energies

TL;DR

The paper analyzes hadronic event shapes in $e^+e^-$ collisions at $183$–$207\ \mathrm{GeV}$ to extract $\alpha_s$ using fixed-order, resummed, and matched QCD predictions, with both hadronisation and power-correction-based corrections. It introduces a rigorous treatment of uncertainties, including a novel logR-based theoretical error and a covariance-based combination across five observables, and validates the running of $\alpha_s$ by comparing measurements across LEP1 and LEP2 energies. The results show consistent $\alpha_s$ values across methods, with the most precise distribution-based result giving $\alpha_s(M_Z)=0.1157\pm0.0033$, and the energy dependence of $\alpha_s^{-1}$ in agreement with the QCD beta function. The study strengthens the LEP-era determination of the strong coupling and its scale dependence, contributing to the global precision on $\alpha_s$ and confirming asymptotic freedom in the tested energy range.

Abstract

Hadronic event shape distributions are determined from data in e+e- collisions between 183 and 207 GeV. From these the strong coupling alpha_s is extracted in O(alpha_s^2), NLLA and matched O(alpha_s^2)+NLLA theory. Hadronisation corrections evaluated with fragmentation model generators as well as an analytical power ansatz are applied. Comparing these measurements to those obtained at and around M_Z allows a combined measurement of alpha_s from all DELPHI data and a test of the energy dependence of the strong coupling.

Figures (7)

• Figure 1: Left: reconstructed centre-of-mass energy $\sqrt{s^{\prime}}$ . Right: simulation of four-fermion background and QCD events in the $N_{\mathrm{charged}}$-$B_{\mathrm{min}}$ plane. The lines delineate the accepted region.
• Figure 2: Event shape distributions of 1-Thrust ($1-T$), heavy jet mass (${M_{\mathrm{h}}^2}/{E_{\mathrm{vis}}^2}$), wide jet broadening ($B_{\mathrm{max}}$) and total jet broadening ($B_{\mathrm{sum}}$) at 189GeexV. The upper inset shows the acceptance corrections. The central part shows data with statistical uncertainties, simulation and the four-fermion background which was subtracted from the data.
• Figure 3: Event shape distributions of 1-Thrust ($1-T$), heavy jet mass (${M_{\mathrm{h}}^2}/{E_{\mathrm{vis}}^2}$), wide jet broadening ($B_{\mathrm{max}}$) and total jet broadening ($B_{\mathrm{sum}}$) at 207GeexV. The upper inset shows the acceptance corrections. The central part shows data with statistical uncertainties, simulation and the four-fermion background which was subtracted from the data.
• Figure 4: Fit ranges for the different observables and methods to determine $\alpha_s$.
• Figure 5: Left: Dokshitzer-Webber fit to several mean values. The dotted line shows the perturbative contribution. Right: the results of the global fits in the $\alpha_s$-$\alpha_0$ plane. The vertical line with shading shows the world average of $\alpha_s$.