NLO QCD corrections to five-jet production at LEP and the extraction of alpha_s(M_Z)

TL;DR

This work delivers the first NLO QCD predictions for exclusive $e^+e^- \to 5$-jet production at LEP, employing generalized $D$-dimensional unitarity for one-loop amplitudes and MadFKS for real emissions, with SHERPA/CKKW used to estimate hadronization corrections. By comparing to ALEPH data on the $y_{45}$ distribution and the $R_5$ observable, the authors demonstrate that NLO calculations reduce renormalization-scale uncertainties and that SHERPA/CKKW provides smaller, more reliable hadronization corrections than traditional generators. A precision extraction of the strong coupling constant yields $\alpha_s(M_Z)=0.1156^{+0.0041}_{-0.0034}$, based on a combined fit to LEP1 and LEP2 data, though this value sits somewhat below the current world average. Overall, the study highlights the viability of high-multiplicity jet observables for precision QCD and the importance of matrix-element–parton-shower matching in controlling non-perturbative effects.

Abstract

The highest exclusive jet multiplicity studied at LEP experiments is five. In this paper we compute the next-to-leading order QCD corrections to e+e- annihilation to five jets, essentially closing the (pure) perturbative QCD studies of exclusive jetty final states at LEP. We compare fixed-order perturbative results with ALEPH data. We estimate hadronization corrections to five-jet observables using the event generator SHERPA, which employs the CKKW procedure to combine a reliable perturbative treatment of high-multiplicity jet final states with parton showers. We show that a competitive value of the strong coupling constant alpha_s(M_Z) = 0.1156 +0.0041 -0.0034 can be extracted from the distribution of the five-jet resolution parameter and the five-jet rate at LEP1 and LEP2.

Figures (3)

• Figure 1: ALEPH data Heister:2003aj for the $y_{45}$ distribution at LEP1, compared to PYTHIA, HERWIG and ARIADNE results. The upper panes show detector and hadronization corrections, respectively. The lowest pane shows the relative difference between data and event generator predictions. This figure was provided to us by H. Stenzel.
• Figure 2: ALEPH data for the $y_{45}$ distribution at LEP1, compared to SHERPA results. Two hadronization models -- Lund string Andersson:1983ia and cluster Winter:2003tt -- are employed. The lower pane in the left plot shows the relative difference between Sherpa predictions with the two hadronization models, and ALEPH data. In the right plot, the hadronization corrections for the two models are shown.
• Figure 3: ALEPH LEP1 data compared to leading and next-to-leading order predictions in QCD, without hadronization corrections. We use $\alpha_s(M_Z) = 0.130$ at the leading and $\alpha_s(M_Z) = 0.118$ at the next-to-leading order in perturbative QCD. The renormalization scale is chosen to be $0.3M_Z$. The uncertainty bands are obtained by considering the scale variation $0.15~M_Z < \mu < 0.6~M_Z$. Solid lines refer to NLO QCD results evaluated with $\mu = 0.3 M_Z$.