Event shapes in e+e- annihilation and deep inelastic scattering

TL;DR

Event shapes in $e^+e^-$ and DIS provide a precise, multi-faceted probe of QCD, combining perturbative predictions with all-order resummation and non-perturbative hadronisation effects. The review synthesizes perturbative frameworks (fixed-order, NLL resummation, and alternative approaches) with analytical and Monte Carlo models of hadronisation, emphasizing universality tests of power corrections and the extraction of $\alpha_s$ and color factors. It highlights the success of the Dokshitzer–Webber power-correction picture, the role of shape functions, and the potential of RG-improved and dressed-gluon formalisms, while noting tensions in certain observables and the need for NNLO/NNLL progress. Looking forward, three-jet observables, new processes, and automated resummation methods are poised to enhance precision and deepen understanding of confinement and hadronisation in QCD.

Abstract

This article reviews the status of event-shape studies in e+e- annihilation and DIS. It includes discussions of perturbative calculations, of various approaches to modelling hadronisation and of comparisons to data.

Figures (13)

• Figure 1: Comparison of the fixed-order (LO, NLO) and resummed (NLL) predictions for the thrust distribution in $e^+e^-$ at $Q=M_Z$. The resummed distribution has been matched ($\ln R$ scheme, see below) so as to include the full LO and NLO contributions. The inset differs from the main plot only in the scales.
• Figure 2: Left: data for the mean value of the $e^+e^-$ thrust, compared to LO, NLO and NLO+${\cal O}\left(\Lambda/Q\right)$; right: data for the Durham jet resolution $y_{23}$ compared to the NLO prediction (figure taken from MovillaFernandez:2001ed).
• Figure 3: Left: $\alpha_s$, $\alpha_0$ fit to $e^+e^-$ data on mean values of event shapes, with the jet masses converted to the $p$-scheme (the arrow indicates the change in going from default to $p$-scheme) Salwick. Right: fits to DIS mean event-shape data by H1 Adloff:2000Martyn:2000jk and ZEUS ZEUSmeans (curves taken from figures in Martyn:2000jkZEUSmeans). Contours indicate 1-$\sigma$ uncertainties (statistical and experimental systematic, except for the ZEUS results which are just statistical).
• Figure 4: The mean value of the thrust distribution in $e^{+}e^{-}$ annihilation as a function of $Q$ with $\alpha_s^{\hbox{$\overline{\hbox{\tiny MS}}\,$}}({\rm M_Z})=0.110$. The upper (dashed) line corresponds to the principal value result which then is fitted to the data adding a $1/Q$ term. Figure taken from Ref. Gardtalk.
• Figure 5: Results for $\alpha_s(M_z)$ from comparisons to $e^{+}e^{-}$ event-shape data using the RGI approach. The band shows the mean value of $\alpha_s$ and uncertainty, as obtained from the observables below the dashed line. Figure taken from Ref. Abdallah:2002xz.