Event Shapes and Power Corrections in e+e- Annihilation

TL;DR

This work develops and validates a power-correction framework for hadronisation effects in e+e- annihilation, anchored by a single non-perturbative parameter $\alpha_0$ with a universal value near 0.5. By combining additive mean-value corrections, resummed predictions, and analyses of higher moments and differential distributions, it demonstrates that power corrections can coherently describe a wide range of observables and scales. The results yield consistent determinations of $\alpha_S(M_Z)$ and support the universality of $\alpha_0$ across different event-shape observables and even in ep scattering. Overall, power corrections offer a principled alternative to phenomenological hadronisation models for precision QCD in jet observables.

Abstract

The effects of the hadronisation of partons on the distribution of event shape observables are associated with corrections which are suppressed by reciprocal powers of the energy scale of the process. The correction is determined by one non-calculable parameter α_0 for which an universal value of 0.5 +/- 20% is found from the investigation of the distribution of event shape observables and their mean values measured in e^+e^- annihilation.

Figures (3)

• Figure 1: Left: Fits of $1/\sqrt{s}$, $\ln s/\sqrt{s}$, $1/s$, and $\ln s/s$ power corrections to $\langle y_3 \rangle$. Right: Mean values of the C-parameter obtained using second order ${\cal O}(\alpha_S^2)$ (dashed) and $\ln R$-matched resummed NLLA plus ${\cal O}(\alpha_S^2)$ (solid line) calculations.
• Figure 2: Power corrections to second moment of thrust (left) and heavy jet mass (right).
• Figure 3: Fit results of $\alpha_0$ and $\alpha_S(M_{\mathrm{Z}})$.