On power corrections to the event shape distributions in QCD

TL;DR

The paper addresses power corrections to differential event shapes in $e^+e^-$ annihilation, focusing on thrust, heavy jet mass, and C-parameter in the two-jet region. It proposes a factorization framework in which nonperturbative effects are encoded by a universal shape function $f(\varepsilon_R, \varepsilon_L)$ describing energy flow into the two hemispheres, convolved with perturbative cross-sections. Away from the end-point, leading $1/Q$ corrections collapse to a single scale $\lambda_1$, while near the end-point a regime requiring resummation of $1/(Qe)^n$ corrections emerges. Fits to data across a wide energy range show that the chosen shape-function ansatz describes both differential distributions and lowest moments, highlighting hemispheric correlations (parameter $b$) in the non-inclusive piece. This framework connects IR-renormalon insights with a universal, $Q$-independent nonperturbative distribution, offering a coherent picture of hadronization effects in two-jet final states.

Abstract

We study power corrections to the differential thrust, heavy jet mass and C-parameter distributions in the two-jet kinematical region in e^+e^- annihilation. We argue that away from the end-point region, e>> Λ_{QCD}/Q, the leading 1/Q-power corrections are parameterized by a single nonperturbative scale while for e Λ_{QCD}/Q one encounters a novel regime in which power corrections of the form 1/(Qe)^n have to be taken into account for arbitrary n. These nonperturbative corrections can be resummed and factor out into a universal nonperturbative distribution, the shape function, and the differential event shape distributions are given by convolution of the shape function with perturbative cross-sections. Choosing a simple ansatz for the shape function we demonstrate a good agreement of the obtained QCD predictions for the distributions and their lowest moments with the existing data over a wide energy interval.

Figures (4)

• Figure 1: Heavy jet mass (a) and $C-$parameter (b) distributions at $Q=M_Z$ with and without power corrections included.
• Figure 2: Comparison of the QCD predictions for the heavy jet mass (a) and $C-$parameter (b) distributions with the data at different center-of-mass energies (from bottom to top): $Q/{\rm GeV} = 35\,, 44\,, 91\,, 133\,, 161\,, 172\,, 183\,,189$, based on the shape function.
• Figure 3: Comparison of the QCD predictions to the mean values $\langle{t}\rangle$, $\langle{\rho}\rangle$ and $\langle{C}\rangle$ with the data. Dotted lines denote ${\cal O}(\alpha_s^2)-$perturbative contribution, solid lines take into account power corrections given by Eqs. (\ref{['mean-t']}), (\ref{['mean-rho']}) and (\ref{['mean-C']}).
• Figure 4: Comparison of the QCD predictions for the second moments $\langle{t^2}\rangle$, $\langle{\rho^2}\rangle$ and $\langle{C^2}\rangle$ with the data. Dotted lines denote ${\cal O}(\alpha_s^2)-$perturbative contribution, solid lines take into account power corrections given by Eq. (\ref{['2nd']}).