Energy flow in QCD and event shape functions

Abstract

Hadronization corrections to the thrust and related event shape distributions in the two-jet kinematical region of e+e- annihilation are summarized by nonperturbative shape functions. The moments of shape functions are given by universal matrix elements in QCD, which describe the energy flow in QCD final states. We show how the nonperturbative structure of these matrix elements may be inferred from resummed perturbation theory and Lorentz invariance. This analysis suggests the same functional forms for the shape functions as were found in phenomenological studies, and sheds light on the physical significance of the parameters that characterize these functions.

Figures (2)

• Figure 1: The pictorial definition of the energy flow operator ${\cal E} (\vec{n})$. The unit vectors $\vec{n}_R$ and $\vec{n}_L$ indicate the directions of the two outgoing jets. The shaded plane orthogonal to these unit vectors goes through the annihilation point, and separates the left and right hemispheres. The energy flux through the infinitesimal surface element $d \omega = d\vec{n} \, \delta \left( \vec{n}^2 - 1 \right)$ is given by ${\cal E} (\vec{n}) d \omega$.
• Figure 2: Diagrammatic representation of the correlation function (\ref{['GreenFunction']}). Here the dashed line represents the unitary cut and the final states are weighted with the product of factors ${\cal E} (\vec{n}_1) \dots {\cal E} (\vec{n}_N)$ defined in Eq. (\ref{['ElguonState']}).