Power corrections to event shapes and factorization

TL;DR

This paper investigates power corrections to event shape distributions in electron-positron annihilation, demonstrating how nonperturbative shape functions and factorization properties organize power corrections and relate to universal QCD matrix elements.

Contribution

It introduces a framework for describing power corrections to event shapes using shape functions that are universal across different observables and independent of collision energy.

Findings

Power corrections are organized by shape functions.

Shape functions are universal and energy-independent.

The approach relates power corrections to energy-momentum tensor matrix elements.

Abstract

We study power corrections to the differential thrust, heavy mass and related event shape distributions in $e^+e^-$-annihilation, whose values, $e$, are proportional to jet masses in the two-jet limit, $e\to 0$. The factorization properties of these differential distributions imply that they may be written as convolutions of nonperturbative "shape" functions, describing the emission of soft quanta by the jets, and resummed perturbative cross sections. The infrared shape functions are different for different event shapes, and depend on a factorization scale, but are independent of the center-of-mass energy $Q$. They organize all power corrections of the form $1/(eQ)^n$, for arbitrary $n$, and carry information on a class of universal matrix elements of the energy-momentum tensor in QCD, directly related to the energy-energy correlations.