Power corrections to event shapes and factorization

TL;DR

The paper develops a factorization framework for power corrections to infrared-safe event shapes in $e^+e^-$ annihilation, valid in the two-jet limit. It introduces infrared shape functions, defined via Wilson lines and energy-flow operators, which capture soft radiation and are independent of the hard scale $Q$. Differential distributions such as thrust and heavy jet mass are expressed as convolutions of perturbative spectra with these shape functions, with nonperturbative content encoded in moments $\lambda_n(\mu)$ and universal energy-flow Green functions. The approach connects to energy-energy correlations and provides a path to analyze power corrections beyond simple shifts, enabling systematic treatment of a broad class of event shapes.

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.

Figures (1)

• Figure 1: The comparison of the data with the QCD prediction for the thrust distribution at different energies (from bottom to top): $Q/{\rm GeV}=14,22,35,44,55,91,133,161,$ based on the shape function. The detailed description of the plot can be found in Moriond98.