Infrared Safety in Factorized Hard Scattering Cross-Sections

TL;DR

This paper discusses how to verify the infrared safety of functions in factorized hard scattering cross-sections using a method applied to e+e- angularity distributions, ensuring the validity of soft-collinear effective theory.

Contribution

It introduces an intuitive, regulator-independent method to test infrared safety of jet and soft functions at one loop, emphasizing the importance of zero-bins in the analysis.

Findings

Method effectively identifies infrared divergences without explicit regulators

Clarifies the distinction between infrared and ultraviolet singularities

Highlights the necessity of zero-bin subtraction for infrared safety

Abstract

The rules of soft-collinear effective theory can be used naively to write hard scattering cross-sections as convolutions of separate hard, jet, and soft functions. One condition required to guarantee the validity of such a factorization is the infrared safety of these functions in perturbation theory. Using e+e- angularity distributions as an example, we propose and illustrate an intuitive method to test this infrared safety at one loop. We look for regions of integration in the sum of Feynman diagrams contributing to the jet and soft functions where the integrals become infrared divergent. Our analysis is independent of an explicit infrared regulator, clarifies how to distinguish infrared and ultraviolet singularities in pure dimensional regularization, and demonstrates the necessity of taking zero-bins into account to obtain infrared-safe jet functions.