Infrared Safety in Factorized Hard Scattering Cross-Sections

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.

6 pages, 7 figures, uses elsarticle.cls. v2: extended introduction and clarified discussion of ingredients necessary for proving factorization

References in corpus (7)

• Jets from Massive Unstable Particles: Top-Mass Determination
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Factorization of e+e- Event Shape Distributions with Hadronic Final States in Soft Collinear Effective Theory
• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• On The Equivalence of Soft and Zero-Bin Subtractions
• Demonstration of the Equivalence of Soft and Zero-Bin Subtractions
• On different ways to quantize Soft-Collinear Effective Theory

Cited by in corpus (2)

• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• Probing the Structure of Jets: Factorized and Resummed Angularity Distributions in SCET