An on-shell approach to factorization

TL;DR

This paper proves a tree-level factorization in QCD using on-shell spinor helicity methods, providing a clearer understanding of soft and collinear limits without gauge-dependent assumptions.

Contribution

It introduces a transparent on-shell proof of perturbative factorization in QCD, linking matrix elements through scaling of physical momenta, facilitating transition to effective theories.

Findings

Factorization proven at tree level using on-shell methods

Matrix elements relate through momentum scaling in soft/collinear limits

Approach simplifies transition to Soft-Collinear Effective Theory

Abstract

Factorization is possible due to the universal behavior of Yang-Mills theories in soft and collinear limits. Here, we take a small step towards a more transparent understanding of these limits by proving a form of perturbative factorization at tree- level using on-shell spinor helicity methods. We present a concrete and self-contained expression of factorization in which matrix elements in QCD are related to products of other matrix elements in QCD up to leading order in a power-counting parameter determined by the momenta of certain physical on-shell states. Our approach uses only the scaling of momenta in soft and collinear limits, avoiding any assignment of scaling behavior to unphysical (and gauge-dependent) fields. The proof of factorization exploits many advantages of helicity spinors, such as the freedom to choose different reference vectors for polarizations in different collinear sectors. An advantage of this approach is that once factorization is shown to hold in QCD, the transition to Soft-Collinear Effective Theory is effortless.