TMD factorization bridging large and small x

TL;DR

This paper proposes a unified TMD factorization framework in QCD that bridges the large-x and small-x regimes, connecting DGLAP, BFKL, and CSS formalisms through a background field approach.

Contribution

It introduces a novel TMD factorization method that unifies different QCD regimes and provides a general evolution framework beyond existing limits.

Findings

Reduces to CSS and DGLAP in large-x limit

Reduces to BFKL in small-x limit

Defines a continuous evolution between regimes

Abstract

QCD factorization takes different forms in the large-x and small-x regimes. At large-x, collinear factorization leads to the DGLAP evolution equation, while at small-x, rapidity factorization results in the BFKL equation. To unify these different regimes, a new TMD factorization based on the background field method is proposed. This factorization not only reduces to CSS and DGLAP in the large-x limit and BFKL in the small-x limit, but also defines a general evolution away from these regimes.