Analytic Regularization in Soft-Collinear Effective Theory

TL;DR

This paper introduces an analytic regularization method for Soft-Collinear Effective Theory that preserves gauge invariance and simplifies factorization proofs in high-energy physics, especially for massless theories.

Contribution

It proposes a new analytic regularization approach that maintains the structure of SCET and provides a straightforward operator definition of transverse parton distributions.

Findings

Regularization preserves gauge invariance.

Simplifies factorization proofs in massless theories.

Provides a new operator definition for transverse parton distributions.

Abstract

In high-energy processes which are sensitive to small transverse momenta, individual contributions from collinear and soft momentum regions are not separately well-defined in dimensional regularization. A simple possibility to solve this problem is to introduce additional analytic regulators. We point out that in massless theories the unregularized singularities only appear in real-emission diagrams and that the additional regulators can be introduced in such a way that gauge invariance and the factorized eikonal structure of soft and collinear emissions is maintained. This simplifies factorization proofs and implies, at least in the massless case, that the structure of Soft-Collinear Effective Theory remains completely unchanged by the presence of the additional regulators. Our formalism also provides a simple operator definition of transverse parton distribution functions.