Non-dipolar Wilson links for transverse-momentum-dependent wave functions

TL;DR

This paper introduces a simplified definition of TMD wave functions using non-dipolar Wilson links, reducing soft subtraction complexity and maintaining infrared consistency with traditional methods.

Contribution

It proposes a new TMD wave function definition with non-dipolar Wilson links that simplifies soft subtraction and preserves infrared behavior, extending equivalence to all orders.

Findings

One-loop level analysis confirms identical infrared behavior with traditional definitions.

No soft function needed when Wilson links are orthogonal.

Definition reduces to naive TMD wave function as Wilson links approach the light cone.

Abstract

We propose a new definition of a transverse-momentum-dependent (TMD) wave function with simpler soft subtraction for $k_T$ factorization of hard exclusive processes. The un-subtracted wave function involves two pieces of non-light-like Wilson links oriented in different directions, so that the rapidity singularity appearing in usual $k_T$ factorization is regularized, and the pinched singularity from Wilson-link self-energy corrections is alleviated to a logarithmic one. In particular no soft function is needed, when the two pieces of Wilson links are orthogonal to each other. We show explicitly at one-loop level that the simpler definition with the non-dipolar Wilson links exhibits the same infrared behavior as the one with the dipolar Wilson links and complicated soft subtraction. It is pointed out that both definitions reduce to the naive TMD wave function as the non-light-like Wilson links approach to the light cone. Their equivalence is then extended to all orders by considering the evolution in the Wilson-link rapidity.