Non-dipolar gauge links for transverse-momentum-dependent pion wave functions

TL;DR

This paper proposes a new definition of TMD pion wave functions using non-dipolar gauge links, reducing soft subtraction complexity while maintaining equivalence with traditional definitions.

Contribution

It introduces a non-dipolar Wilson line approach for TMD pion wave functions that simplifies soft subtraction without losing theoretical consistency.

Findings

Soft subtraction factors can be significantly reduced.

Non-dipolar Wilson lines are equivalent to dipolar gauge links at all orders.

The new definition maintains the same infrared behavior as traditional approaches.

Abstract

I discuss the factorization-compatible definitions of transverse-momentum-dependent (TMD) pion wave functions which are fundamental theory inputs entering QCD factorization formulae for many hard exclusive processes. I will first demonstrate that the soft subtraction factor introduced to remove both rapidity and pinch singularities can be greatly reduced by making the maximal use of the freedom to construct the Wilson-line paths when defining the TMD wave functions. I will then turn to show that the newly proposed TMD definition with non-dipolar Wilson lines is equivalent to the one with dipolar gauge links and with a complicated soft function, to all orders of the perturbative expansion in the strong coupling, as far as the infrared behavior is concerned.