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

Understand

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.