Transverse-momentum-dependent parton distributions at the edge of the lightcone

TL;DR

This paper develops a gauge-invariant operator definition for transverse-momentum-dependent parton densities, addressing divergences and soft factors, and compares different factorization schemes involving lightlike and off-lightcone gauge links.

Contribution

It introduces a fully gauge-invariant framework for TMDs with a consistent treatment of divergences and soft factors, connecting lightcone and covariant gauge approaches.

Findings

Successful construction of gauge-invariant TMD operators.

Resolution of divergences through soft factors.

Comparison of lightcone and off-lightcone gauge link schemes.

Abstract

We present a completely gauge-invariant operator definition of transverse-momentum-dependent parton densities (TMD), supplied with longitudinal lightlike gauge links as well as transverse gauge links at lightcone infinity. Within this framework, we consider the consistent treatment of specific divergences, emerging in the "unsubtracted" TMD beyond the tree approximation, and construct the soft factors to cancel unphysical singularities. We confront this approach with factorization schemes, which make use of covariant gauges with off-the-lightcone gauge links, and discuss their mutual connection.