Collinear matching for leading power gluon transverse momentum distributions

TL;DR

This paper derives tree-level and one-loop matching relations for gluon transverse momentum dependent distributions, including mass corrections and the Wandzura-Wilczek approximation, advancing the theoretical understanding of gluon TMDs.

Contribution

It provides the first derivation of the Wandzura-Wilczek approximation for gluon worm-gear T distributions and introduces a method to include mass corrections at one-loop accuracy.

Findings

Derived complete series of mass corrections for gluon TMDs.

Extended the parton-in-parton framework beyond leading small-b expansion.

Obtained the Wandzura-Wilczek approximation for gluon T distributions.

Abstract

We compute the tree-level and one-loop matching relations for leading power gluon transverse momentum dependent parton distribution functions. At tree-level, working within the spinor formalism, we focus on twist-2 and twist-3 contributions, deriving the complete series of mass corrections for both T-even and T-odd distributions. At one-loop accuracy, we extend the parton-in-parton framework to include contributions beyond the leading term in the small-b expansion. Applying this methodology to the gluon sector, we obtain for the first time the Wandzura-Wilczek approximation for the gluon worm-gear T distribution. Furthermore, we develop a method to include the mass corrections in one-loop results and provide a closed-form expression for the mass series suitable for numerical implementations.