One-loop matching for gluon lattice TMDs

TL;DR

This paper derives the one-loop matching coefficient for gluon TMDs in lattice QCD, enabling more accurate first-principles calculations of gluon transverse momentum distributions.

Contribution

It provides the first calculation of the one-loop gluon matching coefficient for lattice TMDs, showing Casimir scaling and independence from spin and quark mixing.

Findings

Matching coefficient is independent of spin.

Coefficient exhibits Casimir scaling.

Facilitates reliable lattice QCD calculations of gluon TMDs.

Abstract

Transverse-momentum-dependent parton distributions (TMDs) can be calculated from first principles by computing a related set of Euclidean lattice observables and connecting them via a factorization formula. This work focuses on the leading-power factorization formula connecting the lattice quasi-TMD and continuum Collins TMD for gluons. We calculate the one-loop gluon matching coefficient, which is known to be independent of spin and exhibits no mixing with quarks. We demonstrate that this coefficient satisfies Casimir scaling with respect to the quark matching coefficient at one-loop order. Our result facilitates reliable lattice QCD calculations of gluon TMDs.