Matching of transverse momentum dependent distributions at twist-3

TL;DR

This paper derives the leading order matching of polarized TMD distributions onto collinear functions at small transverse distances, considering twist-3 operators and process dependence effects.

Contribution

It provides the first direct position space evaluation of twist-3 TMD distributions and their matching onto collinear functions, including process dependence effects.

Findings

Explicit matching formulas for Sivers, Boer-Mulders, and worm-gear functions.

Analysis of process dependence on TMD matching.

Discussion of moments relevant for lattice QCD calculations.

Abstract

We derive the leading order matching of the quark generated polarized transverse momentum dependent (TMD) distributions onto the collinear functions at small values of the transverse distance. Starting from the very definition of the TMD operator and performing the light-cone operator product expansion up to twist-3 order, we evaluate each distribution directly in position space. We primarily consider the cases of Sivers, Boer-Mulders and worm-gear functions. The effects of the TMD process dependence on the matching are explicitly shown. We also discuss the moments of TMD distributions which can be relevant for lattice calculations.