Eur. Phys. J. C (2018) 78: 802
https://doi.org/10.1140/epjc/s10052-018-6263-5

Regular Article - Theoretical Physics

Matching of transverse momentum dependent distributions at twist-3

¹ Departamento de Física Teórica, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria, 28040, Madrid, Spain
² Institut für Theoretische Physik, Universität Regensburg, 93040, Regensburg, Germany

^* e-mail: ignazios@fis.ucm.es

Received: 26 April 2018
Accepted: 19 September 2018
Published online: 3 October 2018

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.