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.
Highlights
One of the modern challenges of QCD is represented by the study of the effects of polarization in differential cross sections for semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan/vector/scalar-boson production
The main aim of this paper is to uniformly evaluate the matching of quark TMD parton distribution functions (TMDPDFs) at the twist-3 level, using solely the definition of the transverse momentum dependent (TMD) distribution as it is provided by the TMD factorization theorem
In order to realize our computations we start observing that the operators that define TMD distributions have a peculiar structure, which distinguishes them from more traditional parton distribution functions (PDFs) and fragmentation functions (FFs), distributions amplitudes and others
Summary
One of the modern challenges of QCD is represented by the study of the effects of polarization in differential cross sections for semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan/vector/scalar-boson production. In order to realize our computations we start observing that the operators that define TMD distributions have a peculiar structure, which distinguishes them from more traditional parton distribution functions (PDFs) and fragmentation functions (FFs), distributions amplitudes and others They include half-infinite light-like Wilson lines, and they are geometrically non-compact. The direction of the Wilson lines depends on the underline process This direction is future pointing for production mechanisms (such as fragmentation in semi-inclusive deep-inelastic scattering (SIDIS)), and past pointing for collision mechanisms (such as Drell-Yan process). The collinear distributions are perfectly independent on the process, any process dependence of TMD operator must reveal itself within OPE We observe this effect and demonstrate that it appears in the contributions specific for the TMD operators.
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