The role of zero-mode contributions in the matching for the twist-3 PDFs <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>e</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>h</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>

Abstract

The perturbative procedure of matching was proposed to connect parton quasidistributions that are calculable in lattice QCD to the corresponding light cone distributions which enter physical processes. Such a matching procedure has so far been limited to the twist-2 distributions. Recently, we addressed the matching for the twist-3 PDF ${g}_{T}(x)$. In this work, we extend our perturbative calculations to the remaining twist-3 PDFs, $e(x)$ and ${h}_{L}(x)$. In particular, we discuss the nontrivialities involved in the calculation of the singular zero-mode contributions for the quasi-PDFs.

Topics & Concepts