The role of zero-mode contributions in the matching for the twist-3 PDFs $e(x)$ and $h_{L}(x)$

TL;DR

This paper extends the perturbative matching procedure to twist-3 parton distribution functions, specifically $e(x)$ and $h_{L}(x)$, highlighting the importance of zero-mode contributions in lattice QCD calculations.

Contribution

It provides the first detailed analysis of zero-mode contributions in the matching for twist-3 PDFs $e(x)$ and $h_{L}(x)$, expanding the applicability of lattice QCD methods.

Findings

Calculated the matching for $e(x)$ and $h_{L}(x)$ PDFs.

Identified the significance of zero-mode contributions in these calculations.

Extended the perturbative framework to twist-3 distributions.

Abstract

The perturbative procedure of matching was proposed to connect parton quasi-distributions 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 non-trivialities involved in the calculation of the singular zero-mode contributions for the quasi-PDFs.