One-loop matching for the twist-3 parton distribution $g_T (x)$

TL;DR

This paper derives the first one-loop perturbative matching coefficients for the twist-3 parton distribution $g_T(x)$, connecting lattice-calculable quasi-distributions to experimental light-cone distributions.

Contribution

It provides the initial one-loop matching calculation for twist-3 distributions, extending the perturbative framework beyond the previously studied twist-2 case.

Findings

Derived renormalized matching coefficients in $ar{MS}$ and modified $ar{MS}$ schemes.

Analyzed the impact of zero-mode contributions on the matching.

Results facilitate lattice QCD extraction of $g_T(x)$ from Euclidean correlators.

Abstract

Perturbative matching relates the parton quasi-distributions, defined by Euclidean correlators at finite hadron momenta, to the light-cone distributions which are accessible in experiments. Previous matching calculations have exclusively focused on twist-2 distributions. In this work, we address, for the first time, the one-loop matching for the twist-3 parton distribution function $g_T(x)$. The results have been obtained using three different infrared regulators, while dimensional regularization has been adopted to deal with the ultraviolet divergences. We present the renormalized expressions of the matching coefficient for $g_{T}(x)$ in the $\overline{\rm MS}$ and modified $\overline{\rm MS}$ schemes. We also discuss the role played by a zero-mode contribution. Our results have already been used for the extraction of $g_T(x)$ from lattice QCD calculations.