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Perturbative matching relates the parton quasi-distributions, defined byEuclidean correlators at finite hadron momenta, to the light-cone distributionswhich are accessible in experiments. Previous matching calculations haveexclusively focused on twist-2 distributions. In this work, we address, for thefirst time, the one-loop matching for the twist-3 parton distribution function$g_T(x)$. The results have been obtained using three different infraredregulators, while dimensional regularization has been adopted to deal with theultraviolet divergences. We present the renormalized expressions of thematching 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-modecontribution. Our results have already been used for the extraction of $g_T(x)$from lattice QCD calculations.

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