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.
Highlights
Parton distribution functions (PDFs) are important quantities encoding information about spatial and momentum distributions of partons inside hadrons [1]
We address, for the first time, the one-loop matching for the twist-3 parton distribution function gTðxÞ
Until recently, lattice quantum chromodynamics (QCD) computations of PDFs were limited to matrix elements of local operators which are related to Mellin moments of PDFs
Summary
Parton distribution functions (PDFs) are important quantities encoding information about spatial and momentum distributions of partons inside hadrons [1]. At the twist-2 level, one-loop matching relations between light-cone PDFs and quasi-PDFs are obtained by computing both quantities for a quark target in perturbative QCD (pQCD). Diagram by diagram, the IR poles of the light-cone PDF gT and the quasi-PDF gT;Q exactly match This key feature of the quasi-PDF approach is shown here explicitly for the first time for a twist-3 parton correlator, and encourages us to come up with a matching formula which we have used very recently for the first calculation of gTðxÞ in lattice QCD [82]. In the nonperturbative [infrared (IR)] region, we exploit three different regulators: nonzero gluon mass, nonzero quark mass, and DR These regulators have been used before for the calculation of matching relations of twist-2 operators, and whenever results for different regulators were explicitly compared, it was reported that the final matching coefficient is regulator independent. V, we summarize our work and present a brief outlook
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