Abstract
We present the results that form the basis for calculations of the unpolarized gluon parton distributions (PDFs) using the pseudo-PDF approach. We give the results for the most complicated box diagram both for gluon bilocal operators with arbitrary indices and for combinations of indices corresponding to three matrix elements that are most convenient to extract the twist-2 invariant amplitude. We also present detailed results for the gluon-quark transition diagram. The additional results for the box diagram and the gluon-quark contribution may be used for extractions of the gluon PDF from different matrix elements, with a possible cross-check of the results obtained in this way.
Highlights
Extraction of the parton distribution functions (PDFs) from lattice calculations attracts considerable interest
In our earlier paper [27], we outlined the basic points of pseudo-PDF approach to extraction of unpolarized gluon PDFs and presented the one-loop matching conditions for a particular combination of gluon matrix elements, that has the “cleanest” projection on the twist-2 gluon PDF
We present a full result for the most lengthy contribution of the “box” diagram and its projections onto all three matrix elements containing the “twist-2” invariant amplitude
Summary
Extraction of the parton distribution functions (PDFs) from lattice calculations attracts considerable interest (see Refs. [1,2] for recent reviews and references to extensive literature). One may use coordinate-space oriented methods, namely, the “good lattice cross sections” approach [5,6], the Ioffe-time analysis of equal-time correlators [7–9], and the pseudo-PDF approach [10–12] In these cases, parton distributions are extracted through taking the short-distance z3 → 0 limit. [28]), we outlined the basic points of pseudo-PDF approach to extraction of unpolarized gluon PDFs and presented the one-loop matching conditions for a particular combination of gluon matrix elements, that has the “cleanest” projection on the twist-2 gluon PDF. These results have been used already in lattice extractions of the unpolarized gluon PDFs in Refs.
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