Generalized parton distributions and pseudodistributions

Abstract

We derive one-loop matching relations for the Ioffe-time distributions (ITDs) related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs within the parton pseudodistributions approach.

The x-dependence of hadronic parton distributions: A review on the progress of lattice QCD

“…An alternative framework to quasi-PDFs is the pseudo-ITDs 3 developed by Radyushkin [25,[80][81][82][83][84][85][86]. The common feature with quasi-PDFs is the use of the same matrix elements M of boosted hadrons coupled to non-local operators (Eq.…”

“…Similar to quasi-distributions, the pseudo-distributions approach relies on the factorization of pseudo-ITDs obtained on the lattice to extract the lightcone ITDs, using a matching kernel calculable in perturbative QCD. The necessary matching is performed at the level of ITDs [56,83,84,89] in coordinate space, while in the quasi-PDFs approach is done in the momentum space.…”

“…This is in contrast with the quasi-PDFs, where matrix elements at different P 3 are not analyzed together. The M(ν, z 2 ) are matched to light-cone ITDs, Q(ν, μ 2 ) using a matching procedure, and at the same time are converted to the MS and evolved to a common scale, μ = 1/z [56,83,84,89]. Finally, the light-cone PDFs are related to Q(ν, μ 2 ) via a Fourier transform in Ioffe time.…”

“…The calculation addresses the erroneous claims [158,159] that quasi-PDFs cannot be related to light-cone PDFs because the moments of the former exhibit powerdivergent mixing. It should be noted that the claims have been refuted in more than one publications [84,101,160]. For instance, one of the counter-arguments is that, while all moments except for the zeroth do not converge, the light-cone PDFs are extracted from the non-local quasi-distributions avoiding the power divergence problem [160].…”

Notes on lattice observables for parton distributions: nongauge theories

“…We provide the details of the computation in appendix A. The implementation of the factorization theorem in position space, together with the definition of reduced distributions, are the typical approach followed in nonperturbative calculations of pseudo-PDFs [4,21,[24][25][26][27], while the realization of the factorization in momentum space characterizes the quasi-PDF approach [3,[28][29][30][31].…”