Theory and applications of parton pseudodistributions

Abstract

We review the basic theory of the parton pseudodistributions approach and its applications to lattice extractions of parton distribution functions. The crucial idea of the approach is the realization that the correlator M (z, p) of the parton fields is a function M(ν, −z 2 ) of Lorentz invariants ν = −(zp), the Ioffe time, and the invariant interval z 2 . This observation allows to extract the Ioffe-time distribution M(ν, −z 2 ) from Euclidean separations z accessible on the lattice. Another basic feature is the use of the ratio M(ν, −z 2 ) ≡ M(ν, −z 2 )/M(0, −z 2 ), that allows to eliminate artificial ultraviolet divergence generated by the gauge link for space-like intervals. The remaining z 2 -dependence of the reduced Ioffe-time distribution M(ν, −z 2 ) corresponds to perturbative evolution, and can be converted into the scale-dependence of parton distributions f (x, µ 2 ) using matching relations. The ν-dependence of M(ν, −z 2 ) governs the x-dependence of parton densities f (x, µ 2 ). The perturbative evolution was successfully observed in exploratory quenched lattice calculation. The analysis of its precise data provides a framework for extraction of parton densities using the pseudodistributions approach. It was used in the recently performed calculations of the nucleon and pion valence quark distributions. We also discuss matching conditions for the pion distribution amplitude and generalized parton distributions, the lattice studies of which are now in progress.

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.…”

Overview of lattice calculations of the x-dependence of PDFs, GPDs and TMDs

“…This proposal immediately led to first lattice evaluations for the three twist-2 PDFs [7][8][9][10] and soon thereafter to a plethora of theoretical and practical studies. The renewed interest in extracting the x-dependence on the lattice led to the revival of the earlier approaches and to the emergence of new ones [11][12][13][14][15], all of which have since achieved significant progress. This dynamical progress is extensively reported in the reviews [16][17][18][19].…”

Notes on lattice observables for parton distributions: nongauge theories

“…For recent reviews, we refer the reader to refs. [2,[5][6][7][8][9][10]. This program has often been referred to as the "first principles computation of PDFs", generating different reactions among the lattice and high-energy physics communities: on the one hand it has been welcomed with enthusiasm, triggering several dedicated studies; on the other hand it has been criticized in refs.…”