Accessing Gluon Parton Distributions in Large Momentum Effective Theory

Abstract

Gluon parton distribution functions (PDFs) in the proton can be calculated directly on Euclidean lattices using large momentum effective theory (LaMET). To realize this goal, one has to find renormalized gluon quasi-PDFs in which power divergences and operator mixing are thoroughly understood. For the unpolarized distribution, we identify four independent quasi-PDF correlators that can be multiplicatively renormalized on the lattice. Similarly, the helicity distribution can be derived from three independent multiplicatively renormalizable quasi-PDFs. We provide a LaMET factorization formula for these renormalized quasi-PDFs from which one can extract the gluon PDFs.

Parton distributions from lattice data: the nonsinglet case

“…[28], both for non-singlet and singlet quark PDFs, as well as for gluons. Even though one can choose operators for the latter that do not mix with singlet quark quasi-PDFs under renormalization [19,20], mixing under matching is inevitable. No mixing of the flavour nonsinglet sector with flavour singlet or gluon sectors occurs, as stated in Eq.…”

“…Following these novel ideas, a number of publications have appeared (see Refs. [8,9] for recent reviews), from both lattice and high-energy communities, addressing the main theoretical problems of the new lattice approach: the definition and renormalization of the non-local operators involved in the lattice simulation [10][11][12][13][14][15][16][17][18][19][20], the proof of the factorization theorem between PDFs and quasi-PDFs [7,[21][22][23][24][25], the computation of the matching coefficients relating latticecomputable quantities to PDFs in different renormalization schemes [21,22,[24][25][26][27][28][29][30][31][32][33]. Also, data coming from first lattice QCD simulations have started appearing and have gotten into already a relatively advanced stage over the last few years [13,[30][31][32][33][34][35][36][37][38][39][40][41][42]…”

Exploring twist-2 GPDs through quasidistributions in a diquark spectator model

“…By now there has been important progress in understanding the renormalization of quasi-PDFs [20][21][22][23][24][25][26][27][28][29][30][31][32]. A variety of other aspects of quasi-PDFs and, generally, Euclidean correlators have also been extensively studied .…”

Improvement, generalization, and scheme conversion of Wilson-line operators on the lattice in the auxiliary field approach

“…This means that there is no mixing of O Γ with nonlocal gluonic operators of the type discussed in Ref. [34]. On the other hand, the whole-operator approach would predict that those gluonic operators could have a divergent O(a −1 ) contribution from a flavor singlet nonlocal quark operator O Γ .…”