Polarized gluon pseudodistributions at short distances

Abstract

We formulate the basic points of the pseudo-PDF approach to the lattice calculation of polarized gluon PDFs. We present the results of our calculations of the one-loop corrections for the bilocal Gμα(z)$$ \overset{\sim }{G} $$ G ~ λβ (0) correlator of gluonic fields. Expressions are given for a general situation when all four indices are arbitrary, and also for specific combinations of indices corresponding to three matrix elements that contain the twist-2 invariant amplitude related to the polarized PDF. We study the evolution properties of these matrix elements, and derive matching relations between Euclidean and light-cone Ioffe-time distributions. These relations are necessary for extraction of the polarized gluon distributions from the lattice data.

Towards the determination of the gluon helicity distribution in the nucleon from lattice quantum chromodynamics

“…Throughout this paper, we follow the notation of Ref. [27], in which the authors used the tilde-symbol to denote the polarized gluonic matrix elements and associated distributions.…”

“…The recent proposal to use the pseudo-PDF approach [25] to access ∆g(x, Q 2 ) (or equivalently, the corresponding Ioffe-time distribution [26]) offers a gauge-invariant and frame-independent alternative way to study ∆G. The pseudo-PDF approach [25] and the associated proper combination of matrix elements derived in [27] give access to the polarized gluon Ioffe-time distribution (ITD) and corresponding gluon helicity parton distribution function (PDF) in the nucleon. Following the convention for symbols of matrix elements from Ref.…”

“…Following the convention for symbols of matrix elements from Ref. [27], we calculate the gluon helicity Ioffe-time reduced pseudo-distribution function (reduced pseudo-ITD), M(ν, z 2 ) [25,28,29], where we refer to ν ≡ − (p • z) as the Ioffe-time [30]. The related pseudo-PDF, P(x, z 2 ) can be determined from the Fourier transform of the pseudo-ITD.…”

“…The pseudo-PDF and the pseudo-ITD can be factorized into the PDF and perturbatively calculable kernels, similar to the factorization framework for experimental cross-sections. Our calculation applies the reduced pseudo-ITD approach [31], in particular the ratio proposed in [27], for which the multiplicative renormalization factors cancel.…”

“…We apply this recently-established theoretical framework for the polarized gluon pseudo-PDF [27] in a numerical lattice QCD computation. In comparison to the significant progress in lattice QCD calculations of quark structures of the nucleon and mesons in recent years using different approaches [23,25,[57][58][59][60][61][62], there have been only a few attempts to calculate the x-dependent unpolarized gluon PDFs in the nucleon [63][64][65], pion [66], and kaon [67].…”