On the power divergence in quasi gluon distribution function

We present the first attempt to access the x-dependence of the gluon unpolarized parton distribution function (PDF), based on lattice simulations using the large-momentum effective theory (LaMET) approach. The lattice calculation is carried out with pion masses of 340 and 678 MeV on a 2+1-flavor DWF configuration with lattice spacing a = 0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93 GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative O(αs) matching and the mixing from the quark PDFs. PACS numbers: 12.38.Mh, 25.75.Nq Introduction: The unpolarized parton distribution function (PDF) is the probability density for finding the corresponding parton with a certain longitudinal momentum fraction x in an infinite-momentum hadron at MS renormalization scale µ, that satisfies the hadron momentum sum rules,

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“…Due to its linear divergence [14], the bareH 0 (z, P z ) decays exponentially as |z| increases. Fig.…”

mentioning

confidence: 99%

Gluon Quasi-Parton-Distribution Functions from Lattice QCD

et al. 2018

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“…From the point of view of matching, the important contribution of this paper was to confirm that the conclusions of Ref. [140] hold when using gauge-invariant DR instead of the UV cutoff scheme. Moreover, it was pointed out that one can construct gluonic operators that are multiplicatively renormalizable, i.e.…”

Section: Gpdsmentioning

confidence: 53%

“…This issue has been addressed independently by two groups [137][138][139], concluding that the Euclidean spacelike correlation functions leading to the quasi-PDFs are indeed renormalizable. These are based on two different approaches: the auxiliary heavy quark method [137,[139][140][141] and the diagrammatic expansion method [138,142], employed for both quark and gluon quasi-PDFs. Below we highlight their main findings.…”

Section: B Renormalizability Of Quasi-pdfsmentioning

confidence: 99%

“…For completeness, we also address the renormalizability of the gluon quasi-PDFs, which are more complicated to study compared to non-singlet quark PDFs due to the presence of mixing. Their renormalizability was implied using arguments based on the quark quasi-PDFs [138,139], but more recently there are direct studies for the renormalization of gluon quasi-PDFs [140][141][142].…”

Section: Renormalizability Of Gluon Quasi-pdfsmentioning

confidence: 99%

“…In a follow-up work [140], W. Wang and S. Zhao considered in more detail the issue of the power divergence in quasi-gluon PDFs, see Sec. V B 2 for more details from the point of view of renormalizability.…”

Section: Gpdsmentioning

confidence: 99%

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A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

Cichy

Constantinou

2019

Advances in High Energy Physics

220

168

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Within the theory of Quantum Chromodynamics (QCD), the rich structure of hadrons can be quantitatively characterized, among others, using a basis of universal non-perturbative functions: parton distribution functions (PDFs), generalized parton distributions (GPDs), transversemomentum dependent parton distributions (TMDs) and distribution amplitudes (DAs). For more than half a century, there has been a joint experimental and theoretical effort to obtain these partonic functions. However, the complexity of the strong interactions has placed severe limitations, and first-principle information on these distributions was extracted mostly from their moments computed in Lattice QCD. Recently, breakthrough ideas changed the landscape and several approaches were proposed to access the distributions themselves on the lattice.In this paper, we review in considerable detail approaches directly related to partonic distributions. We highlight a recent idea proposed by X. Ji on extracting quasi-distributions that spawned renewed interest in the whole field and sparked the largest amount of numerical studies within Lattice QCD. We discuss theoretical and practical developments, including challenges that had to be overcome, with some yet to be handled. We also review numerical results, including a discussion based on evolving understanding of the underlying concepts and the theoretical and practical progress. Particular attention is given to important aspects that validated the quasi-distribution approach, such as renormalization, matching to light-cone distributions and lattice techniques.In addition to a thorough discussion of quasi-distributions, we consider other approaches: hadronic tensor, auxiliary quark methods, pseudo-distributions, OPE without OPE and good lattice cross sections. In the last part of the paper, we provide a summary and prospects of the field, with emphasis on the necessary conditions to obtain results with controlled uncertainties.

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Polarized gluon pseudodistributions at short distances

Balitsky

Morris

Radyushkin

2022

J. High Energ. Phys.

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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.

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On the power divergence in quasi gluon distribution function

Cited by 40 publications

References 77 publications

Gluon Quasi-Parton-Distribution Functions from Lattice QCD

Gluon Quasi-Parton-Distribution Functions from Lattice QCD

A Guide to Light-Cone PDFs from Lattice QCD: An Overview of Approaches, Techniques, and Results

Polarized gluon pseudodistributions at short distances

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