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)\( \overset{\sim }{G} \)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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M. Constantinou et al., Parton distributions and lattice-QCD calculations: Toward 3D structure, Prog. Part. Nucl. Phys. 121 (2021) 103908 [arXiv:2006.08636] [INSPIRE].
K. Cichy and M. Constantinou, A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results, Adv. High Energy Phys. 2019 (2019) 3036904 [arXiv:1811.07248] [INSPIRE].
X. Ji, Parton Physics on a Euclidean Lattice, Phys. Rev. Lett. 110 (2013) 262002 [arXiv:1305.1539] [INSPIRE].
X. Ji, Parton Physics from Large-Momentum Effective Field Theory, Sci. China Phys. Mech. Astron. 57 (2014) 1407 [arXiv:1404.6680] [INSPIRE].
Y.-Q. Ma and J.-W. Qiu, Extracting Parton Distribution Functions from Lattice QCD Calculations, Phys. Rev. D 98 (2018) 074021 [arXiv:1404.6860] [INSPIRE].
Y.-Q. Ma and J.-W. Qiu, Exploring Partonic Structure of Hadrons Using ab initio Lattice QCD Calculations, Phys. Rev. Lett. 120 (2018) 022003 [arXiv:1709.03018] [INSPIRE].
A.V. Radyushkin, Quasi-parton distribution functions, momentum distributions, and pseudo-parton distribution functions, Phys. Rev. D 96 (2017) 034025 [arXiv:1705.01488] [INSPIRE].
A. Radyushkin, Quasi-PDFs and pseudo-PDFs, PoS QCDEV2017 (2017) 021 [arXiv:1711.06031] [INSPIRE].
K. Orginos, A. Radyushkin, J. Karpie and S. Zafeiropoulos, Lattice QCD exploration of parton pseudo-distribution functions, Phys. Rev. D 96 (2017) 094503 [arXiv:1706.05373] [INSPIRE].
V. Braun and D. Müller, Exclusive processes in position space and the pion distribution amplitude, Eur. Phys. J. C 55 (2008) 349 [arXiv:0709.1348] [INSPIRE].
G.S. Bali et al., Pion distribution amplitude from Euclidean correlation functions, Eur. Phys. J. C 78 (2018) 217 [arXiv:1709.04325] [INSPIRE].
G.S. Bali et al., Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects, Phys. Rev. D 98 (2018) 094507 [arXiv:1807.06671] [INSPIRE].
X. Xiong, X. Ji, J.-H. Zhang and Y. Zhao, One-loop matching for parton distributions: Nonsinglet case, Phys. Rev. D 90 (2014) 014051 [arXiv:1310.7471] [INSPIRE].
X. Ji and J.-H. Zhang, Renormalization of quasiparton distribution, Phys. Rev. D 92 (2015) 034006 [arXiv:1505.07699] [INSPIRE].
T. Izubuchi, X. Ji, L. Jin, I.W. Stewart and Y. Zhao, Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions, Phys. Rev. D 98 (2018) 056004 [arXiv:1801.03917] [INSPIRE].
W. Wang and S. Zhao, On the power divergence in quasi gluon distribution function, JHEP 05 (2018) 142 [arXiv:1712.09247] [INSPIRE].
W. Wang, S. Zhao and R. Zhu, Gluon quasidistribution function at one loop, Eur. Phys. J. C 78 (2018) 147 [arXiv:1708.02458] [INSPIRE].
W. Wang, J.-H. Zhang, S. Zhao and R. Zhu, Complete matching for quasidistribution functions in large momentum effective theory, Phys. Rev. D 100 (2019) 074509 [arXiv:1904.00978] [INSPIRE].
X. Ji, A. Schäfer, X. Xiong and J.-H. Zhang, One-Loop Matching for Generalized Parton Distributions, Phys. Rev. D 92 (2015) 014039 [arXiv:1506.00248] [INSPIRE].
X. Xiong and J.-H. Zhang, One-loop matching for transversity generalized parton distribution, Phys. Rev. D 92 (2015) 054037 [arXiv:1509.08016] [INSPIRE].
Y.-S. Liu et al., Matching generalized parton quasidistributions in the RI/MOM scheme, Phys. Rev. D 100 (2019) 034006 [arXiv:1902.00307] [INSPIRE].
X. Ji, J.-H. Zhang and Y. Zhao, More On Large-Momentum Effective Theory Approach to Parton Physics, Nucl. Phys. B 924 (2017) 366 [arXiv:1706.07416] [INSPIRE].
A.V. Radyushkin, Quark pseudodistributions at short distances, Phys. Lett. B 781 (2018) 433 [arXiv:1710.08813] [INSPIRE].
A. Radyushkin, One-loop evolution of parton pseudo-distribution functions on the lattice, Phys. Rev. D 98 (2018) 014019 [arXiv:1801.02427] [INSPIRE].
J.-H. Zhang, J.-W. Chen and C. Monahan, Parton distribution functions from reduced Ioffe-time distributions, Phys. Rev. D 97 (2018) 074508 [arXiv:1801.03023] [INSPIRE].
A.V. Radyushkin, Generalized parton distributions and pseudodistributions, Phys. Rev. D 100 (2019) 116011 [arXiv:1909.08474] [INSPIRE].
I. Balitsky, W. Morris and A. Radyushkin, Gluon Pseudo-Distributions at Short Distances: Forward Case, Phys. Lett. B 808 (2020) 135621 [arXiv:1910.13963] [INSPIRE].
I. Balitsky, W. Morris and A. Radyushkin, Gluon pseudo-distributions at short distances, in 28th International Workshop on Deep Inelastic Scattering and Related Subjects, (2021) [arXiv:2106.01916] [INSPIRE].
I. Balitsky, W. Morris and A. Radyushkin, Short-distance structure of unpolarized gluon pseudodistributions, Phys. Rev. D 105 (2022) 014008 [arXiv:2111.06797] [INSPIRE].
Z. Fan, R. Zhang and H.-W. Lin, Nucleon gluon distribution function from 2 + 1 + 1-flavor lattice QCD, Int. J. Mod. Phys. A 36 (2021) 2150080 [arXiv:2007.16113] [INSPIRE].
Z. Fan and H.-W. Lin, Gluon Parton Distribution of the Pion and Nucleon from Lattice QCD, in 38th International Symposium on Lattice Field Theory, (2021) [arXiv:2110.14471] [INSPIRE].
HadStruc collaboration, Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics, Phys. Rev. D 104 (2021) 094516 [arXiv:2107.08960] [INSPIRE].
A. Radyushkin and S. Zhao, One-loop structure of parton distribution for the gluon condensate and “zero modes”, JHEP 12 (2021) 010 [arXiv:2111.00887] [INSPIRE].
A.V. Manohar, Polarized parton distribution functions, Phys. Rev. Lett. 66 (1991) 289 [INSPIRE].
V. Braun, P. Gornicki and L. Mankiewicz, Ioffe-time distributions instead of parton momentum distributions in description of deep inelastic scattering, Phys. Rev. D 51 (1995) 6036 [hep-ph/9410318] [INSPIRE].
Z.-Y. Li, Y.-Q. Ma and J.-W. Qiu, Multiplicative Renormalizability of Operators defining Quasiparton Distributions, Phys. Rev. Lett. 122 (2019) 062002 [arXiv:1809.01836] [INSPIRE].
J.-H. Zhang, X. Ji, A. Schäfer, W. Wang and S. Zhao, Accessing Gluon Parton Distributions in Large Momentum Effective Theory, Phys. Rev. Lett. 122 (2019) 142001 [arXiv:1808.10824] [INSPIRE].
I.I. Balitsky and V.M. Braun, Evolution Equations for QCD String Operators, Nucl. Phys. B 311 (1989) 541 [INSPIRE].
J.-W. Chen, X. Ji and J.-H. Zhang, Improved quasi parton distribution through Wilson line renormalization, Nucl. Phys. B 915 (2017) 1 [arXiv:1609.08102] [INSPIRE].
I.I. Balitsky and A.V. Radyushkin, Light ray evolution equations and leading twist parton helicity dependent nonforward distributions, Phys. Lett. B 413 (1997) 114 [hep-ph/9706410] [INSPIRE].
Y.-B. Yang et al., Nonperturbatively renormalized glue momentum fraction at the physical pion mass from lattice QCD, Phys. Rev. D 98 (2018) 074506 [arXiv:1805.00531] [INSPIRE].
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Balitsky, I., Morris, W. & Radyushkin, A. Polarized gluon pseudodistributions at short distances. J. High Energ. Phys. 2022, 193 (2022). https://doi.org/10.1007/JHEP02(2022)193
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DOI: https://doi.org/10.1007/JHEP02(2022)193