Abstract
We study the factorization relations between quasi gluon GPDs and twist-2 GPDs. The perturbative coefficient functions are obtained at one-loop level. They are free from any collinear- or I.R. divergences. Unlike the case of the factorization of quasi quark GPDs at one-loop, we have to add ghost contributions for the factorization of quasi gluon GPDs in order to obtain gauge-invariant results. In general, operators will be mixed beyond tree-level. Our work shows that the mixing pattern of the nonlocal operators in quasi gluon GPDs is the same as those of local operators, i.e., the nonlocal operators considered are mixed with gauge-invariant operators, BRST-variation operators and operators involving EOM operator. The factorization relations are obtained for all quasi gluon GPDs. Taking the forward limit, we also obtain the relations between quasi gluon PDFs and twist-2 PDFs.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
D. Müller et al., Wave functions, evolution equations and evolution kernels from light ray operators of QCD, Fortsch. Phys. 42 (1994) 101 [hep-ph/9812448] [INSPIRE].
X.-D. Ji, Gauge-invariant decomposition of nucleon spin, Phys. Rev. Lett. 78 (1997) 610 [hep-ph/9603249] [INSPIRE].
X.-D. Ji, Deeply virtual Compton scattering, Phys. Rev. D 55 (1997) 7114 [hep-ph/9609381] [INSPIRE].
D. Mueller, Generalized parton distributions — visions, basics, and realities, Few Body Syst. 55 (2014) 317 [arXiv:1405.2817] [INSPIRE].
M. Diehl, Generalized parton distributions, Phys. Rept. 388 (2003) 41 [hep-ph/0307382] [INSPIRE].
A.V. Belitsky and A.V. Radyushkin, Unraveling hadron structure with generalized parton distributions, Phys. Rept. 418 (2005) 1 [hep-ph/0504030] [INSPIRE].
X. Ji, J.-H. Zhang and Y. Zhao, Physics of the gluon-helicity contribution to proton spin, Phys. Rev. Lett. 111 (2013) 112002 [arXiv:1304.6708] [INSPIRE].
X. Ji, Parton physics from large-momentum effective field theory, Sci. China Phys. Mech. Astron. 57 (2014) 1407 [arXiv:1404.6680] [INSPIRE].
X. Ji et al., Large-momentum effective theory, Rev. Mod. Phys. 93 (2021) 035005 [arXiv:2004.03543] [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].
J.P. Ma, Z.Y. Pang and G.P. Zhang, QCD factorization of quasi generalized quark distributions, JHEP 08 (2022) 130 [arXiv:2202.07116] [INSPIRE].
R.K. Ellis, W. Furmanski and R. Petronzio, Power corrections to the parton model in QCD, Nucl. Phys. B 207 (1982) 1 [INSPIRE].
R.K. Ellis, W. Furmanski and R. Petronzio, Unraveling higher twists, Nucl. Phys. B 212 (1983) 29 [INSPIRE].
J.-W. Qiu, Twist four contributions to the parton structure functions, Phys. Rev. D 42 (1990) 30 [INSPIRE].
J.C. Collins and T.C. Rogers, The gluon distribution function and factorization in Feynman gauge, Phys. Rev. D 78 (2008) 054012 [arXiv:0805.1752] [INSPIRE].
S.D. Joglekar and B.W. Lee, General theory of renormalization of gauge invariant operators, Annals Phys. 97 (1976) 160 [INSPIRE].
S.D. Joglekar, Local operator products in gauge theories. 2, Annals Phys. 109 (1977) 210 [INSPIRE].
J.-W. Chen, H.-W. Lin and J.-H. Zhang, Pion generalized parton distribution from lattice QCD, Nucl. Phys. B 952 (2020) 114940 [arXiv:1904.12376] [INSPIRE].
C. Alexandrou et al., Unpolarized and helicity generalized parton distributions of the proton within lattice QCD, Phys. Rev. Lett. 125 (2020) 262001 [arXiv:2008.10573] [INSPIRE].
H.-W. Lin, Nucleon tomography and generalized parton distribution at physical pion mass from lattice QCD, Phys. Rev. Lett. 127 (2021) 182001 [arXiv:2008.12474] [INSPIRE].
H.-W. Lin, Nucleon helicity generalized parton distribution at physical pion mass from lattice QCD, Phys. Lett. B 824 (2022) 136821 [arXiv:2112.07519] [INSPIRE].
X.-N. Xiong, X.-D. 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].
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].
W. Wang, S. Zhao and R. Zhu, Gluon quasidistribution function at one loop, Eur. Phys. J. C 78 (2018) 147 [arXiv:1708.02458] [INSPIRE].
I.W. Stewart and Y. Zhao, Matching the quasiparton distribution in a momentum subtraction scheme, Phys. Rev. D 97 (2018) 054512 [arXiv:1709.04933] [INSPIRE].
T. Izubuchi et al., Factorization theorem relating euclidean and light-cone parton distributions, Phys. Rev. D 98 (2018) 056004 [arXiv:1801.03917] [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].
L.-B. Chen, W. Wang and R. Zhu, Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions, Phys. Rev. D 102 (2020) 011503 [arXiv:2005.13757] [INSPIRE].
Z.-Y. Li, Y.-Q. Ma and J.-W. Qiu, Extraction of next-to-next-to-leading-order parton distribution functions from lattice QCD calculations, Phys. Rev. Lett. 126 (2021) 072001 [arXiv:2006.12370] [INSPIRE].
G. Grammer Jr. and D.R. Yennie, Improved treatment for the infrared divergence problem in quantum electrodynamics, Phys. Rev. D 8 (1973) 4332 [INSPIRE].
A.V. Radyushkin, Nonforward parton distributions, Phys. Rev. D 56 (1997) 5524 [hep-ph/9704207] [INSPIRE].
J. Blumlein, B. Geyer and D. Robaschik, On the evolution kernels of twist-2 light ray operators for unpolarized and polarized deep inelastic scattering, Phys. Lett. B 406 (1997) 161 [hep-ph/9705264] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2212.08238
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Ma, J.P., Pang, Z.Y., Zhang, C.P. et al. QCD factorization of quasi generalized gluon distributions. J. High Energ. Phys. 2023, 1 (2023). https://doi.org/10.1007/JHEP04(2023)001
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2023)001