Parton distributions and lattice-QCD calculations: Toward 3D structure

Martha Constantinou; Aurore Courtoy; Markus A. Ebert; Michael Engelhardt; Tommaso Giani; Tim Hobbs; Tie Jiun Hou; Aleksander Kusina; Krzysztof Kutak; Jian Liang; Huey Wen Lin; Keh Fei Liu; Simonetta Liuti; Cédric Mezrag; Pavel Nadolsky; Emanuele R. Nocera; Fred Olness; Jian Wei Qiu; Marco Radici; Anatoly Radyushkin; Abha Rajan; Ted Rogers; Juan Rojo; Gerrit Schierholz; C. P. Yuan; Jian Hui Zhang; Rui Zhang

doi:10.1016/j.ppnp.2021.103908

Parton distributions and lattice-QCD calculations: Toward 3D structure

Martha Constantinou, Aurore Courtoy, Markus A. Ebert, Michael Engelhardt, Tommaso Giani, Tim Hobbs, Tie Jiun Hou, Aleksander Kusina, Krzysztof Kutak, Jian Liang, Huey Wen Lin, Keh Fei Liu, Simonetta Liuti, Cédric Mezrag, Pavel Nadolsky, Emanuele R. Nocera, Fred Olness, Jian Wei Qiu, Marco Radici, Anatoly RadyushkinAbha Rajan, Ted Rogers, Juan Rojo, Gerrit Schierholz, C. P. Yuan, Jian Hui Zhang, Rui Zhang

Research output: Contribution to journal › Review article › peer-review

80 Scopus citations

Abstract

The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.

Original language	English
Article number	103908
Journal	Progress in Particle and Nuclear Physics
Volume	121
DOIs	https://doi.org/10.1016/j.ppnp.2021.103908
State	Published - Nov 2021

Bibliographical note

Funding Information:
We are grateful to Autumn Hewitt, Nicole Kokx and Brenda Wenzlick, for their help in the organization of the workshop. The workshop was partly supported by Michigan State University, USA and US National Science Foundation via the grant under PHY 1653405 “CAREER: Constraining Parton Distribution Functions for New-Physics Searches”. We thank Kostas Orginos for his early-stage involvement in organizing the workshop, Alberto Accardi, Jorge Benel, Nikhil Karthik, Zhouyou Fan, Paul Reimer, Dave Soper, Michael Wagman, Zhite Yu for their participation and discussions during the PDFLattice2019 workshop, and Xiangdong Ji for a critical reading of the manuscript. We thank Joseph Karpie and Gunnar Bali for providing numbers for Figs. 7 and 22 , respectively, and Phiala Shanahan for remaking Fig. 33 for this paper. We thank H. Moutarde, Ingo Schienbein, P. Sznajder, and Yong Zhao as well as members of the Lattice Hadron Physics Collaboration (LHPC) and the Lattice TMD Collaboration for useful discussion during the preparation of this report.

Funding Information:
We are pleased to acknowledge support from: the U.S. Department of Energy , grants DE-SC0020405 [M. Constantinou], DE-SC0011090 [M. Ebert], DE-FG02-96ER40965 [M. Engelhardt]; DE-SC0010129 [T. Hobbs, F. Olness, P. Nadolsky], DE-SC0016286 [S. Liuti], DE-AC05-06OR23177 [J.W. Qiu], DE-FG02-97ER41028 [A. Radyushkin], DE-SC0012704 [A. Rajan], DE-SC0018106 [T. C. Rogers], and the DOE Topical Collaboration on TMDs, USA [M. Engelhardt, J.W. Qiu]; Jefferson Science Associates, USA , LLC under U.S. DOE Contract DE-AC05-06OR23177 [J.W. Qiu, A. Radyushkin, T.C. Rogers]; the US National Science Foundation grants PHY-1714407 [M. Constantinou], PHY 1653405 [H. Lin, R. Zhang], PHY-1719914 [C. Yuan]; the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program grant agreement N.647981 , 3DSPIN [M. Radici], grant agreement N. 824093 [C. Mezrag], and the Marie Sklodowska-Curie Action grant agreement N. 752748 , ParDHonS [E. Nocera]; the Universidad Nacional Autónoma de México grant DGAPA-PAPIIT IA101720 [A. Courtoy]; the Scottish Funding Council, United Kingdom grant H14027 [T. Giani]; the Narodowe Centrum Nauki, Poland grant DEC-2017/27/B/ST2/01985 [K. Kutak]; the Kosciuszko Foundation, USA [A. Kusina]; the Research Corporation for Science Advancement, USA through the Cottrell Scholar Award [H. Lin]; the Alexander von Humboldt Foundation, Germany through a Feodor Lynen Research Fellowship [M. Ebert]; and the National Natural Science Foundation of China (Grant No. 11975051 , 12061131006 ) and Fundamental Research Funds for the Central Universities, China [J. Zhang]; the JLab EIC Center, USA through an EIC Center Fellowship [T. Hobbs]; the Wu-Ki Tung, USA endowed chair in particle physics [C. Yuan]; and the LDRD program of Brookhaven National Laboratory, USA [A. Rajan].

Funding Information:
We are grateful to Autumn Hewitt, Nicole Kokx and Brenda Wenzlick, for their help in the organization of the workshop. The workshop was partly supported by Michigan State University, USA and US National Science Foundation via the grant under PHY 1653405 ?CAREER: Constraining Parton Distribution Functions for New-Physics Searches?. We thank Kostas Orginos for his early-stage involvement in organizing the workshop, Alberto Accardi, Jorge Benel, Nikhil Karthik, Zhouyou Fan, Paul Reimer, Dave Soper, Michael Wagman, Zhite Yu for their participation and discussions during the PDFLattice2019 workshop, and Xiangdong Ji for a critical reading of the manuscript. We thank Joseph Karpie and Gunnar Bali for providing numbers for Figs. 7 and 22, respectively, and Phiala Shanahan for remaking Fig. 33 for this paper. We thank H. Moutarde, Ingo Schienbein, P. Sznajder, and Yong Zhao as well as members of the Lattice Hadron Physics Collaboration (LHPC) and the Lattice TMD Collaboration for useful discussion during the preparation of this report. We are pleased to acknowledge support from: the U.S. Department of Energy, grants DE-SC0020405 [M. Constantinou], DE-SC0011090 [M. Ebert], DE-FG02-96ER40965 [M. Engelhardt]; DE-SC0010129 [T. Hobbs, F. Olness, P. Nadolsky], DE-SC0016286 [S. Liuti], DE-AC05-06OR23177 [J.W. Qiu], DE-FG02-97ER41028 [A. Radyushkin], DE-SC0012704 [A. Rajan], DE-SC0018106 [T. C. Rogers], and the DOE Topical Collaboration on TMDs, USA [M. Engelhardt, J.W. Qiu]; Jefferson Science Associates, USA, LLC under U.S. DOE Contract DE-AC05-06OR23177 [J.W. Qiu, A. Radyushkin, T.C. Rogers]; the US National Science Foundation grants PHY-1714407 [M. Constantinou], PHY 1653405 [H. Lin, R. Zhang], PHY-1719914 [C. Yuan]; the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program grant agreement N.647981, 3DSPIN [M. Radici], grant agreement N. 824093 [C. Mezrag], and the Marie Sklodowska-Curie Action grant agreement N. 752748, ParDHonS [E. Nocera]; the Universidad Nacional Aut?noma de M?xico grant DGAPA-PAPIIT IA101720 [A. Courtoy]; the Scottish Funding Council, United Kingdom grant H14027 [T. Giani]; the Narodowe Centrum Nauki, Poland grant DEC-2017/27/B/ST2/01985 [K. Kutak]; the Kosciuszko Foundation, USA [A. Kusina]; the Research Corporation for Science Advancement, USA through the Cottrell Scholar Award [H. Lin]; the Alexander von Humboldt Foundation, Germany through a Feodor Lynen Research Fellowship [M. Ebert]; and the National Natural Science Foundation of China (Grant No. 11975051, 12061131006) and Fundamental Research Funds for the Central Universities, China [J. Zhang]; the JLab EIC Center, USA through an EIC Center Fellowship [T. Hobbs]; the Wu-Ki Tung, USA endowed chair in particle physics [C. Yuan]; and the LDRD program of Brookhaven National Laboratory, USA [A. Rajan].

Publisher Copyright:
© 2021 Elsevier B.V.

Keywords

Generalized Parton Distributions (GPD)
Global QCD fits
Lattice QCD
Transverse Momentum Dependent PDFs (TMD PDFs)
Unpolarized/polarized parton distribution functions (PDFs)

ASJC Scopus subject areas

Nuclear and High Energy Physics

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10.1016/j.ppnp.2021.103908

Cite this

Constantinou, M., Courtoy, A., Ebert, M. A., Engelhardt, M., Giani, T., Hobbs, T., Hou, T. J., Kusina, A., Kutak, K., Liang, J., Lin, H. W., Liu, K. F., Liuti, S., Mezrag, C., Nadolsky, P., Nocera, E. R., Olness, F., Qiu, J. W., Radici, M., ... Zhang, R. (2021). Parton distributions and lattice-QCD calculations: Toward 3D structure. Progress in Particle and Nuclear Physics, 121, Article 103908. https://doi.org/10.1016/j.ppnp.2021.103908

@article{ec35affb7b524f0e8e28c6125c6a5a2a,

title = "Parton distributions and lattice-QCD calculations: Toward 3D structure",

abstract = "The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.",

keywords = "Generalized Parton Distributions (GPD), Global QCD fits, Lattice QCD, Transverse Momentum Dependent PDFs (TMD PDFs), Unpolarized/polarized parton distribution functions (PDFs)",

author = "Martha Constantinou and Aurore Courtoy and Ebert, {Markus A.} and Michael Engelhardt and Tommaso Giani and Tim Hobbs and Hou, {Tie Jiun} and Aleksander Kusina and Krzysztof Kutak and Jian Liang and Lin, {Huey Wen} and Liu, {Keh Fei} and Simonetta Liuti and C{\'e}dric Mezrag and Pavel Nadolsky and Nocera, {Emanuele R.} and Fred Olness and Qiu, {Jian Wei} and Marco Radici and Anatoly Radyushkin and Abha Rajan and Ted Rogers and Juan Rojo and Gerrit Schierholz and Yuan, {C. P.} and Zhang, {Jian Hui} and Rui Zhang",

note = "Funding Information: We are grateful to Autumn Hewitt, Nicole Kokx and Brenda Wenzlick, for their help in the organization of the workshop. The workshop was partly supported by Michigan State University, USA and US National Science Foundation via the grant under PHY 1653405 “CAREER: Constraining Parton Distribution Functions for New-Physics Searches”. We thank Kostas Orginos for his early-stage involvement in organizing the workshop, Alberto Accardi, Jorge Benel, Nikhil Karthik, Zhouyou Fan, Paul Reimer, Dave Soper, Michael Wagman, Zhite Yu for their participation and discussions during the PDFLattice2019 workshop, and Xiangdong Ji for a critical reading of the manuscript. We thank Joseph Karpie and Gunnar Bali for providing numbers for Figs. 7 and 22 , respectively, and Phiala Shanahan for remaking Fig. 33 for this paper. We thank H. Moutarde, Ingo Schienbein, P. Sznajder, and Yong Zhao as well as members of the Lattice Hadron Physics Collaboration (LHPC) and the Lattice TMD Collaboration for useful discussion during the preparation of this report. Funding Information: We are pleased to acknowledge support from: the U.S. Department of Energy , grants DE-SC0020405 [M. Constantinou], DE-SC0011090 [M. Ebert], DE-FG02-96ER40965 [M. Engelhardt]; DE-SC0010129 [T. Hobbs, F. Olness, P. Nadolsky], DE-SC0016286 [S. Liuti], DE-AC05-06OR23177 [J.W. Qiu], DE-FG02-97ER41028 [A. Radyushkin], DE-SC0012704 [A. Rajan], DE-SC0018106 [T. C. Rogers], and the DOE Topical Collaboration on TMDs, USA [M. Engelhardt, J.W. Qiu]; Jefferson Science Associates, USA , LLC under U.S. DOE Contract DE-AC05-06OR23177 [J.W. Qiu, A. Radyushkin, T.C. Rogers]; the US National Science Foundation grants PHY-1714407 [M. Constantinou], PHY 1653405 [H. Lin, R. Zhang], PHY-1719914 [C. Yuan]; the European Research Council (ERC) under the European Union{\textquoteright}s Horizon 2020 research and innovation program grant agreement N.647981 , 3DSPIN [M. Radici], grant agreement N. 824093 [C. Mezrag], and the Marie Sklodowska-Curie Action grant agreement N. 752748 , ParDHonS [E. Nocera]; the Universidad Nacional Aut{\'o}noma de M{\'e}xico grant DGAPA-PAPIIT IA101720 [A. Courtoy]; the Scottish Funding Council, United Kingdom grant H14027 [T. Giani]; the Narodowe Centrum Nauki, Poland grant DEC-2017/27/B/ST2/01985 [K. Kutak]; the Kosciuszko Foundation, USA [A. Kusina]; the Research Corporation for Science Advancement, USA through the Cottrell Scholar Award [H. Lin]; the Alexander von Humboldt Foundation, Germany through a Feodor Lynen Research Fellowship [M. Ebert]; and the National Natural Science Foundation of China (Grant No. 11975051 , 12061131006 ) and Fundamental Research Funds for the Central Universities, China [J. Zhang]; the JLab EIC Center, USA through an EIC Center Fellowship [T. Hobbs]; the Wu-Ki Tung, USA endowed chair in particle physics [C. Yuan]; and the LDRD program of Brookhaven National Laboratory, USA [A. Rajan]. Funding Information: We are grateful to Autumn Hewitt, Nicole Kokx and Brenda Wenzlick, for their help in the organization of the workshop. The workshop was partly supported by Michigan State University, USA and US National Science Foundation via the grant under PHY 1653405 ?CAREER: Constraining Parton Distribution Functions for New-Physics Searches?. We thank Kostas Orginos for his early-stage involvement in organizing the workshop, Alberto Accardi, Jorge Benel, Nikhil Karthik, Zhouyou Fan, Paul Reimer, Dave Soper, Michael Wagman, Zhite Yu for their participation and discussions during the PDFLattice2019 workshop, and Xiangdong Ji for a critical reading of the manuscript. We thank Joseph Karpie and Gunnar Bali for providing numbers for Figs. 7 and 22, respectively, and Phiala Shanahan for remaking Fig. 33 for this paper. We thank H. Moutarde, Ingo Schienbein, P. Sznajder, and Yong Zhao as well as members of the Lattice Hadron Physics Collaboration (LHPC) and the Lattice TMD Collaboration for useful discussion during the preparation of this report. We are pleased to acknowledge support from: the U.S. Department of Energy, grants DE-SC0020405 [M. Constantinou], DE-SC0011090 [M. Ebert], DE-FG02-96ER40965 [M. Engelhardt]; DE-SC0010129 [T. Hobbs, F. Olness, P. Nadolsky], DE-SC0016286 [S. Liuti], DE-AC05-06OR23177 [J.W. Qiu], DE-FG02-97ER41028 [A. Radyushkin], DE-SC0012704 [A. Rajan], DE-SC0018106 [T. C. Rogers], and the DOE Topical Collaboration on TMDs, USA [M. Engelhardt, J.W. Qiu]; Jefferson Science Associates, USA, LLC under U.S. DOE Contract DE-AC05-06OR23177 [J.W. Qiu, A. Radyushkin, T.C. Rogers]; the US National Science Foundation grants PHY-1714407 [M. Constantinou], PHY 1653405 [H. Lin, R. Zhang], PHY-1719914 [C. Yuan]; the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program grant agreement N.647981, 3DSPIN [M. Radici], grant agreement N. 824093 [C. Mezrag], and the Marie Sklodowska-Curie Action grant agreement N. 752748, ParDHonS [E. Nocera]; the Universidad Nacional Aut?noma de M?xico grant DGAPA-PAPIIT IA101720 [A. Courtoy]; the Scottish Funding Council, United Kingdom grant H14027 [T. Giani]; the Narodowe Centrum Nauki, Poland grant DEC-2017/27/B/ST2/01985 [K. Kutak]; the Kosciuszko Foundation, USA [A. Kusina]; the Research Corporation for Science Advancement, USA through the Cottrell Scholar Award [H. Lin]; the Alexander von Humboldt Foundation, Germany through a Feodor Lynen Research Fellowship [M. Ebert]; and the National Natural Science Foundation of China (Grant No. 11975051, 12061131006) and Fundamental Research Funds for the Central Universities, China [J. Zhang]; the JLab EIC Center, USA through an EIC Center Fellowship [T. Hobbs]; the Wu-Ki Tung, USA endowed chair in particle physics [C. Yuan]; and the LDRD program of Brookhaven National Laboratory, USA [A. Rajan]. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

year = "2021",

month = nov,

doi = "10.1016/j.ppnp.2021.103908",

language = "English",

volume = "121",

}

Constantinou, M, Courtoy, A, Ebert, MA, Engelhardt, M, Giani, T, Hobbs, T, Hou, TJ, Kusina, A, Kutak, K, Liang, J, Lin, HW, Liu, KF, Liuti, S, Mezrag, C, Nadolsky, P, Nocera, ER, Olness, F, Qiu, JW, Radici, M, Radyushkin, A, Rajan, A, Rogers, T, Rojo, J, Schierholz, G, Yuan, CP, Zhang, JH & Zhang, R 2021, 'Parton distributions and lattice-QCD calculations: Toward 3D structure', Progress in Particle and Nuclear Physics, vol. 121, 103908. https://doi.org/10.1016/j.ppnp.2021.103908

TY - JOUR

T1 - Parton distributions and lattice-QCD calculations

T2 - Toward 3D structure

AU - Constantinou, Martha

AU - Courtoy, Aurore

AU - Ebert, Markus A.

AU - Engelhardt, Michael

AU - Giani, Tommaso

AU - Hobbs, Tim

AU - Hou, Tie Jiun

AU - Kusina, Aleksander

AU - Kutak, Krzysztof

AU - Liang, Jian

AU - Lin, Huey Wen

AU - Liu, Keh Fei

AU - Liuti, Simonetta

AU - Mezrag, Cédric

AU - Nadolsky, Pavel

AU - Nocera, Emanuele R.

AU - Olness, Fred

AU - Qiu, Jian Wei

AU - Radici, Marco

AU - Radyushkin, Anatoly

AU - Rajan, Abha

AU - Rogers, Ted

AU - Rojo, Juan

AU - Schierholz, Gerrit

AU - Yuan, C. P.

AU - Zhang, Jian Hui

AU - Zhang, Rui

N1 - Funding Information: We are grateful to Autumn Hewitt, Nicole Kokx and Brenda Wenzlick, for their help in the organization of the workshop. The workshop was partly supported by Michigan State University, USA and US National Science Foundation via the grant under PHY 1653405 “CAREER: Constraining Parton Distribution Functions for New-Physics Searches”. We thank Kostas Orginos for his early-stage involvement in organizing the workshop, Alberto Accardi, Jorge Benel, Nikhil Karthik, Zhouyou Fan, Paul Reimer, Dave Soper, Michael Wagman, Zhite Yu for their participation and discussions during the PDFLattice2019 workshop, and Xiangdong Ji for a critical reading of the manuscript. We thank Joseph Karpie and Gunnar Bali for providing numbers for Figs. 7 and 22 , respectively, and Phiala Shanahan for remaking Fig. 33 for this paper. We thank H. Moutarde, Ingo Schienbein, P. Sznajder, and Yong Zhao as well as members of the Lattice Hadron Physics Collaboration (LHPC) and the Lattice TMD Collaboration for useful discussion during the preparation of this report. Funding Information: We are pleased to acknowledge support from: the U.S. Department of Energy , grants DE-SC0020405 [M. Constantinou], DE-SC0011090 [M. Ebert], DE-FG02-96ER40965 [M. Engelhardt]; DE-SC0010129 [T. Hobbs, F. Olness, P. Nadolsky], DE-SC0016286 [S. Liuti], DE-AC05-06OR23177 [J.W. Qiu], DE-FG02-97ER41028 [A. Radyushkin], DE-SC0012704 [A. Rajan], DE-SC0018106 [T. C. Rogers], and the DOE Topical Collaboration on TMDs, USA [M. Engelhardt, J.W. Qiu]; Jefferson Science Associates, USA , LLC under U.S. DOE Contract DE-AC05-06OR23177 [J.W. Qiu, A. Radyushkin, T.C. Rogers]; the US National Science Foundation grants PHY-1714407 [M. Constantinou], PHY 1653405 [H. Lin, R. Zhang], PHY-1719914 [C. Yuan]; the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program grant agreement N.647981 , 3DSPIN [M. Radici], grant agreement N. 824093 [C. Mezrag], and the Marie Sklodowska-Curie Action grant agreement N. 752748 , ParDHonS [E. Nocera]; the Universidad Nacional Autónoma de México grant DGAPA-PAPIIT IA101720 [A. Courtoy]; the Scottish Funding Council, United Kingdom grant H14027 [T. Giani]; the Narodowe Centrum Nauki, Poland grant DEC-2017/27/B/ST2/01985 [K. Kutak]; the Kosciuszko Foundation, USA [A. Kusina]; the Research Corporation for Science Advancement, USA through the Cottrell Scholar Award [H. Lin]; the Alexander von Humboldt Foundation, Germany through a Feodor Lynen Research Fellowship [M. Ebert]; and the National Natural Science Foundation of China (Grant No. 11975051 , 12061131006 ) and Fundamental Research Funds for the Central Universities, China [J. Zhang]; the JLab EIC Center, USA through an EIC Center Fellowship [T. Hobbs]; the Wu-Ki Tung, USA endowed chair in particle physics [C. Yuan]; and the LDRD program of Brookhaven National Laboratory, USA [A. Rajan]. Funding Information: We are grateful to Autumn Hewitt, Nicole Kokx and Brenda Wenzlick, for their help in the organization of the workshop. The workshop was partly supported by Michigan State University, USA and US National Science Foundation via the grant under PHY 1653405 ?CAREER: Constraining Parton Distribution Functions for New-Physics Searches?. We thank Kostas Orginos for his early-stage involvement in organizing the workshop, Alberto Accardi, Jorge Benel, Nikhil Karthik, Zhouyou Fan, Paul Reimer, Dave Soper, Michael Wagman, Zhite Yu for their participation and discussions during the PDFLattice2019 workshop, and Xiangdong Ji for a critical reading of the manuscript. We thank Joseph Karpie and Gunnar Bali for providing numbers for Figs. 7 and 22, respectively, and Phiala Shanahan for remaking Fig. 33 for this paper. We thank H. Moutarde, Ingo Schienbein, P. Sznajder, and Yong Zhao as well as members of the Lattice Hadron Physics Collaboration (LHPC) and the Lattice TMD Collaboration for useful discussion during the preparation of this report. We are pleased to acknowledge support from: the U.S. Department of Energy, grants DE-SC0020405 [M. Constantinou], DE-SC0011090 [M. Ebert], DE-FG02-96ER40965 [M. Engelhardt]; DE-SC0010129 [T. Hobbs, F. Olness, P. Nadolsky], DE-SC0016286 [S. Liuti], DE-AC05-06OR23177 [J.W. Qiu], DE-FG02-97ER41028 [A. Radyushkin], DE-SC0012704 [A. Rajan], DE-SC0018106 [T. C. Rogers], and the DOE Topical Collaboration on TMDs, USA [M. Engelhardt, J.W. Qiu]; Jefferson Science Associates, USA, LLC under U.S. DOE Contract DE-AC05-06OR23177 [J.W. Qiu, A. Radyushkin, T.C. Rogers]; the US National Science Foundation grants PHY-1714407 [M. Constantinou], PHY 1653405 [H. Lin, R. Zhang], PHY-1719914 [C. Yuan]; the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program grant agreement N.647981, 3DSPIN [M. Radici], grant agreement N. 824093 [C. Mezrag], and the Marie Sklodowska-Curie Action grant agreement N. 752748, ParDHonS [E. Nocera]; the Universidad Nacional Aut?noma de M?xico grant DGAPA-PAPIIT IA101720 [A. Courtoy]; the Scottish Funding Council, United Kingdom grant H14027 [T. Giani]; the Narodowe Centrum Nauki, Poland grant DEC-2017/27/B/ST2/01985 [K. Kutak]; the Kosciuszko Foundation, USA [A. Kusina]; the Research Corporation for Science Advancement, USA through the Cottrell Scholar Award [H. Lin]; the Alexander von Humboldt Foundation, Germany through a Feodor Lynen Research Fellowship [M. Ebert]; and the National Natural Science Foundation of China (Grant No. 11975051, 12061131006) and Fundamental Research Funds for the Central Universities, China [J. Zhang]; the JLab EIC Center, USA through an EIC Center Fellowship [T. Hobbs]; the Wu-Ki Tung, USA endowed chair in particle physics [C. Yuan]; and the LDRD program of Brookhaven National Laboratory, USA [A. Rajan]. Publisher Copyright: © 2021 Elsevier B.V.

PY - 2021/11

Y1 - 2021/11

N2 - The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.

AB - The strong force which binds hadrons is described by the theory of quantum chromodynamics (QCD). Determining the character and manifestations of QCD is one of the most important and challenging outstanding issues necessary for a comprehensive understanding of the structure of hadrons. Within the context of the QCD parton picture, the parton distribution functions (PDFs) have been remarkably successful in describing a wide variety of processes. However, these PDFs have generally been confined to the description of collinear partons within the hadron. New experiments and facilities provide the opportunity to additionally explore the transverse structure of hadrons which is described by generalized parton distributions (GPDs) and transverse-momentum-dependent parton distribution functions (TMD PDFs). In our previous report Lin et al. (2018), we compared and contrasted the two main approaches used to determine the collinear PDFs: the first based on perturbative QCD factorization theorems, and the second based on lattice-QCD calculations. In the present report, we provide an update of recent progress on the collinear PDFs, and also expand the scope to encompass the generalized PDFs (GPDs and TMD PDFs). We review the current state of the various calculations, and consider what new data might be available in the near future. We also examine how a shared effort can foster dialog between the PDF and lattice-QCD communities, and yield improvements for these generalized PDFs.

KW - Generalized Parton Distributions (GPD)

KW - Global QCD fits

KW - Lattice QCD

KW - Transverse Momentum Dependent PDFs (TMD PDFs)

KW - Unpolarized/polarized parton distribution functions (PDFs)

UR - http://www.scopus.com/inward/record.url?scp=85114514615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85114514615&partnerID=8YFLogxK

U2 - 10.1016/j.ppnp.2021.103908

DO - 10.1016/j.ppnp.2021.103908

M3 - Review article

AN - SCOPUS:85114514615

SN - 0146-6410

VL - 121

JO - Progress in Particle and Nuclear Physics

JF - Progress in Particle and Nuclear Physics

M1 - 103908

ER -

Parton distributions and lattice-QCD calculations: Toward 3D structure

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