Parton distributions and lattice QCD calculations: A community white paper

Lin, Huey-Wen; Nocera, Emanuele R.; Olness, Fred; Orginos, Kostas; Rojo, Juan; Accardi, Alberto; Alexandrou, Constantia; Bacchetta, Alessandro; Bozzi, Giuseppe; Chen, Jiunn-Wei; Collins, Sara; Cooper-Sarkar, Amanda; Constantinou, Martha; Del Debbio, Luigi; Engelhardt, Michael; Green, Jeremy; Gupta, Rajan; Harland-Lang, Lucian A.; Ishikawa, Tomomi; Kusina, Aleksander; Liu, Keh-Fei; Liuti, Simonetta; Monahan, Christopher; Nadolsky, Pavel; Qiu, Jian-Wei; Schienbein, Ingo; Schierholz, Gerrit; Thorne, Robert S.; Vogelsang, Werner; Wittig, Hartmut; Yuan, C. -P.; Zanotti, James

doi:10.1016/j.ppnp.2018.01.007

Title: Parton distributions and lattice QCD calculations: A community white paper

Abstract

In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this paper we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. Finally, this document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.

Authors:

Lin, Huey-Wen ^[1]; Nocera, Emanuele R. ^[2]; Olness, Fred ^[3]; Orginos, Kostas ^[4]; Rojo, Juan ^[5]; Accardi, Alberto ^[6]; Alexandrou, Constantia ^[7]; Bacchetta, Alessandro ^[8]; Bozzi, Giuseppe ^[8]; Chen, Jiunn-Wei ^[9]; Collins, Sara ^[10]; Cooper-Sarkar, Amanda ^[11]; Constantinou, Martha ^[12]; Del Debbio, Luigi ^[13]; Engelhardt, Michael ^[14]; Green, Jeremy ^[15]; Gupta, Rajan ^[16]; Harland-Lang, Lucian A. ^[17]; Ishikawa, Tomomi ^[18]; Kusina, Aleksander ^[19] more »

Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy. Dept. of Computational Mathematics
Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics; Univ. of Edinburgh, Scotland (United Kingdom). Higgs Centre for Theoretical Physics. School of Physics and Astronomy
Southern Methodist Univ., Dallas, TX (United States). Dept. of Physics
College of William and Mary, Williamsburg, VA (United States). Physics Dept.; Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Vrije Univ. (VU), Amsterdam (Netherlands). Dept. of Physics and Astronomy; Nikhef, Amsterdam (Netherlands)
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Hampton Univ., Hampton, VA (United States)
Univ. of Cyprus, Nicosia (Cyprus). Dept. of Physics; The Cyprus Inst., Nicosia (Cyprus). Computation-based Science and Technology Research
Univ. of Pavia (Italy). Dept. of Physics; National Inst. of Nuclear Physics (INFN), Pavia (Italy)
National Taiwan Univ., Taipei (Taiwan). Dept. of Physics. Center for Theoretical Sciences. Leung Center for Cosmology and Particle Astrophysics
Univ. of Regensburg (Germany). Inst. for Theoretical Physics
Univ. of Oxford (United Kingdom). Dept. of Physics
Temple Univ., Philadelphia, PA (United States). Dept. of Physics
Univ. of Edinburgh, Scotland (United Kingdom). Higgs Centre for Theoretical Physics. School of Physics and Astronomy
New Mexico State Univ., Las Cruces, NM (United States). Dept. of Physics
Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. for Computing (NIC)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Oxford (United Kingdom). Rudolf Peierls Centre for Theoretical Physics; Univ. College London (United Kingdom). Dept. of Physics and Astronomy
Shanghai Jiao Tong Univ. (China). T. D. Lee Inst.
Polish Academy of Sciences, Krakow (Poland). Inst. of Nuclear Physics
Univ. of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
Univ. of Virginia, Charlottesville, VA (United States). Physics Dept.; National Inst. of Nuclear Physics (INFN), Frascati (Italy). National Lab. of Frascati
Univ. of Washington, Seattle, WA (United States). Inst. for Nuclear Theory
Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Univ. Grenoble-Alpes, Grenoble (France). Lab. of Subatomic Physics and Cosmology
Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
Univ. College London (United Kingdom). Dept. of Physics and Astronomy
Tubingen Univ. (Germany). Inst. for Theoretical Physics
Johannes Gutenberg Univ., Mainz (Germany). PRISMA Cluster of Excellence. Inst. for Nuclear Physics
Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy
Univ. of Adelaide, SA (Australia). Special Research Centre for the Subatomic Structure of Matter (CSSM). Dept. of Physics

Publication Date:: Wed Jan 31 00:00:00 EST 2018

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Univ. of Washington, Seattle, WA (United States); College of William and Mary, Williamsburg, VA (United States); Southern Methodist Univ., Dallas, TX (United States); Hampton Univ., Hampton, VA (United States); New Mexico State Univ., Las Cruces, NM (United States); Univ. of Virginia, Charlottesville, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE Office of Science (SC), High Energy Physics (HEP); BNL Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 1433816

Alternate Identifier(s):: OSTI ID: 1548771

Report Number(s):: JLAB-THY-17-2604; DOE/OR/23177-4281; arXiv:1711.07916
Journal ID: ISSN 0146-6410; PII: S0146641018300073; TRN: US1802667

Grant/Contract Number:: AC05-06OR23177; FG02-00ER41132; FG02-04ER41302; SC0010129; SC0008791; FG02-96ER40965; SC0016286; SC008791; KA-1401020

Resource Type:: Accepted Manuscript

Journal Name:: Progress in Particle and Nuclear Physics

Additional Journal Information:: Journal Volume: 100; Journal ID: ISSN 0146-6410

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; lattice QCD; global QCD fits; unpolarized/polarized parton distribution functions (PDFs)

Citation Formats


                    Lin, Huey-Wen, Nocera, Emanuele R., Olness, Fred, Orginos, Kostas, Rojo, Juan, Accardi, Alberto, Alexandrou, Constantia, Bacchetta, Alessandro, Bozzi, Giuseppe, Chen, Jiunn-Wei, Collins, Sara, Cooper-Sarkar, Amanda, Constantinou, Martha, Del Debbio, Luigi, Engelhardt, Michael, Green, Jeremy, Gupta, Rajan, Harland-Lang, Lucian A., Ishikawa, Tomomi, Kusina, Aleksander, Liu, Keh-Fei, Liuti, Simonetta, Monahan, Christopher, Nadolsky, Pavel, Qiu, Jian-Wei, Schienbein, Ingo, Schierholz, Gerrit, Thorne, Robert S., Vogelsang, Werner, Wittig, Hartmut, Yuan, C. -P., and Zanotti, James. Parton distributions and lattice QCD calculations: A community white paper.  United States: N. p., 2018. 
Web.  doi:10.1016/j.ppnp.2018.01.007.

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                    Lin, Huey-Wen, Nocera, Emanuele R., Olness, Fred, Orginos, Kostas, Rojo, Juan, Accardi, Alberto, Alexandrou, Constantia, Bacchetta, Alessandro, Bozzi, Giuseppe, Chen, Jiunn-Wei, Collins, Sara, Cooper-Sarkar, Amanda, Constantinou, Martha, Del Debbio, Luigi, Engelhardt, Michael, Green, Jeremy, Gupta, Rajan, Harland-Lang, Lucian A., Ishikawa, Tomomi, Kusina, Aleksander, Liu, Keh-Fei, Liuti, Simonetta, Monahan, Christopher, Nadolsky, Pavel, Qiu, Jian-Wei, Schienbein, Ingo, Schierholz, Gerrit, Thorne, Robert S., Vogelsang, Werner, Wittig, Hartmut, Yuan, C. -P., & Zanotti, James. Parton distributions and lattice QCD calculations: A community white paper.  United States.  https://doi.org/10.1016/j.ppnp.2018.01.007

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                    Lin, Huey-Wen, Nocera, Emanuele R., Olness, Fred, Orginos, Kostas, Rojo, Juan, Accardi, Alberto, Alexandrou, Constantia, Bacchetta, Alessandro, Bozzi, Giuseppe, Chen, Jiunn-Wei, Collins, Sara, Cooper-Sarkar, Amanda, Constantinou, Martha, Del Debbio, Luigi, Engelhardt, Michael, Green, Jeremy, Gupta, Rajan, Harland-Lang, Lucian A., Ishikawa, Tomomi, Kusina, Aleksander, Liu, Keh-Fei, Liuti, Simonetta, Monahan, Christopher, Nadolsky, Pavel, Qiu, Jian-Wei, Schienbein, Ingo, Schierholz, Gerrit, Thorne, Robert S., Vogelsang, Werner, Wittig, Hartmut, Yuan, C. -P., and Zanotti, James. Wed .  
"Parton distributions and lattice QCD calculations: A community white paper".  United States.  https://doi.org/10.1016/j.ppnp.2018.01.007.  https://www.osti.gov/servlets/purl/1433816.

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@article{osti_1433816,

  title        = {Parton distributions and lattice QCD calculations: A community white paper},

  author       = {Lin, Huey-Wen and Nocera, Emanuele R. and Olness, Fred and Orginos, Kostas and Rojo, Juan and Accardi, Alberto and Alexandrou, Constantia and Bacchetta, Alessandro and Bozzi, Giuseppe and Chen, Jiunn-Wei and Collins, Sara and Cooper-Sarkar, Amanda and Constantinou, Martha and Del Debbio, Luigi and Engelhardt, Michael and Green, Jeremy and Gupta, Rajan and Harland-Lang, Lucian A. and Ishikawa, Tomomi and Kusina, Aleksander and Liu, Keh-Fei and Liuti, Simonetta and Monahan, Christopher and Nadolsky, Pavel and Qiu, Jian-Wei and Schienbein, Ingo and Schierholz, Gerrit and Thorne, Robert S. and Vogelsang, Werner and Wittig, Hartmut and Yuan, C. -P. and Zanotti, James},

  abstractNote = {In the framework of quantum chromodynamics (QCD), parton distribution functions (PDFs) quantify how the momentum and spin of a hadron are divided among its quark and gluon constituents. Two main approaches exist to determine PDFs. The first approach, based on QCD factorization theorems, realizes a QCD analysis of a suitable set of hard-scattering measurements, often using a variety of hadronic observables. The second approach, based on first-principle operator definitions of PDFs, uses lattice QCD to compute directly some PDF-related quantities, such as their moments. Motivated by recent progress in both approaches, in this paper we present an overview of lattice-QCD and global-analysis techniques used to determine unpolarized and polarized proton PDFs and their moments. We provide benchmark numbers to validate present and future lattice-QCD calculations and we illustrate how they could be used to reduce the PDF uncertainties in current unpolarized and polarized global analyses. Finally, this document represents a first step towards establishing a common language between the two communities, to foster dialogue and to further improve our knowledge of PDFs.},

  doi          = {10.1016/j.ppnp.2018.01.007},

  journal      = {Progress in Particle and Nuclear Physics},

  number       = ,

  volume       = 100,

  place        = {United States},

  year         = {Wed Jan 31 00:00:00 EST 2018},

  month        = {Wed Jan 31 00:00:00 EST 2018}

}

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The European Physical Journal C, Vol. 80, Issue 2
DOI: 10.1140/epjc/s10052-019-7354-7

Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass
text, January 2020

Alexandrou, C.; Bacchio, S.; Constantinou, M.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-02369

The spin structure of the nucleon
journal, January 1994

Bass, S. D.; Thomas, A. W.
Progress in Particle and Nuclear Physics, Vol. 33
DOI: 10.1016/0146-6410(94)90048-5

Light-Cone Parton Distribution Functions from Lattice QCD
text, January 2018

Alexandrou, Constantia; Cichy, Krzysztof; Constantinou, Martha
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2018-03714

Measurement of the longitudinal spin asymmetries for weak boson production in proton-proton collisions at s =510 GeV
text, January 2019

Unknown, (:Unkn)
My University
DOI: 10.34944/dspace/4323

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
text, January 2018

Bali, Gunnar S.; Braun, Vladimir M.; Gläßle, Benjamin
Universität Regensburg
DOI: 10.5283/epub.38344

FLAG Review 2019
text, January 2020

Aoki, S.; Aoki, Y.; Bečirević, D.
Springer
DOI: 10.7892/boris.141201

Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass
text, January 2020

Alexandrou, C.; Bacchio, S.; Constantinou, M.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-01424

FLAG Review 2019
text, January 2020

Aoki, S.; Aoki, Y.; Becirevic, D.
Deutsches Elektronen-Synchrotron, DESY, Hamburg
DOI: 10.3204/pubdb-2020-04064

The Spin Structure of the Nucleon: Proceeding of International School of Nucleon Structure: 1st Course
conference, April 2017

Frois, B.; Hughes, V. W.; de Groot, N.
International School of Nucleon Structure, The Spin Structure of the Nucleon
DOI: 10.1142/9789814529051

Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions
text, January 2018

Izubuchi, Taku; Ji, Xiangdong; Jin, Luchang
arXiv
DOI: 10.48550/arxiv.1801.03917

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation
text, January 2018

Salajegheh, Maral; Nejad, S. Mohammad Moosavi; Khanpour, Hamzeh
arXiv
DOI: 10.48550/arxiv.1801.04471

Finite-volume effects due to spatially non-local operators
text, January 2018

Briceño, Raúl A.; Guerrero, Juan V.; Hansen, Maxwell T.
arXiv
DOI: 10.48550/arxiv.1805.01034

Renormalization of Wilson-line operators in the presence of nonzero quark masses
text, January 2018

Spanoudes, G.; Panagopoulos, H.
arXiv
DOI: 10.48550/arxiv.1805.01164

First global QCD analysis of charged hadron fragmentation functions and their uncertainties at next-to-next-to-leading order
text, January 2018

Soleymaninia, Maryam; Goharipour, Muhammad; Khanpour, Hamzeh
arXiv
DOI: 10.48550/arxiv.1805.04847

A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics
text, January 2018

Chang, Chia Cheng; Nicholson, Amy; Rinaldi, Enrico
arXiv
DOI: 10.48550/arxiv.1805.12130

Pion distribution amplitude from Euclidean correlation functions: Exploring universality and higher-twist effects
text, January 2018

Bali, Gunnar S.; Braun, Vladimir M.; Gläßle, Benjamin
arXiv
DOI: 10.48550/arxiv.1807.06671

Proton Mass Decomposition from the QCD Energy Momentum Tensor
text, January 2018

Yang, Yi-Bo; Liang, Jian; Bi, Yu-Jiang
arXiv
DOI: 10.48550/arxiv.1808.08677

Nonperturbative strange-quark sea from lattice QCD, light-front holography, and meson-baryon fluctuation models
text, January 2018

Sufian, Raza Sabbir; Liu, Tianbo; de Téramond, Guy F.
arXiv
DOI: 10.48550/arxiv.1809.04975

A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
text, January 2018

Cichy, Krzysztof; Constantinou, Martha
arXiv
DOI: 10.48550/arxiv.1811.07248

The Spin Budget of the Proton at NNLO and Beyond
text, January 2019

de Florian, Daniel; Vogelsang, Werner
arXiv
DOI: 10.48550/arxiv.1902.04636

Non-quadratic improved Hessian PDF reweighting and application to CMS dijet measurements at 5.02 TeV
text, January 2019

Eskola, Kari J.; Paakkinen, Petja; Paukkunen, Hannu
arXiv
DOI: 10.48550/arxiv.1903.09832

Nuclear gluons at RHIC in a multi-observable approach
text, January 2019

Helenius, Ilkka; Lajoie, John; Osborn, Joseph D.
arXiv
DOI: 10.48550/arxiv.1904.09921

Lattice QCD and Neutrino-Nucleus Scattering
text, January 2019

Kronfeld, Andreas S.; Richards, David G.; Detmold, William
arXiv
DOI: 10.48550/arxiv.1904.09931

Parton Distribution Functions from Ioffe time pseudo-distributions
text, January 2019

Joó, Bálint; Karpie, Joseph; Orginos, Kostas
arXiv
DOI: 10.48550/arxiv.1908.09771

Role of higher twist effects in diffractive DIS and determination of diffractive parton distribution functions
text, January 2019

Maktoubian, Atefeh; Mehraban, Hossein; Khanpour, Hamzeh
arXiv
DOI: 10.48550/arxiv.1908.10154

Moments of nucleon generalized parton distributions from lattice QCD simulations at physical pion mass
text, January 2019

Alexandrou, C.; Bacchio, S.; Constantinou, M.
arXiv
DOI: 10.48550/arxiv.1908.10706

A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics
text, January 2018

Chang, Chia Cheng; Nicholson, Amy; Rinaldi, Enrico
arXiv
DOI: 10.48550/arxiv.1805.12130

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Title: Parton distributions and lattice QCD calculations: A community white paper

Abstract

Citation Formats

The asymptotic behaviour of parton distributions at small and large x journal, July 2016

Small- and large- x nucleon spin structure from a global QCD analysis of polarized parton distribution functions journal, March 2015

The quark and gluon structure of the proton journal, March 2013

Structure functions journal, October 2011

Parton distribution benchmarking with LHC data journal, April 2013

Progress in the Determination of the Partonic Structure of the Proton journal, October 2013

Parton momentum and helicity distributions in the nucleon journal, August 2013

The PDF4LHC report on PDFs and LHC data: results from Run I and preparation for Run II journal, September 2015

PDF4LHC recommendations for LHC Run II journal, January 2016

A critical appraisal and evaluation of modern PDFs journal, August 2016

The structure of the proton in the LHC precision era journal, May 2018

Parton distributions from high-precision collider data: NNPDF Collaboration journal, October 2017

Parton distributions in the LHC era: MMHT 2014 PDFs journal, May 2015

New parton distribution functions from a global analysis of quantum chromodynamics journal, February 2016

Parton distribution functions, α s , and heavy-quark masses for LHC Run II journal, July 2017

Constraints on large- x parton distributions from new weak boson production and deep-inelastic scattering data journal, June 2016

A first unbiased global determination of polarized PDFs and their uncertainties journal, October 2014

Extraction of spin-dependent parton densities and their uncertainties journal, August 2009

Iterative Monte Carlo analysis of spin-dependent parton distributions journal, April 2016

Determination of gluon polarization from deep inelastic scattering and collider data journal, May 2009

Combination of measurements of inclusive deep inelastic $${e^{\pm }p}$$ e ± p scattering cross sections and QCD analysis of HERA data: H1 and ZEUS Collaborations journal, December 2015

Impact of heavy-flavour production cross sections measured by the LHCb experiment on parton distribution functions at low x: PROSA Collaboration journal, August 2015

The impact of the LHC Z-boson transverse momentum data on PDF determinations journal, July 2017

Next-to-Next-to Leading Order QCD Predictions for Single Jet Inclusive Production at the LHC journal, February 2017

Pinning down the large-x gluon with NNLO top-quark pair differential distributions journal, April 2017

Evidence for Polarization of Gluons in the Proton journal, July 2014

Review of Particle Physics journal, October 2016

Flavor structure of the nucleon sea from lattice QCD journal, March 2015

Lattice calculation of parton distributions journal, July 2015

Nucleon helicity and transversity parton distributions from lattice QCD journal, October 2016

Updated lattice results for parton distributions journal, July 2017

Asymptotically Free Gauge Theories. I journal, November 1973

Ultraviolet Behavior of Non-Abelian Gauge Theories journal, June 1973

Asymptotically free gauge theories. II journal, February 1974

Asymptotic freedom: An approach to strong interactions journal, November 1974

The Theorems of Perturbative QCD journal, December 1987

Factorization Of Hard Processes In QCD book, July 1989

Hard interactions of quarks and gluons: a primer for LHC physics journal, December 2006

Chiral perturbation theory to one loop journal, November 1984

The angular momentum controversy: What’s it all about and does it matter? journal, August 2014

Dimensional regularization and the renormalization group journal, September 1973

New Approach to the Renormalization Group journal, November 1973

Polarized deep inelastic scattering at high energies and parity violating structure functions journal, June 1994

Polarized deep inelastic scattering and the parton model journal, October 1992

Parton distribution and decay functions journal, January 1982

Evolution of parton densities beyond leading order journal, November 1980

Parton model interpretation of the cut vertex formalism journal, April 1980

Asymptotic freedom in parton language journal, August 1977

The three-loop splitting functions in QCD: the non-singlet case journal, June 2004

The three-loop splitting functions in QCD: the singlet case journal, July 2004

Large- n f contributions to the four-loop splitting functions in QCD journal, February 2017

Four-loop non-singlet splitting functions in the planar limit and beyond journal, October 2017

The three-loop splitting functions in QCD: The helicity-dependent case journal, December 2014

Efficient evolution of unpolarized and polarized parton distributions with QCD-Pegasus journal, July 2005

A Higher Order Perturbative Parton Evolution Toolkit (HOPPET) journal, January 2009

QCDNUM: Fast QCD evolution and convolution journal, February 2011

APFEL: A PDF evolution library with QED corrections journal, June 2014

Reference results for time-like evolution up to O α s 3 $$ \mathcal{O}\left({\alpha}_s^3\right) $$ journal, March 2015

Pre-Town Meeting on spin physics at an Electron-Ion Collider journal, April 2017

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG) journal, February 2017

Confinement, chiral symmetry, and the lattice journal, February 2011

An introduction to chiral symmetry on the lattice journal, October 2004

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states journal, June 1986

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states journal, June 1986

A general method for non-perturbative renormalization of lattice operators journal, July 1995

Lattice operators for moments of the structure functions and their transformation under the hypercubic group journal, November 1996

A lattice determination of moments of unpolarized nucleon structure functions using improved Wilson fermions journal, June 2005

Properties and uses of the Wilson flow in lattice QCD journal, August 2010

High-precision scale setting in lattice QCD journal, September 2012

Ab Initio Determination of Light Hadron Masses journal, November 2008

Extraction of Parton Distributions from Lattice qcd journal, December 2003

Normal products and the short distance expansion in the perturbation theory of renormalizable interactions journal, May 1973

Polarized and unpolarized nucleon structure functions from lattice QCD journal, March 1996

On the difficulty of computing higher-twist corrections journal, November 1996

Restoration of rotational symmetry in the continuum limit of lattice field theories journal, September 2012

Locally smeared operator product expansions in scalar field theory journal, April 2015

Deep-inelastic scattering and the operator product expansion in lattice QCD journal, January 2006

The asymptotic behaviour of parton distributions at small and large x
journal, July 2016

Small- and large- x nucleon spin structure from a global QCD analysis of polarized parton distribution functions
journal, March 2015

The quark and gluon structure of the proton
journal, March 2013

Structure functions
journal, October 2011

Parton distribution benchmarking with LHC data
journal, April 2013

Progress in the Determination of the Partonic Structure of the Proton
journal, October 2013

Parton momentum and helicity distributions in the nucleon
journal, August 2013

The PDF4LHC report on PDFs and LHC data: results from Run I and preparation for Run II
journal, September 2015

PDF4LHC recommendations for LHC Run II
journal, January 2016

A critical appraisal and evaluation of modern PDFs
journal, August 2016

The structure of the proton in the LHC precision era
journal, May 2018

Parton distributions from high-precision collider data: NNPDF Collaboration
journal, October 2017

Parton distributions in the LHC era: MMHT 2014 PDFs
journal, May 2015

New parton distribution functions from a global analysis of quantum chromodynamics
journal, February 2016

Parton distribution functions, $α_{s}$ , and heavy-quark masses for LHC Run II
journal, July 2017

Constraints on large- $x$ parton distributions from new weak boson production and deep-inelastic scattering data
journal, June 2016

A first unbiased global determination of polarized PDFs and their uncertainties
journal, October 2014

Extraction of spin-dependent parton densities and their uncertainties
journal, August 2009

Iterative Monte Carlo analysis of spin-dependent parton distributions
journal, April 2016

Determination of gluon polarization from deep inelastic scattering and collider data
journal, May 2009

Combination of measurements of inclusive deep inelastic $${e^{\pm }p}$$ e ± p scattering cross sections and QCD analysis of HERA data: H1 and ZEUS Collaborations
journal, December 2015

Impact of heavy-flavour production cross sections measured by the LHCb experiment on parton distribution functions at low x: PROSA Collaboration
journal, August 2015

The impact of the LHC Z-boson transverse momentum data on PDF determinations
journal, July 2017

Next-to-Next-to Leading Order QCD Predictions for Single Jet Inclusive Production at the LHC
journal, February 2017

Pinning down the large-x gluon with NNLO top-quark pair differential distributions
journal, April 2017

Evidence for Polarization of Gluons in the Proton
journal, July 2014

Review of Particle Physics
journal, October 2016

Flavor structure of the nucleon sea from lattice QCD
journal, March 2015

Lattice calculation of parton distributions
journal, July 2015

Nucleon helicity and transversity parton distributions from lattice QCD
journal, October 2016

Updated lattice results for parton distributions
journal, July 2017

Asymptotically Free Gauge Theories. I
journal, November 1973

Ultraviolet Behavior of Non-Abelian Gauge Theories
journal, June 1973

Asymptotically free gauge theories. II
journal, February 1974

Asymptotic freedom: An approach to strong interactions
journal, November 1974

The Theorems of Perturbative QCD
journal, December 1987

Factorization Of Hard Processes In QCD
book, July 1989

Hard interactions of quarks and gluons: a primer for LHC physics
journal, December 2006

Chiral perturbation theory to one loop
journal, November 1984

The angular momentum controversy: What’s it all about and does it matter?
journal, August 2014

Dimensional regularization and the renormalization group
journal, September 1973

New Approach to the Renormalization Group
journal, November 1973

Polarized deep inelastic scattering at high energies and parity violating structure functions
journal, June 1994

Polarized deep inelastic scattering and the parton model
journal, October 1992

Parton distribution and decay functions
journal, January 1982

Evolution of parton densities beyond leading order
journal, November 1980

Parton model interpretation of the cut vertex formalism
journal, April 1980

Asymptotic freedom in parton language
journal, August 1977

The three-loop splitting functions in QCD: the non-singlet case
journal, June 2004

The three-loop splitting functions in QCD: the singlet case
journal, July 2004

Large- n f contributions to the four-loop splitting functions in QCD
journal, February 2017

Four-loop non-singlet splitting functions in the planar limit and beyond
journal, October 2017

The three-loop splitting functions in QCD: The helicity-dependent case
journal, December 2014

Efficient evolution of unpolarized and polarized parton distributions with QCD-Pegasus
journal, July 2005

A Higher Order Perturbative Parton Evolution Toolkit (HOPPET)
journal, January 2009

QCDNUM: Fast QCD evolution and convolution
journal, February 2011

APFEL: A PDF evolution library with QED corrections
journal, June 2014

Reference results for time-like evolution up to O α s 3 $$ \mathcal{O}\left({\alpha}_s^3\right) $$
journal, March 2015

Pre-Town Meeting on spin physics at an Electron-Ion Collider
journal, April 2017

Review of lattice results concerning low-energy particle physics: Flavour Lattice Averaging Group (FLAG)
journal, February 2017

Confinement, chiral symmetry, and the lattice
journal, February 2011

An introduction to chiral symmetry on the lattice
journal, October 2004

Volume dependence of the energy spectrum in massive quantum field theories: I. Stable particle states
journal, June 1986

Volume dependence of the energy spectrum in massive quantum field theories: II. Scattering states
journal, June 1986

A general method for non-perturbative renormalization of lattice operators
journal, July 1995

Lattice operators for moments of the structure functions and their transformation under the hypercubic group
journal, November 1996

A lattice determination of moments of unpolarized nucleon structure functions using improved Wilson fermions
journal, June 2005

Properties and uses of the Wilson flow in lattice QCD
journal, August 2010

High-precision scale setting in lattice QCD
journal, September 2012

Ab Initio Determination of Light Hadron Masses
journal, November 2008

Extraction of Parton Distributions from Lattice qcd
journal, December 2003

Normal products and the short distance expansion in the perturbation theory of renormalizable interactions
journal, May 1973

Polarized and unpolarized nucleon structure functions from lattice QCD
journal, March 1996

On the difficulty of computing higher-twist corrections
journal, November 1996

Restoration of rotational symmetry in the continuum limit of lattice field theories
journal, September 2012

Locally smeared operator product expansions in scalar field theory
journal, April 2015

Deep-inelastic scattering and the operator product expansion in lattice QCD
journal, January 2006

Exclusive processes in position space and the pion distribution amplitude
journal, May 2008

Origin of difference between u ¯ and d ¯ partons in the nucleon
journal, March 1994

Parton degrees of freedom from the path-integral formalism
journal, August 2000