The NNPDF collaboration

The NNPDF collaboration performs research in the field of high-energy physics. The NNPDF collaboration determines the structure of the proton using contemporary methods of artificial intelligence. A precise knowledge of the so-called Parton Distribution Functions (PDFs) of the proton, which describe their structure in terms of their quark and gluon constituents, is a crucial ingredient of the physics program of the Large Hadron Collider of CERN.

The NNPDF code

The scientific output of the collaboration is freely available to the public through the arXiv, journal repositories, and software repositories. Along with this online documentation, we release the NNPDF code, used to produce the latest family of PDFs from NNPDF: NNPDF4.0. The code is made available as an open-source package together with the user-friendly examples and an extensive documentation presented here.

The code can be used to produce the ingredients needed for PDF fits, to run the fits themselves, and to analyse the results. This is the first framework used to produce a global PDF fit made publicly available, enabling for detailed external validation and reproducibility of the NNPDF4.0 analysis. Moreover, the code enables the user to explore a number of phenomenological applications, such as the assessment of the impact of new experimental data on PDFs, the effect of changes in theory settings on the resulting PDFs and a fast quantitative comparison between theoretical predictions and experimental data over a broad range of observables.

If you are a new user head along to getstarted and check out the Tutorials.

The NNPDF team

The NNPDF collaboration is currently composed by the following members:

  • Richard D. Ball - University of Edinburgh

  • Andrea Barontini - Università degli Studi di Milano and INFN

  • Alessandro Candido - Università degli Studi di Milano and INFN

  • Stefano Carrazza - Università degli Studi di Milano and INFN

  • Juan Cruz-Martinez - Università degli Studi di Milano and INFN

  • Luigi Del Debbio - University of Edinburgh

  • Stefano Forte - Università degli Studi di Milano and INFN

  • Tommaso Giani - Vrije University Amsterdam and Nikhef

  • Felix Hekhorn - Università degli Studi di Milano and INFN

  • Zahari Kassabov - University of Cambridge

  • José Ignacio Latorre - Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, United Arab Emirates and Center for Quantum Technologies, National University of Singapore

  • Niccolò Laurenti - Università degli Studi di Milano and INFN

  • Giacomo Magni - Vrije University Amsterdam and Nikhef

  • Emanuele R. Nocera - Università degli Studi di Torino and INFN

  • Juan Rojo - Vrije University Amsterdam and Nikhef

  • Christopher Schwan - University of Würzburg

  • Roy Stegeman - Università degli Studi di Milano and INFN

  • Maria Ubiali - University of Cambridge

Former members of the NNPDF collaboration include

  • Rabah Abdul Khalek - Post-doc at Jefferson Lab, USA

  • Valerio Bertone - Post-doc at CEA Saclay, FR

  • Francesco Cerutti

  • Christopher S. Deans

  • Alberto Guffanti - Data Scientist at PIVIGO, UK

  • Patrick Groth-Merrild

  • Nathan P. Hartland - Senior Data Analyst at Dott, NL

  • Shayan Iranipour - Quantitative Researcher at Tudor Investment Corporation, UK

  • Rosalyn Pearson - Information Analyst at Public Health Scotland, UK

  • Andrea Piccione - High School Teacher at IPIA G. Piana, IT

  • Luca Rottoli - Post-doc at the University of Zurich, CH

  • Emma Slade - Senior AI/ML Engineer at GSK, UK

  • Cameron Voisey

  • Michael Wilson

The NNPDF publications

  • *”Evidence for intrinsic charm quarks in the proton”, Richard D. Ball et al. [BCCM+22]

  • “Regularising experimental correlations in LHC data: theory and application to a global analysis of parton distributions”, Zahari Kassabov, Emanuele R. Nocera, Michael Wilson [KNW22]

  • “Bayesian approach to inverse problems: an application to NNPDF closure testing”, Luigi Del Debbio, Tommaso Giani, Michael Wilson [DDGW22]

  • “A data-based parametrization of parton distribution functions”, Stefano Carrazza, Juan Cruz-Martinez, Roy Stegeman [CCMS22]

  • “Correlation and combination of sets of parton distributions”, Richard D. Ball, Stefano Forte, Roy Stegeman [BFS21]

  • “The path to proton structure at 1% accuracy”, Richard D. Ball et al. [B+22]

  • “An open-source machine learning framework for global analyses of parton distributions”, Richard D. Ball et al. [B+21a]

  • “Future tests of parton distributions”, Juan Cruz-Martinez, Stefano Forte, Emanuele R. Nocera [CMFN21]

  • “Deuteron Uncertainties in the Determination of Proton PDFs”, Richard D. Ball, Emanuele R. Nocera, Rosalyn L. Pearson, [BNP21]

  • “Parton Distribution Functions”, Stefano Carrazza, Stefano Forte [FC20]

  • “Phenomenology of NNLO jet production at the LHC and its impact on parton distributions”, Rabah Abdul Khalek, Stefano Forte, Thomas Gehrmann, Aude Gehrmann-De Ridder, Tommaso Giani, Nigel Glover, Alexander Huss, Emanuele R. Nocera, Joao Pires, Juan Rojo, Giovanni Stagnitto [AK+20]

  • “Why αs Cannot be Determined from Hadronic Processes without Simultaneously Determining the Parton Distributions”, Stefano Forte, Zahari Kassabov, [FK20]

  • “Single top production in PDF fits”, Emanuele R. Nocera, Maria Ubiali, Cameron Voisey, [NUV20]

  • “Parton Distributions with Theory Uncertainties: General Formalism and First Phenomenological Studies”, Rabah Abdul Khalek, Richard D. Ball, Stefano Carrazza, Stefano Forte, Tommaso Giani, Zahari Kassabov, Rosalyn L. Pearson, Emanuele R. Nocera, Juan Rojo, Luca Rottoli, Maria Ubiali, Cameron Voisey and Michael Wilson [AK+19a]

  • “Nuclear Parton Distributions from Lepton-Nucleus Scattering and the Impact of an Electron-Ion Collider”, Rabah Abdul Khalek, Jacob J. Ethier, Juan Rojo, [AKER19]

  • “A First Determination of Parton Distributions with Theoretical Uncertainties”, Rabah Abdul Khalek, Richard D. Ball, Stefano Carrazza, Stefano Forte, Tommaso Giani, Zahari Kassabov, Emanuele R. Nocera, Rosalyn L. Pearson, Juan Rojo, Luca Rottoli, Maria Ubiali, Cameron Voisey, and Michael Wilson [AK+19b]

  • “Towards a new generation of parton densities with deep learning models”, Stefano Carrazza and Juan Cruz-Martinez [CCM19]

  • “Parton distributions from high-precision collider data”, Richard D. Ball, Valerio Bertone, Stefano Carrazza, Luigi Del Debbio, Stefano Forte, Patrick Groth-Merrild, Alberto Guffanti, Nathan P. Hartland, Zahari Kassabov, Jose I. Latorre, Emanuele R. Nocera, Juan Rojo, Luca Rottoli, Emma Slade, and Maria Ubiali [B+17]

Contents

Bibliography

AKER19

Rabah Abdul Khalek, Jacob J. Ethier, and Juan Rojo. Nuclear parton distributions from lepton-nucleus scattering and the impact of an electron-ion collider. Eur. Phys. J. C, 79(6):471, 2019. arXiv:1904.00018, doi:10.1140/epjc/s10052-019-6983-1.

AK+19a

Rabah Abdul Khalek and others. A first determination of parton distributions with theoretical uncertainties. Eur. Phys. J., C:79:838, 2019. arXiv:1905.04311, doi:10.1140/epjc/s10052-019-7364-5.

AK+19b

Rabah Abdul Khalek and others. Parton Distributions with Theory Uncertainties: General Formalism and First Phenomenological Studies. Eur. Phys. J. C, 79(11):931, 2019. arXiv:1906.10698, doi:10.1140/epjc/s10052-019-7401-4.

AK+20

Rabah Abdul Khalek and others. Phenomenology of NNLO jet production at the LHC and its impact on parton distributions. Eur. Phys. J. C, 80(8):797, 2020. arXiv:2005.11327, doi:10.1140/epjc/s10052-020-8328-5.

BCCM+22

Richard D. Ball, Alessandro Candido, Juan Cruz-Martinez, Stefano Forte, Tommaso Giani, Felix Hekhorn, Kirill Kudashkin, Giacomo Magni, and Juan Rojo. Evidence for intrinsic charm quarks in the proton. Nature, 608(7923):483–487, 2022. arXiv:2208.08372, doi:10.1038/s41586-022-04998-2.

BDDF+10

Richard D. Ball, Luigi Del Debbio, Stefano Forte, Alberto Guffanti, Jose I. Latorre, Juan Rojo, and Maria Ubiali. Fitting Parton Distribution Data with Multiplicative Normalization Uncertainties. JHEP, 05:075, 2010. arXiv:0912.2276, doi:10.1007/JHEP05(2010)075.

BFS21

Richard D. Ball, Stefano Forte, and Roy Stegeman. Correlation and combination of sets of parton distributions. Eur. Phys. J. C, 81(11):1046, 2021. arXiv:2110.08274, doi:10.1140/epjc/s10052-021-09863-6.

BNP21

Richard D. Ball, Emanuele R. Nocera, and Rosalyn L. Pearson. Deuteron Uncertainties in the Determination of Proton PDFs. Eur. Phys. J. C, 81(1):37, 2021. arXiv:2011.00009, doi:10.1140/epjc/s10052-020-08826-7.

B+17

Richard D. Ball and others. Parton distributions from high-precision collider data. Eur. Phys. J. C, 77(10):663, 2017. arXiv:1706.00428, doi:10.1140/epjc/s10052-017-5199-5.

B+21a

Richard D. Ball and others. An open-source machine learning framework for global analyses of parton distributions. Eur. Phys. J. C, 81(10):958, 2021. arXiv:2109.02671, doi:10.1140/epjc/s10052-021-09747-9.

B+21b

missing journal in nnpdf40code

B+22

Richard D. Ball and others. The path to proton structure at 1% accuracy. Eur. Phys. J. C, 82(5):428, 2022. arXiv:2109.02653, doi:10.1140/epjc/s10052-022-10328-7.

BGYZ16

Edmond L. Berger, Jun Gao, C. -P. Yuan, and Hua Xing Zhu. NNLO QCD Corrections to t-channel Single Top-Quark Production and Decay. Phys. Rev. D, 94(7):071501, 2016. arXiv:1606.08463, doi:10.1103/PhysRevD.94.071501.

BGZ17

Edmond L. Berger, Jun Gao, and Hua Xing Zhu. Differential Distributions for t-channel Single Top-Quark Production and Decay at Next-to-Next-to-Leading Order in QCD. JHEP, 11:158, 2017. arXiv:1708.09405, doi:10.1007/JHEP11(2017)158.

BCE+16

Radja Boughezal, John M. Campbell, R. Keith Ellis, Christfried Focke, Walter T. Giele, Xiaohui Liu, and Frank Petriello. Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD. Phys. Rev. Lett., 116(15):152001, 2016. arXiv:1512.01291, doi:10.1103/PhysRevLett.116.152001.

BFLP15

Radja Boughezal, Christfried Focke, Xiaohui Liu, and Frank Petriello. $W$-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD. Phys. Rev. Lett., 115(6):062002, 2015. arXiv:1504.02131, doi:10.1103/PhysRevLett.115.062002.

BGPU17

Radja Boughezal, Alberto Guffanti, Frank Petriello, and Maria Ubiali. The impact of the LHC Z-boson transverse momentum data on PDF determinations. JHEP, 07:130, 2017. arXiv:1705.00343, doi:10.1007/JHEP07(2017)130.

BLP15

Radja Boughezal, Xiaohui Liu, and Frank Petriello. $N$-jettiness soft function at next-to-next-to-leading order. Phys. Rev. D, 91(9):094035, 2015. arXiv:1504.02540, doi:10.1103/PhysRevD.91.094035.

BLP16

Radja Boughezal, Xiaohui Liu, and Frank Petriello. Phenomenology of the Z-boson plus jet process at NNLO. Phys. Rev. D, 94(7):074015, 2016. arXiv:1602.08140, doi:10.1103/PhysRevD.94.074015.

CEW17

John M. Campbell, R. Keith Ellis, and Ciaran Williams. Direct Photon Production at Next-to–Next-to-Leading Order. Phys. Rev. Lett., 118(22):222001, 2017. [Erratum: Phys.Rev.Lett. 124, 259901 (2020)]. arXiv:1612.04333, doi:10.1103/PhysRevLett.118.222001.

CRSW18

John M. Campbell, Juan Rojo, Emma Slade, and Ciaran Williams. Direct photon production and PDF fits reloaded. Eur. Phys. J. C, 78(6):470, 2018. arXiv:1802.03021, doi:10.1140/epjc/s10052-018-5944-4.

CCM19

Stefano Carrazza and Juan Cruz-Martinez. Towards a new generation of parton densities with deep learning models. Eur. Phys. J. C, 79(8):676, 2019. arXiv:1907.05075, doi:10.1140/epjc/s10052-019-7197-2.

CCMS22

Stefano Carrazza, Juan M. Cruz-Martinez, and Roy Stegeman. A data-based parametrization of parton distribution functions. Eur. Phys. J. C, 82(2):163, 2022. arXiv:2111.02954, doi:10.1140/epjc/s10052-022-10136-z.

CFKR16

Stefano Carrazza, Stefano Forte, Zahari Kassabov, and Juan Rojo. Specialized minimal PDFs for optimized LHC calculations. Eur. Phys. J. C, 76(4):205, 2016. arXiv:1602.00005, doi:10.1140/epjc/s10052-016-4042-8.

CMFN21

Juan Cruz-Martinez, Stefano Forte, and Emanuele R. Nocera. Future tests of parton distributions. Acta Phys. Polon. B, 52:243, 2021. arXiv:2103.08606, doi:10.5506/APhysPolB.52.243.

CGP17

J Currie, E. W. N. Glover, and J Pires. Next-to-Next-to Leading Order QCD Predictions for Single Jet Inclusive Production at the LHC. Phys. Rev. Lett., 118(7):072002, 2017. arXiv:1611.01460, doi:10.1103/PhysRevLett.118.072002.

CGDRG+17

James Currie, Aude Gehrmann-De Ridder, Thomas Gehrmann, E. W. N. Glover, Alexander Huss, and Joao Pires. Precise predictions for dijet production at the LHC. Phys. Rev. Lett., 119(15):152001, 2017. arXiv:1705.10271, doi:10.1103/PhysRevLett.119.152001.

CFM13

Michał Czakon, Paul Fiedler, and Alexander Mitov. Total Top-Quark Pair-Production Cross Section at Hadron Colliders Through $O(\alpha ^4_S)$. Phys. Rev. Lett., 110:252004, 2013. arXiv:1303.6254, doi:10.1103/PhysRevLett.110.252004.

CHM+17

Michał Czakon, Nathan P. Hartland, Alexander Mitov, Emanuele R. Nocera, and Juan Rojo. Pinning down the large-x gluon with NNLO top-quark pair differential distributions. JHEP, 04:044, 2017. arXiv:1611.08609, doi:10.1007/JHEP04(2017)044.

CHM17

missing journal in Czakon:2017dip

DDGW22

Luigi Del Debbio, Tommaso Giani, and Michael Wilson. Bayesian approach to inverse problems: an application to NNPDF closure testing. Eur. Phys. J. C, 82(4):330, 2022. arXiv:2111.05787, doi:10.1140/epjc/s10052-022-10297-x.

DDKM11

Ansgar Denner, Stefan Dittmaier, Tobias Kasprzik, and Alexander Muck. Electroweak corrections to dilepton + jet production at hadron colliders. JHEP, 06:069, 2011. arXiv:1103.0914, doi:10.1007/JHEP06(2011)069.

FC20

missing journal in Forte:2020yip

FK20

Stefano Forte and Zahari Kassabov. Why $\alpha _s$ cannot be determined from hadronic processes without simultaneously determining the parton distributions. Eur. Phys. J. C, 80(3):182, 2020. arXiv:2001.04986, doi:10.1140/epjc/s10052-020-7748-6.

Gao18

Jun Gao. Massive charged-current coefficient functions in deep-inelastic scattering at NNLO and impact on strange-quark distributions. JHEP, 02:026, 2018. arXiv:1710.04258, doi:10.1007/JHEP02(2018)026.

GSTW15

Jonathan Gaunt, Maximilian Stahlhofen, Frank J. Tackmann, and Jonathan R. Walsh. N-jettiness Subtractions for NNLO QCD Calculations. JHEP, 09:058, 2015. arXiv:1505.04794, doi:10.1007/JHEP09(2015)058.

GLPQ11

Ryan Gavin, Ye Li, Frank Petriello, and Seth Quackenbush. FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order. Comput. Phys. Commun., 182:2388–2403, 2011. arXiv:1011.3540, doi:10.1016/j.cpc.2011.06.008.

Kas19

Zahari Kassabov. Reportengine: A framework for declarative data analysis. February 2019. URL: https://doi.org/10.5281/zenodo.2571601, doi:10.5281/zenodo.2571601.

KNW22

missing journal in Kassabov:2022pps

NUV20

Emanuele R. Nocera, Maria Ubiali, and Cameron Voisey. Single Top Production in PDF fits. JHEP, 05:067, 2020. arXiv:1912.09543, doi:10.1007/JHEP05(2020)067.

BallCarrazzaCruzMartinez+21

Richard D. Ball, Stefano Carrazza, Juan Cruz-Martinez, Luigi Del Debbio, Stefano Forte, Tommaso Giani, Shayan Iranipour, Zahari Kassabov, Jose I. Latorre, Emanuele R. Nocera, Rosalyn L. Pearson, Juan Rojo, Roy Stegeman, Christopher Schwan, Maria Ubiali, Cameron Voisey, and Michael Wilson. The Path to Proton Structure at One-Percent Accuracy. arXiv e-prints, pages arXiv:2109.02653, September 2021. arXiv:2109.02653.

Indices and tables