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. The code is made available as an open-source package together with 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 Getting started and check out the Tutorials.

The NNPDF team

The NNPDF collaboration is currently composed of 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

• Mark Costantini - University of Cambridge

• Juan M. Cruz-Martinez - CERN

• 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

• 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

• Tanishq Sharma - Università di Torino and INFN

• Roy Stegeman - University of Edinburgh

• 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 - Deployment of the Fly-Eye Telescope for NEO Survey - ESA/ASI

• 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

• Zahari Kassabov - Research Engineer, Opificio, London, 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 - Data Scientist at Privacy Hub by Datavant

• Michael Wilson

The NNPDF publications

• “The Path to N3LO Parton Distributions”, Richard D. Ball et al. [B+24c]

• “Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy”, Richard D. Ball et al. [B+24a]

• “Photons in the proton: implications for the LHC”, Richard D. Ball et al. [B+24b]

• “The intrinsic charm quark valence distribution of the proton”, Richard D. Ball et al. [BCCM+24a]

• “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+22a]

• “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

• Getting started
  • Installing the code on Linux or macOS
  • Code structure
  • References
• Tutorials
  • Running fits
  • Analysing results
  • Closure tests
  • Special PDF sets
  • Miscellaneous
• Fitting code: n3fit
  • Methodology overview
  • n3fit runcard detailed guide
  • Hyperoptimization algorithm
• Code for data: validphys
  • Introduction to validphys 2
  • Some things that validphys does
  • Using validphys
  • How validphys handles data
  • More detailed functionality
• Storage of data and theory predictions
  • Introduction
  • Experimental data files
  • NNPDF’s dataset naming convention
  • The process options module
  • Theory data files
  • Organisation of data files
  • Example: CFACTOR file format
  • Plotting format
• Theory
  • Fast Interface (FK tables)
  • Theory parameter definitions
  • Theory indexes
  • Looking up the parameters of a theory
  • Perturbative PDF evolution
• Chi square figures of merit
  • The basis of the loss functions: 𝜒²
  • Missing higher order uncertainties
  • Future test: including PDF errors
  • Regularized covariance matrices
  • The weighted fit method
  • Experimental, validation, and training 𝜒²
  • Hyperoptimized figure of merit
• Contributing guidelines and tools
  • Development installation on Linux or macOS
  • Git and GitHub
  • Contributing Guidelines
  • Adding to the Documentation
  • Tools for developing with the Python programming language
• Releases and compatibility policy
  • Tags
  • Compatibility Policy
• Continuous integration and deployment
  • Operation of CI tools
  • Configuration of GitHub Actions
  • Operation of automatic fit bot
• Servers
  • Access
  • Web scripts
  • Cron jobs
  • Web server Configuration
• External codes
  • PDF set storage and interpolation
  • Grid generation
  • Partonic cross section generation

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.

BCCM+24a

Richard D. Ball, Alessandro Candido, Juan Cruz-Martinez, Stefano Forte, Tommaso Giani, Felix Hekhorn, Giacomo Magni, Emanuele R. Nocera, Juan Rojo, and Roy Stegeman. Intrinsic charm quark valence distribution of the proton. Phys. Rev. D, 109(9):L091501, 2024. arXiv:2311.00743, doi:10.1103/PhysRevD.109.L091501.

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

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+22a

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.

B+22b

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.

B+24a

Richard D. Ball and others. Determination of the theory uncertainties from missing higher orders on NNLO parton distributions with percent accuracy. Eur. Phys. J. C, 84(5):517, 2024. arXiv:2401.10319, doi:10.1140/epjc/s10052-024-12772-z.

B+24b

Richard D. Ball and others. Photons in the proton: implications for the LHC. Eur. Phys. J. C, 84(5):540, 2024. arXiv:2401.08749, doi:10.1140/epjc/s10052-024-12731-8.

B+24c

Richard D. Ball and others. The path to $\hbox N^3\hbox LO$ parton distributions. Eur. Phys. J. C, 84(7):659, 2024. arXiv:2402.18635, doi:10.1140/epjc/s10052-024-12891-7.

BCCM+24b

Andrea Barontini, Alessandro Candido, Juan M. Cruz-Martinez, Felix Hekhorn, and Christopher Schwan. Pineline: Industrialization of high-energy theory predictions. Comput. Phys. Commun., 297:109061, 2024. arXiv:2302.12124, doi:10.1016/j.cpc.2023.109061.

CHM22

Alessandro Candido, Felix Hekhorn, and Giacomo Magni. EKO: evolution kernel operators. Eur. Phys. J. C, 82(10):976, 2022. arXiv:2202.02338, doi:10.1140/epjc/s10052-022-10878-w.

CNSZ20

S. Carrazza, E. R. Nocera, C. Schwan, and M. Zaro. PineAPPL: combining EW and QCD corrections for fast evaluation of LHC processes. JHEP, 12:108, 2020. arXiv:2008.12789, doi:10.1007/JHEP12(2020)108.

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.

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.

FC20

Stefano Forte and Stefano Carrazza. Parton distribution functions. 8 2020. arXiv:2008.12305.

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.

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

Zahari Kassabov, Emanuele R. Nocera, and Michael Wilson. Regularising experimental correlations in LHC data: theory and application to a global analysis of parton distributions. Eur. Phys. J. C, 82(10):956, 2022. arXiv:2207.00690, doi:10.1140/epjc/s10052-022-10932-7.

MNSZ16

Aneesh Manohar, Paolo Nason, Gavin P. Salam, and Giulia Zanderighi. How bright is the proton? A precise determination of the photon parton distribution function. Phys. Rev. Lett., 117(24):242002, 2016. arXiv:1607.04266, doi:10.1103/PhysRevLett.117.242002.

MNSZ17

Aneesh V. Manohar, Paolo Nason, Gavin P. Salam, and Giulia Zanderighi. The Photon Content of the Proton. JHEP, 12:046, 2017. arXiv:1708.01256, doi:10.1007/JHEP12(2017)046.

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.

Indices and tables

• Index

• Module Index

• Search Page