Abstract
We present a new set of parton distribution functions (PDFs) based on a fully global dataset and machine learning techniques: NNPDF4.0. We expand the NNPDF3.1 determination with 44 new datasets, mostly from the LHC. We derive a novel methodology through hyperparameter optimization, leading to an efficient fitting algorithm built upon stochastic gradient descent. We use NNLO QCD calculations and account for NLO electroweak corrections and nuclear uncertainties. Theoretical improvements in the PDF description include a systematic implementation of positivity constraints and integrability of sum rules. We validate our methodology by means of closure tests and “future tests” (i.e. tests of backward and forward data compatibility), and assess its stability, specifically upon changes of PDF parametrization basis. We study the internal compatibility of our dataset, and investigate the dependence of results both upon the choice of input dataset and of fitting methodology. We perform a first study of the phenomenological implications of NNPDF4.0 on representative LHC processes. The software framework used to produce NNPDF4.0 is made available as an open-source package together with documentation and examples.
| Original language | English |
|---|---|
| Article number | 428 |
| Pages (from-to) | 1-119 |
| Number of pages | 119 |
| Journal | European Physical Journal C |
| Volume | 82 |
| Issue number | 5 |
| Early online date | 11 May 2022 |
| DOIs | |
| Publication status | Published - May 2022 |
Bibliographical note
Funding Information:We thank Amanda Cooper-Sarkar, Thomas Cridge, Lucian Harland-Lang, Timothy Hobbs, Joey Houston, Pavel Nadolsky, Gavin Salam and Robert Thorne for discussions. We thank Andrew Pilkington and Reinhard Schwienhorst for help with the ATLAS measurements; Maria Aldaya, Emanuela Barberis and Alberto Orso Maria Iorio for assistance with the CMS data; and Stephen Farry and Oliver Lupton for help with the LHCb data. We are grateful to Jun Gao for providing us with the NNLO K-factors for the NuTeV, NOMAD, and ATLAS and CMS single-top measurements, and for helping us with the benchmark of the corresponding NLO calculations. We are grateful to Daniel Britzger for providing us with NNLO fast interpolation grids for the HERA jet data and to Thomas Gehrmann, Aude Gehrmann-De Ridder, Nigel Glover, Alexander Huss and Joao Pires for providing us with NNLO K-factors for ATLAS and CMS jet measurements. We thank Valerio Bertone for assistance with the correction of a bug in APFEL, Marco Zaro for support with MadGraph5_aMC@NLO and Luca Rottoli for guidance in the computation of NNLO corrections for fixed-target Drell–Yan measurements on deuteron targets. We acknowledge contributions from Rabah Abdul Khalek, Alessandro Candido, Felix Hekhorn, Giacomo Magni, Tanjona Rabemananjara and Giovanni Stagnitto at various stages of this work. S. C., S. F., J. C.-M., R. S and C. S. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 740006). M. U. and Z. K. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 950246). M. U. and S. I. are supported by the Royal Society Grant RGF/EA/180148. The work of M. U. is also funded by the Royal Society Grant DH150088. The work of M. U., S. I., C. V. and Z. K. is partially supported by the STFC consolidated Grant ST/L000385/1. The work of Z.K. was partly supported by supported by the European Research Council Consolidator Grant “NNLOforLHC2”. The work of ZK was previously supported by the European Commission Grant (683211) R. D. B, L. D. D. and E. R. N. are supported by the U.K. Science and Technology Facility Council (STFC) Grant ST/P000630/1. E. R. N. was also supported by the European Commission through the Marie Skłodowska-Curie Action ParDHonS (Grant number 752748). J. R. is partially supported by NWO, the Dutch Research Council. T. G. is supported by The Scottish Funding Council, Grant H14027, R. L. P. and M. W. by the STFC Grant ST/R504737/1 and C. V by the STFC Grant ST/R504671/1.
Funding Information:
We thank Amanda Cooper-Sarkar, Thomas Cridge, Lucian Harland-Lang, Timothy Hobbs, Joey Houston, Pavel Nadolsky, Gavin Salam and Robert Thorne for discussions. We thank Andrew Pilkington and Reinhard Schwienhorst for help with the ATLAS measurements; Maria Aldaya, Emanuela Barberis and Alberto Orso Maria Iorio for assistance with the CMS data; and Stephen Farry and Oliver Lupton for help with the LHCb data. We are grateful to Jun Gao for providing us with the NNLO K -factors for the NuTeV, NOMAD, and ATLAS and CMS single-top measurements, and for helping us with the benchmark of the corresponding NLO calculations. We are grateful to Daniel Britzger for providing us with NNLO fast interpolation grids for the HERA jet data and to Thomas Gehrmann, Aude Gehrmann-De Ridder, Nigel Glover, Alexander Huss and Joao Pires for providing us with NNLO K -factors for ATLAS and CMS jet measurements. We thank Valerio Bertone for assistance with the correction of a bug in APFEL, Marco Zaro for support with MadGraph5_aMC@NLO and Luca Rottoli for guidance in the computation of NNLO corrections for fixed-target Drell–Yan measurements on deuteron targets. We acknowledge contributions from Rabah Abdul Khalek, Alessandro Candido, Felix Hekhorn, Giacomo Magni, Tanjona Rabemananjara and Giovanni Stagnitto at various stages of this work. S. C., S. F., J. C.-M., R. S and C. S. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 740006). M. U. and Z. K. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 950246). M. U. and S. I. are supported by the Royal Society Grant RGF/EA/180148. The work of M. U. is also funded by the Royal Society Grant DH150088. The work of M. U., S. I., C. V. and Z. K. is partially supported by the STFC consolidated Grant ST/L000385/1. The work of Z.K. was partly supported by supported by the European Research Council Consolidator Grant “NNLOforLHC2”. The work of ZK was previously supported by the European Commission Grant (683211) R. D. B, L. D. D. and E. R. N. are supported by the U.K. Science and Technology Facility Council (STFC) Grant ST/P000630/1. E. R. N. was also supported by the European Commission through the Marie Skłodowska-Curie Action ParDHonS (Grant number 752748). J. R. is partially supported by NWO, the Dutch Research Council. T. G. is supported by The Scottish Funding Council, Grant H14027, R. L. P. and M. W. by the STFC Grant ST/R504737/1 and C. V by the STFC Grant ST/R504671/1.
Publisher Copyright:
© 2022, The Author(s).
Funding
We thank Amanda Cooper-Sarkar, Thomas Cridge, Lucian Harland-Lang, Timothy Hobbs, Joey Houston, Pavel Nadolsky, Gavin Salam and Robert Thorne for discussions. We thank Andrew Pilkington and Reinhard Schwienhorst for help with the ATLAS measurements; Maria Aldaya, Emanuela Barberis and Alberto Orso Maria Iorio for assistance with the CMS data; and Stephen Farry and Oliver Lupton for help with the LHCb data. We are grateful to Jun Gao for providing us with the NNLO K-factors for the NuTeV, NOMAD, and ATLAS and CMS single-top measurements, and for helping us with the benchmark of the corresponding NLO calculations. We are grateful to Daniel Britzger for providing us with NNLO fast interpolation grids for the HERA jet data and to Thomas Gehrmann, Aude Gehrmann-De Ridder, Nigel Glover, Alexander Huss and Joao Pires for providing us with NNLO K-factors for ATLAS and CMS jet measurements. We thank Valerio Bertone for assistance with the correction of a bug in APFEL, Marco Zaro for support with MadGraph5_aMC@NLO and Luca Rottoli for guidance in the computation of NNLO corrections for fixed-target Drell–Yan measurements on deuteron targets. We acknowledge contributions from Rabah Abdul Khalek, Alessandro Candido, Felix Hekhorn, Giacomo Magni, Tanjona Rabemananjara and Giovanni Stagnitto at various stages of this work. S. C., S. F., J. C.-M., R. S and C. S. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 740006). M. U. and Z. K. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 950246). M. U. and S. I. are supported by the Royal Society Grant RGF/EA/180148. The work of M. U. is also funded by the Royal Society Grant DH150088. The work of M. U., S. I., C. V. and Z. K. is partially supported by the STFC consolidated Grant ST/L000385/1. The work of Z.K. was partly supported by supported by the European Research Council Consolidator Grant “NNLOforLHC2”. The work of ZK was previously supported by the European Commission Grant (683211) R. D. B, L. D. D. and E. R. N. are supported by the U.K. Science and Technology Facility Council (STFC) Grant ST/P000630/1. E. R. N. was also supported by the European Commission through the Marie Skłodowska-Curie Action ParDHonS (Grant number 752748). J. R. is partially supported by NWO, the Dutch Research Council. T. G. is supported by The Scottish Funding Council, Grant H14027, R. L. P. and M. W. by the STFC Grant ST/R504737/1 and C. V by the STFC Grant ST/R504671/1. We thank Amanda Cooper-Sarkar, Thomas Cridge, Lucian Harland-Lang, Timothy Hobbs, Joey Houston, Pavel Nadolsky, Gavin Salam and Robert Thorne for discussions. We thank Andrew Pilkington and Reinhard Schwienhorst for help with the ATLAS measurements; Maria Aldaya, Emanuela Barberis and Alberto Orso Maria Iorio for assistance with the CMS data; and Stephen Farry and Oliver Lupton for help with the LHCb data. We are grateful to Jun Gao for providing us with the NNLO K -factors for the NuTeV, NOMAD, and ATLAS and CMS single-top measurements, and for helping us with the benchmark of the corresponding NLO calculations. We are grateful to Daniel Britzger for providing us with NNLO fast interpolation grids for the HERA jet data and to Thomas Gehrmann, Aude Gehrmann-De Ridder, Nigel Glover, Alexander Huss and Joao Pires for providing us with NNLO K -factors for ATLAS and CMS jet measurements. We thank Valerio Bertone for assistance with the correction of a bug in APFEL, Marco Zaro for support with MadGraph5_aMC@NLO and Luca Rottoli for guidance in the computation of NNLO corrections for fixed-target Drell–Yan measurements on deuteron targets. We acknowledge contributions from Rabah Abdul Khalek, Alessandro Candido, Felix Hekhorn, Giacomo Magni, Tanjona Rabemananjara and Giovanni Stagnitto at various stages of this work. S. C., S. F., J. C.-M., R. S and C. S. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 740006). M. U. and Z. K. are supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n. 950246). M. U. and S. I. are supported by the Royal Society Grant RGF/EA/180148. The work of M. U. is also funded by the Royal Society Grant DH150088. The work of M. U., S. I., C. V. and Z. K. is partially supported by the STFC consolidated Grant ST/L000385/1. The work of Z.K. was partly supported by supported by the European Research Council Consolidator Grant “NNLOforLHC2”. The work of ZK was previously supported by the European Commission Grant (683211) R. D. B, L. D. D. and E. R. N. are supported by the U.K. Science and Technology Facility Council (STFC) Grant ST/P000630/1. E. R. N. was also supported by the European Commission through the Marie Skłodowska-Curie Action ParDHonS (Grant number 752748). J. R. is partially supported by NWO, the Dutch Research Council. T. G. is supported by The Scottish Funding Council, Grant H14027, R. L. P. and M. W. by the STFC Grant ST/R504737/1 and C. V by the STFC Grant ST/R504671/1.
| Funders | Funder number |
|---|---|
| Marie Skłodowska-Curie Action ParDHonS | 752748 |
| Horizon 2020 Framework Programme | 950246, 740006 |
| Horizon 2020 Framework Programme | |
| Science and Technology Facilities Council | ST/L000385/1, ST/P000630/1 |
| Science and Technology Facilities Council | |
| Royal Society | DH150088, RGF/EA/180148 |
| Royal Society | |
| Scottish Funding Council | ST/R504737/1, H14027, ST/R504671/1 |
| Scottish Funding Council | |
| European Commission | 683211 |
| European Commission | |
| European Research Council | |
| Nederlandse Organisatie voor Wetenschappelijk Onderzoek | |
| ARC Training Centre in Lightweight Automotive Structures |
