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, Michael Wilson

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


The parton distribution functions (PDFs) which characterize the structure of the proton are currently one of the dominant sources of uncertainty in the predictions for most processes measured at the Large Hadron Collider (LHC). Here we present the first extraction of the proton PDFs that accounts for the missing higher order uncertainty (MHOU) in the fixed-order QCD calculations used in PDF determinations. We demonstrate that the MHOU can be included as a contribution to the covariance matrix used for the PDF fit, and then introduce prescriptions for the computation of this covariance matrix using scale variations. We validate our results at next-to-leading order (NLO) by comparison to the known next order (NNLO) corrections. We then construct variants of the NNPDF3.1 NLO PDF set that include the effect of the MHOU, and assess their impact on the central values and uncertainties of the resulting PDFs.

Original languageEnglish
Article number838
Pages (from-to)1-6
Number of pages6
JournalEuropean Physical Journal C
Issue number10
Early online date10 Oct 2019
Publication statusPublished - Oct 2019


R. D. B. is supported by the UK Science and Technology Facility Council through Grant ST/P000630/1.S. F. is supported by the European Research Council under the European Union’s Horizon 2020 research and innovation Programme (Grant agreement n.740006). T. G. is supported by The Scottish Funding Council, grant H14027. Z. K. is supported by the European Research Council Consolidator Grant “NNLOforLHC2”. E. R. N. is supported by the European Commission through the Marie Skłodowska-Curie Action ParDHonS_FFs.TMDs (Grant number 752748). R. L. P. and M. W. are supported by the STFC Grant ST/R504737/1. J. R. is supported by the European Research Council Starting Grant “PDF4BSM” and by the Netherlands Organization for Scientific Research (NWO). L. R. is supported by the European Research Council Starting Grant “REINVENT” (Grant number 714788). M. U. is partially supported by the STFC Grant ST/L000385/1 and funded by the Royal Society grants DH150088 and RGF/EA/180148. C. V. is supported by the STFC grant ST/R504671/1.

FundersFunder number
Not addedST/P000681/1
Marie Skłodowska-Curie Action ParDHonS_FFs
Horizon 2020 Framework Programme683211, 714788, 740006
Science and Technology Facilities CouncilST/R504737/1, ST/P000630/1
Royal SocietyDH150088, RGF/EA/180148, ST/R504671/1
Scottish Funding CouncilH14027
European Commission752748
European Research Council
Nederlandse Organisatie voor Wetenschappelijk OnderzoekST/L000385/1


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