A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties

Valerio Bertone, Stefano Carrazza, Nathan P. Hartland, Emanuele R. Nocera, Juan Rojo

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We present NNFF1.0, a new determination of the fragmentation functions (FFs) of charged pions, charged kaons, and protons/antiprotons from an analysis of single-inclusive hadron production data in electron-positron annihilation. This determination, performed at leading, next-to-leading, and next-to-next-to-leading order in perturbative QCD, is based on the NNPDF methodology, a fitting framework designed to provide a statistically sound representation of FF uncertainties and to minimise any procedural bias. We discuss novel aspects of the methodology used in this analysis, namely an optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation strategy, and validate the FF fitting procedure by means of closure tests. We then present the NNFF1.0 sets, and discuss their fit quality, their perturbative convergence, and their stability upon variations of the kinematic cuts and the fitted dataset. We find that the systematic inclusion of higher-order QCD corrections significantly improves the description of the data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other recent sets of FFs, finding in general a reasonable agreement, but also important differences. Together with existing sets of unpolarised and polarised parton distribution functions (PDFs), FFs and PDFs are now available from a common fitting framework for the first time.
Original languageEnglish
Article number516
JournalEuropean Journal of Physics C
Issue number8
Publication statusPublished - 3 Aug 2017

Bibliographical note

50 pages, 22 figures, 5 tables


We thank A. Accardi, D. P. Anderle, R. Sassot and N. Sato for useful discussions. We thank I. Garzia for assistance with the BABAR measurements, and R. Seidl for his help with the BELLE measurements, in particular for providing us with the proton/antiproton cross-section measurements of Ref. []. We thank N. Sato for providing us with the TPC tagged data of Ref. []. We thank D. P. Anderle for a benchmark of the NNLO computation of SIA observables. We thank M. Stratmann for providing us with the charged pion FF sets determined in Ref. []. We thank R. Sassot for providing us with the charged kaon FF sets determined in Ref. [], and for his help with the corresponding interpolating routines. We are finally grateful to our colleagues of the NNPDF Collaboration for their support. In particular, we thank S. Forte and M. Ubiali for a critical reading of the manuscript. V. B., N. P. H. and J. R. are supported by an European Research Council Starting Grant “PDF4BSM”; S. C. is supported by the HICCUP ERC Consolidator Grant (614577); E. R. N. is supported by the UK STFC Grant ST/M003787/1.

FundersFunder number
Seventh Framework Programme614577
Science and Technology Facilities CouncilST/M003787/1
European Research Council


    • hep-ex
    • hep-ph
    • nucl-ex
    • nucl-th


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