A determination of the fragmentation functions of pions, kaons, and protons with faithful uncertainties: The NNPDF Collaboration.

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 [Formula: see text] 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.

Parton distributions from high-precision collider data: NNPDF Collaboration.

We present a new set of parton distributions, NNPDF3.1, which updates NNPDF3.0, the first global set of PDFs determined using a methodology validated by a closure test. The update is motivated by recent progress in methodology and available data, and involves both. On the methodological side, we now parametrize and determine the charm PDF alongside the light-quark and gluon ones, thereby increasing from seven to eight the number of independent PDFs. On the data side, we now include the D0 electron and muon W asymmetries from the final Tevatron dataset, the complete LHCb measurements of W and Z production in the forward region at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. We also include for the first time top-quark pair differential distributions and the transverse momentum of the Z bosons from ATLAS and CMS. We investigate the impact of parametrizing charm and provide evidence that the accuracy and stability of the PDFs are thereby improved. We study the impact of the new data by producing a variety of determinations based on reduced datasets. We find that both improvements have a significant impact on the PDFs, with some substantial reductions in uncertainties, but with the new PDFs generally in agreement with the previous set at the one-sigma level. The most significant changes are seen in the light-quark flavor separation, and in increased precision in the determination of the gluon. We explore the implications of NNPDF3.1 for LHC phenomenology at Run II, compare with recent LHC measurements at 13 TeV, provide updated predictions for Higgs production cross-sections and discuss the strangeness and charm content of the proton in light of our improved dataset and methodology. The NNPDF3.1 PDFs are delivered for the first time both as Hessian sets, and as optimized Monte Carlo sets with a compressed number of replicas.

The asymptotic behaviour of parton distributions at small and large x.

It has been argued from the earliest days of quantum chromodynamics that at asymptotically small values of x the parton distribution functions (PDFs) of the proton behave as [Formula: see text], where the values of [Formula: see text] can be deduced from Regge theory, while at asymptotically large values of x the PDFs behave as [Formula: see text], where the values of [Formula: see text] can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents [Formula: see text] and [Formula: see text] from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio [Formula: see text] at large x, and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.