Search

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order (aN$^3$LO). We construct an approximation to the N$^3$LO splitting functions that includes all available partial information from both fixed-order computations and from small and large $x$ resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known N$^3$LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $\mathcal{O}\left( \alpha_s^3\right)$ accuracy. We determine a set of aN$^3$LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N$^3$LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the aN$^3$LO PDFs from the MSHT group. We examine the phenomenological impact of aN$^3$LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN$^3$LO PDFs on the Higgs and Drell-Yan total production cross-sections. We find that the aN$^3$LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell-Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order., Comment: 63 pages, 41 figures. Final version, as published in EPJC. Various clarifications added. Fig 2.9 and Tab. 4.6, 5.1 and 5.2 added. In particular, comparison to approximate YR4 estimate of PDF uncertainties added (Tab 4.1, 4.2 and associate discussion in sect. 5)

We include uncertainties due to missing higher order corrections to QCD computations (MHOU) used in the determination of parton distributions (PDFs) in the recent NNPDF4.0 set of PDFs. We use our previously published methodology, based on the treatment of MHOUs and their full correlations through a theory covariance matrix determined by scale variation, now fully incorporated in the new NNPDF theory pipeline. We assess the impact of the inclusion of MHOUs on the NNPDF4.0 central values and uncertainties, and specifically show that they lead to improved consistency of the PDF determination with an ensuing moderate reduction of PDF uncertainties at NNLO., Comment: 23 pages, 6 figures. Final version, as published in EPJC. Several small improvements; expanded discussion of the phi indicator in sect 4.2

We construct a set of parton distribution functions (PDFs), based on the recent NNPDF4.0 PDF set, that also include a photon PDF. The photon PDF is constructed using the LuxQED formalism, while QED evolution accounting for O(alpha), O(alpha alphas) and O(alpha^2) corrections is implemented and benchmarked by means of the EKO code. We investigate the impact of QED effects on NNPDF4.0, and compare our results both to our previous NNPDF3.1QED PDF set and to other recent PDF sets that include the photon. We assess the impact of photon-initiated processes and electroweak corrections on a variety of representative LHC processes, and find that they can reach the 5% level in vector boson pair production at large invariant mass., Comment: 32 pages, 19 figures. Final; version, as published on EPJC. Pheno discussion in Sect 4.2 improved, a few typos corrected

We respond to the criticism raised by Courtoy et al., in which the faithfulness of the NNPDF4.0 sampling is questioned and an under-estimate of the NNPDF4.0 PDF uncertainties is implied. We list, correct, and clarify in detail a number of inaccurate or misleading claims that are made in this Reference. Specifically, we explain and explicitly demonstrate why the central value of the PDF distribution does not generally coincide with the absolute minimum of the $\chi^{2}$ to the data. We examine some PDFs that have been constructed in the above study and claimed to be "good solutions": we show that similar PDFs are found with the NNPDF methodology, but with very low probability., Comment: 18 pages, 12 figures

We formulate a general approach to the inclusion of theoretical uncertainties, specifically those related to the missing higher order uncertainty (MHOU), in the determination of parton distribution functions (PDFs). We demonstrate how, under quite generic assumptions, theory uncertainties can be included as an extra contribution to the covariance matrix when determining PDFs from data. We then review, clarify, and systematize the use of renormalization and factorization scale variations as a means to estimate MHOUs consistently in deep inelastic and hadronic processes. We define a set of prescriptions for constructing a theory covariance matrix using scale variations, which can be used in global fits of data from a wide range of different processes, based on choosing a set of independent scale variations suitably correlated within and across processes. We set up an algebraic framework for the choice and validation of an optimal prescription by comparing the estimate of MHOU encoded in the next-to-leading order (NLO) theory covariance matrix to the observed shifts between NLO and NNLO predictions. We perform a NLO PDF determination which includes the MHOU, assess the impact of the inclusion of MHOUs on the PDF central values and uncertainties, and validate the results by comparison to the known shift between NLO and NNLO PDFs. We finally study the impact of the inclusion of MHOUs in a global PDF determination on LHC cross-sections, and provide guidelines for their use in precision phenomenology. In addition, we also compare the results based on the theory covariance matrix formalism to those obtained by performing PDF determinations based on different scale choices., Comment: 73 pages, 27 figures. Final version, to be published in EPJC. Numerous changes and improvements including: discussion of phi added, Eq.s 6.3-6.5 and revised Tab 6.2 & 6.4; improved Figs 7.1-7.3; revised Sect. 81; revised Figs. B.1-B.4

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., Comment: 8 pages, 6 figures, PDF sets available from https://data.nnpdf.science/nnpdf31_th/. Final Version, to be published in EPJC letters. Appendix removed, several small improvements including brief discussion of usage

We present NNFF1.1h, a new determination of unidentified charged-hadron fragmentation functions (FFs) and their uncertainties. Experimental measurements of transverse-momentum distributions for charged-hadron production in proton-(anti)proton collisions at the Tevatron and at the LHC are used to constrain a set of FFs originally determined from electron-positron annihilation data. Our analysis is performed at next-to-leading order in perturbative quantum chromodynamics. We find that the hadron-collider data is consistent with the electron-positron data and that it significantly constrains the gluon FF. We verify the reliability of our results upon our choice of the kinematic cut in the hadron transverse momentum applied to the hadron-collider data and their consistency with NNFF1.0, our previous determination of the FFs of charged pions, kaons, and protons/antiprotons., Comment: 11 pages, 8 figures, 3 tables, final version accepted for publication in EPJC - added a reference ([40]) to validphys

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 quarks 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., Comment: Revised version, to be publ.in EPJC. Typos corrected and points clarified. Figs 2.4, 4.21, 4.30 and 4.31 added. PDF comparison plots added. Fit with nuclear corrections added in Sect 4.11. Labeling of all distance plots corrected (u and d were interchanged). Points in charm cross-sections without cuts added to Tab 3.2

We present an unbiased determination of the charm content of the proton, in which the charm parton distribution function (PDF) is parametrized on the same footing as the light quarks and the gluon in a global PDF analysis. This determination relies on the calculation of deep-inelastic structure functions in the FONLL scheme, generalized to account for massive charm-initiated contributions. In contrast to the usual situation in which the charm PDF is assumed to be generated perturbatively by pair radiation off gluons and light quarks, vanishing at a scale set by the value of the charm mass m_c, we find that the fitted charm PDF vanishes within uncertainties at a scale Q~1.5 GeV for all x<~0.1, independent of the value of m_c used in the coefficient functions. We also find some evidence that the charm PDF at large x>~0.1 and low scales does not vanish, but rather has an "intrinsic" component, very weakly scale dependent and almost independent of the value of m_c, carrying about 1% of the total momentum of the proton. The uncertainties in all other PDFs are only slightly increased by the inclusion of fitted charm, while the dependence of these PDFs on m_c is significantly reduced. When the EMC charm structure function dataset is included, it is well described by the fit, and PDF uncertainties in the fitted charm PDF are significantly reduced, though we verify that excluding the EMC data does not qualitatively modify any of our findings. The increased stability with respect to m_c persists at high scales and is the main implication of our results for LHC phenomenology. Fitting the charm PDF modifies the predictions for processes such as high p_T and large rapidity charm pair production and Z+c production, and thus we expect that future LHC data will further constrain the charm content of the proton., Comment: 46 pages, 32 figures. Final version, to be published in EPJC. Sections 3.2, 3.3, 3.4 and conclusions substantially rewritten and improved. Figs 11 and 14 improved, figs 10, 13, 16 added. Last typos fixed

We present NNPDF3.0, the first set of parton distribution functions (PDFs) determined with a methodology validated by a closure test. NNPDF3.0 uses a global dataset including HERA-II deep-inelastic inclusive cross-sections, the combined HERA charm data, jet production from ATLAS and CMS, vector boson rapidity and transverse momentum distributions from ATLAS, CMS and LHCb, W+c data from CMS and top quark pair production total cross sections from ATLAS and CMS. Results are based on LO, NLO and NNLO QCD theory and also include electroweak corrections. To validate our methodology, we show that PDFs determined from pseudo-data generated from a known underlying law correctly reproduce the statistical distributions expected on the basis of the assumed experimental uncertainties. This closure test ensures that our methodological uncertainties are negligible in comparison to the generic theoretical and experimental uncertainties of PDF determination. This enables us to determine with confidence PDFs at different perturbative orders and using a variety of experimental datasets ranging from HERA-only up to a global set including the latest LHC results, all using precisely the same validated methodology. We explore some of the phenomenological implications of our results for the upcoming 13 TeV Run of the LHC, in particular for Higgs production cross-sections., Comment: 151 pages, 69 figures. More typos corrected: published version

We study the potential impact of inclusive deep-inelastic scattering data from a future electron-ion collider (EIC) on longitudinally polarized parton distribution (PDFs). We perform a PDF determination using the NNPDF methodology, based on sets of deep-inelastic EIC pseudodata, for different realistic choices of the electron and proton beam energies. We compare the results to our current polarized PDF set, NNPDFpol1.0, based on a fit to fixed-target inclusive DIS data. We show that the uncertainties on the first moments of the polarized quark singlet and gluon distributions are substantially reduced in comparison to NNPDFpol1.0, but also that more measurements may be needed to ultimately pin down the size of the gluon contribution to the nucleon spin., Comment: 11 pages, 6 figures. Two plots in Fig.5 added and discussion of extrapolation uncertainties expanded. Final version, published in Phys. Lett. B

We present a set of parton distribution functions (PDFs), based on the NNPDF2.3 set, which includes a photon PDF, and QED contributions to parton evolution. We describe the implementation of the combined QCD+QED evolution in the NNPDF framework. We then provide a first determination of the full set of PDFs based on deep-inelastic scattering data and LHC data for W and Z/gamma* Drell-Yan production, using leading-order QED and NLO or NNLO QCD. We compare the ensuing NNPDF2.3QED PDF set to the older MRST2004QED set. We perform a preliminary investigation of the phenomenological implications of NNPDF2.3QED: specifically, photon-induced corrections to direct photon production at HERA, and high-mass dilepton and W pair production at the LHC., Comment: 38 pages, 27 figures. Final version, to be published in Nucl. Phys. B. Several corrections and improvements, in particular Fig.5 added, Fig.2, Fig. 6 and Fig.8 improved, Fig.21 corrected

We present a determination of a set of polarized parton distributions (PDFs) of the nucleon, at next-to-leading order, from a global set of longitudinally polarized deep-inelastic scattering data: NNPDFpol1.0. The determination is based on the NNPDF methodology: a Monte Carlo approach, with neural networks used as unbiased interpolants, previously applied to the determination of unpolarized parton distributions, and designed to provide a faithful and statistically sound representation of PDF uncertainties. We present our dataset, its statistical features, and its Monte Carlo representation. We summarize the technique used to solve the polarized evolution equations and its benchmarking, and the method used to compute physical observables. We review the NNPDF methodology for parametrization and fitting of neural networks, the algorithm used to determine the optimal fit, and its adaptation to the polarized case. We finally present our set of polarized parton distributions. We discuss its statistical properties, test for its stability upon various modifications of the fitting procedure, and compare it to other recent polarized parton sets, and in particular obtain predictions for polarized first moments of PDFs based on it. We find that the uncertainties on the gluon, and to a lesser extent the strange PDF, were substantially underestimated in previous determinations., Comment: 55 pages, 21 figures

We study several sources of theoretical uncertainty in the determination of parton distributions (PDFs) which may affect current PDF sets used for precision physics at the Large Hadron Collider, and explain discrepancies between them. We consider in particular the use of fixed-flavor versus variable-flavor number renormalization schemes, higher twist corrections, and nuclear corrections. We perform our study in the framework of the NNPDF2.3 global PDF determination, by quantifying in each case the impact of different theoretical assumptions on the output PDFs. We also study in each case the implications for benchmark cross sections at the LHC. We find that the impact in a global fit of a fixed-flavor number scheme is substantial, the impact of higher twists is negligible, and the impact of nuclear corrections is moderate and circumscribed., Comment: 18 pages, 13 figures. Final version, to be published in Phys. Lett. B. Tab. 2 added and Fig 13 updated. Several small improvements, including revised discussion of Ref.[24]

We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the underlying parametrization and that it behaves according to Bayes' theorem upon the addition of new data. We then study the dependence of results on consistent or inconsistent datasets and present tools to assess the consistency of new data. Finally we estimate the relative size of the PDF uncertainty due to data uncertainties, and that due to the need to infer a functional form from a finite set of data., Comment: 11 pages, 8 figures, presented by Stefano Forte at PHYSTAT 2011 (to be published in the proceedings)

We develop in more detail our reweighting method for incorporating new datasets in parton fits based on a Monte Carlo representation of PDFs. After revisiting the derivation of the reweighting formula, we show how to construct an unweighted PDF replica set which is statistically equivalent to a given reweighted set. We then use reweighting followed by unweighting to test the consistency of the method, specifically by verifying that results do not depend on the order in which new data are included in the fit via reweighting. We apply the reweighting method to study the impact of LHC W lepton asymmetry data on the NNPDF2.1 set. We show how these data reduce the PDF uncertainties of light quarks in the medium and small x region, providing the first solid constraints on PDFs from LHC data., Comment: 34 pages, 24 figures: published version

We present a determination of the parton distributions of the nucleon from a global set of hard scattering data using the NNPDF methodology at LO and NNLO in perturbative QCD, thereby generalizing to these orders the NNPDF2.1 NLO parton set. Heavy quark masses are included using the so-called FONLL method, which is benchmarked here at NNLO. We demonstrate the stability of PDFs upon inclusion of NNLO corrections, and we investigate the convergence of the perturbative expansion by comparing LO, NLO and NNLO results. We show that the momentum sum rule can be tested with increasing accuracy at LO, NLO and NNLO. We discuss the impact of NNLO corrections on collider phenomenology, specifically by comparing to recent LHC data. We present PDF determinations using a range of values of alpha_s, m_c and m_b. We also present PDF determinations based on various subsets of the global dataset, show that they generally lead to less accurate phenomenology, and discuss the possibility of future PDF determinations based on collider data only., Comment: 80 pages, 51 figures. Final version, to be published in Nuclear Physics B. Many typos corrected and several plots improved: in particular Figs 5, 12, 19, 22, 23. Small corrections in Figs 33, 34. Refs 103-104 added - now fig 22-23 correctly updated. Typos in Tab.1 and Tab.10 (N_dat) corrected

We discuss the impact of the treatment of NMC structure function data on parton distributions in the context of the NNPDF2.1 global PDF determination at NLO and NNLO. We show that the way these data are treated, and even their complete removal, has no effect on parton distributions at NLO, and at NNLO has an effect which is below one sigma. In particular, the Higgs production cross-section in the gluon fusion channel is very stable., Comment: 12 pages, 8 figures. Discussion extended to NNLO, and paper accordingly rewritten altogether. Several further small improvements, including new comparison plots to SLAC and NMC data

We present a method for incorporating the information contained in new datasets into an existing set of parton distribution functions without the need for refitting. The method involves reweighting the ensemble of parton densities through the computation of the chi-square to the new dataset. We explain how reweighting may be used to assess the impact of any new data or pseudodata on parton densities and thus on their predictions. We show that the method works by considering the addition of inclusive jet data to a DIS+DY fit, and comparing to the refitted distribution. We then use reweighting to determine the impact of recent high statistics lepton asymmetry data from the D0 experiment on the NNPDF2.0 parton set. We find that the D0 inclusive muon and electron data are perfectly compatible with the rest of the data included in the NNPDF2.0 analysis and impose additional constraints on the large-x d/u ratio. The more exclusive D0 electron datasets are however inconsistent both with the other datasets and among themselves, suggesting that here the experimental uncertainties have been underestimated., Comment: 36 pages, 22 figures: errors in Eqns.12,36,37 corrected and parts of Figs.1,6,10,13,15,19 replaced

We consider the generic problem of performing a global fit to many independent data sets each with a different overall multiplicative normalization uncertainty. We show that the methods in common use to treat multiplicative uncertainties lead to systematic biases. We develop a method which is unbiased, based on a self--consistent iterative procedure. We demonstrate the use of this method by applying it to the determination of parton distribution functions with the NNPDF methodology, which uses a Monte Carlo method for uncertainty estimation., Comment: 33 pages, 5 figures: published version

We use recent neutrino dimuon production data combined with a global deep-inelastic parton fit to construct a new parton set, NNPDF1.2, which includes a determination of the strange and antistrange distributions of the nucleon. The result is characterized by a faithful estimation of uncertainties thanks to the use of the NNPDF methodology, and is free of model or theoretical assumptions other than the use of NLO perturbative QCD and exact sum rules. Better control of the uncertainties of the strange and antistrange parton distributions allows us to reassess the determination of electroweak parameters from the NuTeV dimuon data. We perform a direct determination of the |V_cd| and |V_cs| CKM matrix elements, obtaining central values in agreement with the current global CKM fit: specifically we find |V_cd|=0.244\pm 0.019 and |V_cs|=0.96\pm 0.07. Our result for |V_cs| is more precise than any previous direct determination. We also reassess the uncertainty on the NuTeV determination of \sin^2\theta_W through the Paschos-Wolfenstein relation: we find that the very large uncertainties in the strange valence momentum fraction are sufficient to bring the NuTeV result into complete agreement with the results from precision electroweak data., Comment: 46 pages, 20 figures; fig.12 and discussion on positivity added, several typos corrected. Final version, to be published in Nucl. Phys. B

We present recent progress within the NNPDF parton analysis framework. After a brief review of the results from the DIS NNPDF analysis, NNPDF1.0, we discuss results from an updated analysis with independent parametrizations for the strange and anti-strange distributions, denoted by NNPDF1.1. We examine the phenomenological implications of this improved analysis for the strange PDFs., Comment: 5 pages, 6 figures, proceedings of the International Symposium on Multiparticle Dynamics 08, 15-20 september 2008, DESY

We present recent results of the NNPDF collaboration on a full DIS analysis of Parton Distribution Functions (PDFs). Our method is based on the idea of combining a Monte Carlo sampling of the probability measure in the space of PDFs with the use of neural networks as unbiased universal interpolating functions. The general structure of the project and the features of the fit are described and compared to those of the traditional approaches., Comment: 4 pages, 6 figures, contribution for the proceedings of the conference "Rencontres de Moriond, QCD and High Energy Interactions"

We give a status report on the determination of a set of parton distributions based on neural networks. In particular, we summarize the determination of the nonsinglet quark distribution up to NNLO, we compare it with results obtained using other approaches, and we discuss its use for a determination of $\alpha_s$., Comment: 4 pages, 2 figs, uses dis2007.cls, to appear in the DIS 2007 workshop proceedings

We provide a determination of the isotriplet quark distribution from available deep--inelastic data using neural networks. We give a general introduction to the neural network approach to parton distributions, which provides a solution to the problem of constructing a faithful and unbiased probability distribution of parton densities based on available experimental information. We discuss in detail the techniques which are necessary in order to construct a Monte Carlo representation of the data, to construct and evolve neural parton distributions, and to train them in such a way that the correct statistical features of the data are reproduced. We present the results of the application of this method to the determination of the nonsinglet quark distribution up to next--to--next--to--leading order, and compare them with those obtained using other approaches., Comment: 46 pages, 18 figures, LaTeX with JHEP3 class

We construct a parametrization of the deep-inelastic structure function of the proton F_2 based on all available experimental information from charged lepton deep-inelastic scattering experiments. The parametrization effectively provides a bias-free determination of the probability measure in the space of structure functions, which retains information on experimental errors and correlations. The result is obtained in the form of a Monte Carlo sample of neural networks trained on an ensemble of replicas of the experimental data. We discuss in detail the techniques required for the construction of bias-free parameterizations of large amounts of structure function data, in view of future applications to the determination of parton distributions based on the same method., Comment: 19 pages, 8 figures. Corrected treatment of normalization uncertainties. Tables 3-6 and Figures 3-7 updated, eqs 13-14 added