Neural network determination of parton distributions: the nonsinglet case

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 clas

Neural network parametrization of the lepton energy spectrum in semileptonic B meson decays

We construct a parametrization of the lepton energy spectrum in inclusive semileptonic decays of B mesons, based on the available experimental information: moments of the spectrum with cuts, their errors and their correlations, together with kinematical constraints. The result is obtained in the form of a Monte Carlo sample of neural networks trained on replicas of the experimental data, which represents the probability density in the space of lepton energy spectra. This parametrization is then used to extract the b quark mass m_b^{1S} in a way that theoretical uncertainties are minimized, for which the value m_b^{1S}=4.84 \pm 0.14^{exp}\pm 0.05^{th} GeV is obtained.Comment: 32 pages, 22 figures, JHEP3 class. v4 version accepted for publication in JHE

Polarized Parton Distributions at an Electron-Ion Collider

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.

Parton distributions: determining probabilities in a space of functions

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

PENGARUH PENGGUNAAN METODE PEMBELAJARAN KOOPERATIF MAKE A MATCH TERHADAP

bstract: The purpose of this research is to looking for the influence of the using Cooperative learning type make a match to the student’s achievment. This research uses experiment method. The population is all students of 5 grade elementary school Wonogiri Wonogiri. The sample was selected using stratified cluster random sampling. The data resources focused in the achievement learning that gotten by pretest and posttest using questions test that had trough the research of validity, reability, difficulty index and ability of differentiation of question test. The pre-analytic of data are test of balance, normality test, and homogenity test. The technique of analytic of data that used to hipotesis test is t test. The result of the research can be concluded that there is a positif influence of using cooperative learning type make a match to the student’s achievement (t calculate > t table=56,691>2,00). Abstrak: Tujuan penelitian ini adalah untuk mengetahui pengaruh metode pembelajaran kooperatif make a match terhadap hasil belajar IPS. Penelitian ini menggunakan metode eksperimen. Populasi penelitian ini adalah siswa kelas 5 SDN Wonogiri, Wonogiri. Teknik pengambilan sampel yang digunakan adalah stratified cluster random sampling. Sumber data difokuskan pada proses belajar dan hasil belajar yang diperoleh melalui pretest dan posttest dengan instrument soal yang telah melalui uji validitas, reabilitas, indeks kesukaran dan daya pembeda soal. Uji prasyarat analisis menggunakan uji keseimbangan, uji normalitas, uji homogenitas. Sedangkan teknik analisis data sebagai uji hipotesis memakai uji t. Hasil dari penelitian ini dapat disimpulkan ada pengaruh yang positif signifikan model pembelajaran kooperatif Make a Match terhadap hasil belajar IPS (t hitung > t tabel =56,691>2,00). Kata Kunci: Pembelajaran Kooperatif, Make a Matc

Unbiased determination of polarized parton distributions and their uncertainties

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 figure

A first determination of parton distributions with theoretical uncertainties

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

Unbiased determination of the proton structure function F_2^p with faithful uncertainty estimation

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.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

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.V. B., N. H., J. R., L. R. and E. S. are supported by an European Research Council Starting Grant “PDF4BSM”. R. D. B. and L. D. D. are supported by the UK STFC grants ST/L000458/1 and ST/P000630/1. L. D. D. is supported by the Royal Society, Wolfson Research Merit Award, grant WM140078. S. F. is supported by the European Research Council under the Grant Agreement 740006NNNPDFERC-2016-ADG/ERC-2016-ADG. E. R. N. is supported by the UK STFC grant ST/M003787/1. S. C. is supported by the HICCUP ERC Consolidator grant (614577). M. U. is supported by a Royal Society Dorothy Hodgkin Research Fellowship and partially supported by the STFC grant ST/L000385/1. S. F and Z. K. are supported by the Executive Research Agency (REA) of the European Commission under the Grant Agreement PITN-GA-2012-316704 (HiggsTools). A. G. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 659128-NEXTGENPDF

Parton distributions with theory uncertainties: general formalism and first phenomenological studies

Abstract: 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