The Bjorken sum rule with Monte Carlo and Neural Network techniques

Determinations of structure functions and parton distribution functions have been recently obtained using Monte Carlo methods and neural networks as universal, unbiased interpolants for the unknown functional dependence. In this work the same methods are applied to obtain a parametrization of polarized Deep Inelastic Scattering (DIS) structure functions. The Monte Carlo approach provides a bias--free determination of the probability measure in the space of structure functions, while retaining all the information on experimental errors and correlations. In particular the error on the data is propagated into an error on the structure functions that has a clear statistical meaning. We present the application of this method to the parametrization from polarized DIS data of the photon asymmetries $A_1^p$ and $A_1^d$ from which we determine the structure functions $g_1^p(x,Q^2)$ and $g_1^d(x,Q^2)$, and discuss the possibility to extract physical parameters from these parametrizations. This work can be used as a starting point for the determination of polarized parton distributions.Comment: 24 pages, 6 figure

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

Progress on neural parton distributions

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 proceeding

EPS09 - a New Generation of NLO and LO Nuclear Parton Distribution Functions

We present a next-to-leading order (NLO) global DGLAP analysis of nuclear parton distribution functions (nPDFs) and their uncertainties. Carrying out an NLO nPDF analysis for the first time with three different types of experimental input -- deep inelastic $\ell$+A scattering, Drell-Yan dilepton production in p+$A$ collisions, and inclusive pion production in d+Au and p+p collisions at RHIC -- we find that these data can well be described in a conventional collinear factorization framework. Although the pion production has not been traditionally included in the global analyses, we find that the shape of the nuclear modification factor $R_{\rm dAu}$ of the pion $p_T$-spectrum at midrapidity retains sensitivity to the gluon distributions, providing evidence for shadowing and EMC-effect in the nuclear gluons. We use the Hessian method to quantify the nPDF uncertainties which originate from the uncertainties in the data. In this method the sensitivity of $\chi^2$ to the variations of the fitting parameters is mapped out to orthogonal error sets which provide a user-friendly way to calculate how the nPDF uncertainties propagate to any factorizable nuclear cross-section. The obtained NLO and LO nPDFs and the corresponding error sets are collected in our new release called {\ttfamily EPS09}. These results should find applications in precision analyses of the signatures and properties of QCD matter at the LHC and RHIC.Comment: 34 pages, 16 figures. The version accepted for publicatio

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

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 distributions (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, NNPDFpoll. 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 NNPDFpoll. 0, but also that more measurements may be needed to ultimately pin down the size of the gluon contribution to the nucleon spin

Update on Neural Network Parton Distributions: NNPDF1.1

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, DES

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

Reweighting NNPDFs : the W lepton asymmetry

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 χ2 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