We construct a parametrization of deep-inelastic structure functions which retains information on experimental errors and correlations, and which does not introduce any theoretical bias while interpolating between existing data points. We generate a Monte Carlo sample of pseudo-data configurations and we train an ensemble of neural networks on them. This effectively provides us with a probability measure in the space of structure functions, within the whole kinematic region where data are available. This measure can then be used to determine the value of the structure function, its error, point-to-point correlations and generally the value and uncertainty of any function of the structure function itself. We apply this technique to the determination of the structure function F 2 of the proton and deuteron, and a precision determination of the isotriplet combination F 2 [p-d]. We discuss in detail these results, check their stability and accuracy, and make them available in various formats for applications.April 2002

Abstract:We present the determination of a set of parton distributions of the nucleon, at nextto-leading order, from a global set of deep-inelastic scattering data: NNPDF1.0. The determination is based on a Monte Carlo approach, with neural networks used as unbiased interpolants. This method, previously discussed by us and applied to a determination of the nonsinglet quark distribution, is designed to provide a faithful and statistically sound representation of the uncertainty on parton distributions. We discuss our dataset, its statistical features, and its Monte Carlo representation. We summarize the technique used to solve the evolution equations and its benchmarking, and the method used to compute physical observables. We discuss the parametrization and fitting of neural networks, and the algorithm used to determine the optimal fit. We finally present our set of parton distributions. We discuss its statistical properties, test for its stability upon various modifications of the fitting procedure, and compare it to other recent parton sets. We use it to compute the benchmark W and Z cross sections at the LHC. We discuss issues of delivery and interfacing to commonly used packages such as LHAPDF.1

We present a computation of nucleon mass corrections to nucleon structure functions for polarized deep-inelastic scattering. We perform a fit to existing data including mass corrections at first order in m 2 /Q 2 and we study the effect of these corrections on physically interesting quantities. We conclude that mass corrections are generally small, and compatible with current estimates of higher twist uncertainties, when available.

No abstract

Abstract: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 ± 0.019 and |V cs | = 0.96 ± 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 θ 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.1

The technique of truncated moments of parton distributions allows us to study scaling violations without making any assumption on the shape of parton distributions. The numerical implementation of the method is however difficult, since the evolution equations for truncated moments are not diagonal. We present a simple way to improve the efficiency of the numerical solution of the evolution equations for truncated moments. As a result, the number of truncated moments needed to achieve the required precision in the evolution is significantly smaller than in the original formulation of the technique. The method presented here can also be used to obtain the value of parton distributions in terms of truncated moments, and therefore it can be viewed as a technique for the solution of the Altarelli-Parisi equations.

We define truncated Mellin moments of parton distributions by restricting the integration range over the Bjorken variable to the experimentally accessible subset x_0 < x < 1 of the allowed kinematic range 0 < x < 1. We derive the evolution equations satisfied by truncated moments in the general (singlet) case in terms of an infinite triangular matrix of anomalous dimensions which couple each truncated moment to all higher moments with orders differing by integers. We show that the evolution of any moment can be determined to arbitrarily good accuracy by truncating the system of coupled moments to a sufficiently large but finite size, and show how the equations can be solved in a way suitable for numerical applications. We discuss in detail the accuracy of the method in view of applications to precision phenomenology.Comment: 23 pages, 6 figures, LaTeX; factors of 2nf in Appendix C correcte

We determine the strong coupling α S (M Z ) from scaling violations of truncated moments of the nonsinglet deep inelastic structure function F 2 . Truncated moments are determined from BCDMS and NMC data using a neural network parametrization which retains the full experimental information on errors and correlations. Our method minimizes all sources of theoretical uncertainty and bias which characterize extractions of α s from scaling violations. We obtain α S (M Z ) = 0.124 + 0.004 − 0.007 (exp.) + 0.003 − 0.004 (th.).