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Fitting parton distribution data with multiplicative normalization uncertainties

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Abstract

The extraction of robust parton distribution functions with faithful errors requires a careful treatment of the uncertainties in the experimental results. In particular, the data sets used in current analyses each have a different overall multiplicative normalization uncertainty that needs to be properly accounted for in the fitting procedure. Here 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 then apply our generic method to the determination of parton distribution functions with the NNPDF methodology, which uses a Monte Carlo method for uncertainty estimation.

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Authors and Affiliations

  1. School of Physics and Astronomy, University of Edinburgh, JCMB, KB, Mayfield Rd, Edinburgh, EH9 3JZ, Scotland, U.K.

    Richard D. Ball, Luigi Del Debbio & Maria Ubiali

  2. Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Via Celoria 16, I-20133, Milano, Italy

    Stefano Forte & Juan Rojo

  3. Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104, Freiburg i. B., Germany

    Alberto Guffanti

  4. Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Diagonal 647, E-08028, Barcelona, Spain

    José I. Latorre

  5. Center for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron, B-1348, Louvain-la-Neuve, Belgium

    Maria Ubiali

Authors
  1. Richard D. Ball
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  2. Luigi Del Debbio
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  3. Stefano Forte
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  4. Alberto Guffanti
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  5. José I. Latorre
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  6. Juan Rojo
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  7. Maria Ubiali
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The NNPDF collaboration

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Correspondence to Richard D. Ball.

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The NNPDF collaboration., Ball, R.D., Del Debbio, L. et al. Fitting parton distribution data with multiplicative normalization uncertainties. J. High Energ. Phys. 2010, 75 (2010). https://doi.org/10.1007/JHEP05(2010)075

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  • DOI: https://doi.org/10.1007/JHEP05(2010)075

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