Fitting parton distribution data with multiplicative normalization uncertainties

  • The NNPDF collaboration
  • Richard D. Ball
  • Luigi Del Debbio
  • Stefano Forte
  • Alberto Guffanti
  • José I. Latorre
  • Juan Rojo
  • Maria Ubiali


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.


QCD Phenomenology 


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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • The NNPDF collaboration
  • Richard D. Ball
    • 1
  • Luigi Del Debbio
    • 1
  • Stefano Forte
    • 2
  • Alberto Guffanti
    • 3
  • José I. Latorre
    • 4
  • Juan Rojo
    • 2
  • Maria Ubiali
    • 1
    • 5
  1. 1.School of Physics and AstronomyUniversity of EdinburghEdinburghU.K.
  2. 2.Dipartimento di FisicaUniversità di Milano and INFN, Sezione di MilanoMilanoItaly
  3. 3.Physikalisches InstitutAlbert-Ludwigs-Universität FreiburgFreiburg i. B.Germany
  4. 4.Departament d’Estructura i Constituents de la MatèriaUniversitat de BarcelonaBarcelonaSpain
  5. 5.Center for Particle Physics and Phenomenology (CP3)Université Catholique de LouvainLouvain-la-NeuveBelgium

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