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
Article

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.

Keywords

QCD Phenomenology 

References

  1. [1]
    M. Dittmar et al., Working Group I: Parton distributions: Summary report for the HERA LHC Workshop Proceedings, hep-ph/0511119 [SPIRES].
  2. [2]
    M. Dittmar et al., Parton distributions, arXiv:0901.2504 [SPIRES].
  3. [3]
    S. Forte, L. Garrido, J.I. Latorre and A. Piccione, Neural network parametrization of deep-inelastic structure functions, JHEP 05 (2002) 062 [hep-ph/0204232] [SPIRES].CrossRefADSGoogle Scholar
  4. [4]
    NNPDF collaboration, L. Del Debbio, S. Forte, J.I. Latorre, A. Piccione and J. Rojo, Unbiased determination of the proton structure function F2(p) with faithful uncertainty estimation, JHEP 03 (2005) 080 [hep-ph/0501067] [SPIRES].Google Scholar
  5. [5]
    NNPDF collaboration, L. Del Debbio, S. Forte, J.I. Latorre, A. Piccione and J. Rojo, Neural network determination of parton distributions: the nonsinglet case, JHEP 03 (2007) 039 [hep-ph/0701127] [SPIRES].Google Scholar
  6. [6]
    NNPDF collaboration, R.D. Ball et al., A determination of parton distributions with faithful uncertainty estimation, Nucl. Phys. B 809 (2009) 1 [Erratum ibid. B 816 (2009) 293] [arXiv:0808.1231] [SPIRES].CrossRefADSGoogle Scholar
  7. [7]
    NNPDF collaboration, J. Rojo et al., Update on Neural Network Parton Distributions: NNPDF1.1, arXiv:0811.2288 [SPIRES].
  8. [8]
    The NNPDF collaboration, R.D. Ball et al., Precision determination of electroweak parameters and the strange content of the proton from neutrino deep-inelastic scattering, Nucl. Phys. B 823 (2009) 195 [arXiv:0906.1958] [SPIRES].CrossRefADSGoogle Scholar
  9. [9]
    W.T. Giele, S.A. Keller and D.A. Kosower, Parton distribution function uncertainties, hep-ph/0104052 [SPIRES].
  10. [10]
    G. D’Agostini, Bayesian reasoning in data analysis: A critical introduction, World Scientific, Singapore (2003).MATHCrossRefGoogle Scholar
  11. [11]
    CELLO collaboration, H.J. Behrend et al., Determination of α s and sin2 θ w from Measurements of the Total Hadronic Cross-Section in e + e Annihilation, Phys. Lett. B 183 (1987) 400 [SPIRES].ADSGoogle Scholar
  12. [12]
    G. D’Agostini, On the use of the covariance matrix to fit correlated data, Nucl. Instrum. Meth. A 346 (1994) 306 [SPIRES].ADSGoogle Scholar
  13. [13]
    T. Takeuchi, The Status of the determination of α(m Z) and α s(m Z), Prog. Theor. Phys. Suppl. 123 (1996) 247 [hep-ph/9603415] [SPIRES].CrossRefADSGoogle Scholar
  14. [14]
    H. Collaboration, Measurement of the Inclusive ep Scattering Cross Section at Low Q 2 and x at HERA, Eur. Phys. J. C 63 (2009) 625 [arXiv:0904.0929] [SPIRES].Google Scholar
  15. [15]
    H1 collaboration, F.D. Aaron et al., Combined Measurement and QCD Analysis of the Inclusive ep Scattering Cross Sections at HERA, JHEP 01 (2010) 109 [arXiv:0911.0884] [SPIRES].CrossRefGoogle Scholar
  16. [16]
    W.T. Eadie, D. Dryard, F.E. James, M. Roos and B. Sadoulet, Statistical Methods in Experimental Physics, North Holland, The Neatherland (1971).MATHGoogle Scholar
  17. [17]
    R.D. Ball et al., A first unbiased global NLO determination of parton distributions and their uncertainties, arXiv:1002.4407 [SPIRES].
  18. [18]
    A.D. Martin, W.J. Stirling, R.S. Thorne and G. Watt, Parton distributions for the LHC, Eur. Phys. J. C 63 (2009) 189 [arXiv:0901.0002] [SPIRES].CrossRefADSGoogle Scholar
  19. [19]
    P.M. Nadolsky et al., Implications of CTEQ global analysis for collider observables, Phys. Rev. D 78 (2008) 013004 [arXiv:0802.0007] [SPIRES].ADSGoogle Scholar
  20. [20]
    P.M. Nadolsky, private communication.Google Scholar
  21. [21]
    L. Lyons, A.J. Martin and D.H. Saxon, On the determination of the B lifetime by combining the results of different experiments, Phys. Rev. D 41 (1990) 982 [SPIRES].ADSGoogle Scholar

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

Personalised recommendations