Study of Monte Carlo approach to experimental uncertainty propagation with MSTW 2008 PDFs

Open Access
Article

Abstract

We investigate the Monte Carlo approach to propagation of experimental uncertainties within the context of the established “MSTW 2008” global analysis of parton distribution functions (PDFs) of the proton at next-to-leading order in the strong coupling. We show that the Monte Carlo approach using replicas of the original data gives PDF uncertainties in good agreement with the usual Hessian approach using the standard Δχ2 = 1 criterion, then we explore potential parameterisation bias by increasing the number of free parameters, concluding that any parameterisation bias is likely to be small, with the exception of the valence-quark distributions at low momentum fractions x. We motivate the need for a larger tolerance, Δχ2> 1, by making fits to restricted data sets and idealised consistent or inconsistent pseudodata. Instead of using data replicas, we alternatively produce PDF sets randomly distributed according to the covariance matrix of fit parameters including appropriate tolerance values, then we demonstrate a simpler method to produce an arbitrary number of random predictions on-the-fly from the existing eigenvector PDF sets. Finally, as a simple example application, we use Bayesian reweighting to study the effect of recent LHC data on the lepton charge asymmetry from W boson decays.

Keywords

QCD Phenomenology Deep Inelastic Scattering (Phenomenology) 

References

  1. [1]
    G. Watt, Parton distribution function dependence of benchmark standard model total cross sections at the 7 TeV LHC, JHEP 09 (2011) 069 [arXiv:1106.5788] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    R.S. Thorne and G. Watt, PDF dependence of Higgs cross sections at the Tevatron and LHC: response to recent criticism, JHEP 08 (2011) 100 [arXiv:1106.5789] [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    W.T. Giele and S. Keller, Implications of hadron collider observables on parton distribution function uncertainties, Phys. Rev. D 58 (1998) 094023 [hep-ph/9803393] [INSPIRE].ADSGoogle Scholar
  4. [4]
    W.T. Giele, S.A. Keller and D.A. Kosower, Parton distribution function uncertainties, hep-ph/0104052 [INSPIRE].
  5. [5]
    NNPDF collaboration, R.D. Ball et al., Parton distributions: determining probabilities in a space of functions, arXiv:1110.1863 [INSPIRE].
  6. [6]
    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] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    CMS collaboration, S. Chatrchyan et al., Measurement of the lepton charge asymmetry in inclusive W production in pp collisions at \( \sqrt {s} = {7} \) TeV, JHEP 04 (2011) 050 [arXiv:1103.3470] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    ATLAS collaboration, G. Aad et al., Measurement of the inclusive W ± and Z/γ * cross sections in the electron and muon decay channels in pp collisions at \( \sqrt {s} = {7} \) TeV with the ATLAS detector, Phys. Rev. D 85 (2012) 072004 [arXiv:1109.5141] [INSPIRE].ADSGoogle Scholar
  9. [9]
    J. Pumplin et al., Uncertainties of predictions from parton distribution functions. 2. The Hessian method, Phys. Rev. D 65 (2001) 014013 [hep-ph/0101032] [INSPIRE].ADSGoogle Scholar
  10. [10]
    J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis, JHEP 07 (2002) 012 [hep-ph/0201195] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A.D. Martin, R.G. Roberts, W.J. Stirling and R.S. Thorne, Uncertainties of predictions from parton distributions. 1: Experimental errors, Eur. Phys. J. C 28 (2003) 455 [hep-ph/0211080] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    J.C. Collins and J. Pumplin, Tests of goodness of fit to multiple data sets, hep-ph/0105207 [INSPIRE].
  13. [13]
    Particle Data Group collaboration, K. Nakamura et. al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].ADSGoogle Scholar
  14. [14]
    R. Devenish and A. Cooper-Sarkar, Deep inelastic scattering, Oxford University Press, Oxford U.K. (2004) [INSPIRE].Google Scholar
  15. [15]
    J. Feltesse, A. Glazov and V. Radescu, Experimental error propagation, in Parton distributions, M. Dittmar et al. eds., arXiv:0901.2504 [INSPIRE].
  16. [16]
    W.K. Tung et al., Heavy quark mass effects in deep inelastic scattering and global QCD analysis, JHEP 02 (2007) 053 [hep-ph/0611254] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    J. Pumplin, Parametrization dependence and Δχ 2 in parton distribution fitting, Phys. Rev. D 82 (2010) 114020 [arXiv:0909.5176] [INSPIRE].ADSGoogle Scholar
  18. [18]
    A. Glazov, S. Moch and V. Radescu, Parton distribution uncertainties using smoothness prior, Phys. Lett. B 695 (2011) 238 [arXiv:1009.6170] [INSPIRE].ADSGoogle Scholar
  19. [19]
    H1 and ZEUS collaborations, F. Aaron et al., Combined measurement and QCD analysis of the inclusive e ± p scattering cross sections at HERA, JHEP 01 (2010) 109 [arXiv:0911.0884] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    H1 and ZEUS collaborations, PDF fits including HERA-II high Q 2 data, H1prelim-10-142, ZEUS-prel-10-018 (2010).Google Scholar
  21. [21]
    H1 and ZEUS collaborations, HERAPDF1.5 NNLO, H1prelim-11-042, ZEUS-prel-11-002 (2011).Google Scholar
  22. [22]
    G. Watt, MSTW PDFs and impact of PDFs on cross sections at Tevatron and LHC, Nucl. Phys. Proc. Suppl. 222224 (2012) 61 [arXiv:1201.1295] [INSPIRE].CrossRefGoogle Scholar
  23. [23]
    NNPDF collaboration, R.D. Ball et al., Unbiased global determination of parton distributions and their uncertainties at NNLO and at LO, Nucl. Phys. B 855 (2012) 153 [arXiv:1107.2652] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    J. Pumplin, Experimental consistency in parton distribution fitting, Phys. Rev. D 81 (2010) 074010 [arXiv:0909.0268] [INSPIRE].ADSGoogle Scholar
  25. [25]
    ATLAS collaboration, G. Aad et al., Determination of the strange quark density of the proton from ATLAS measurements of the Wℓν and Zℓℓ cross sections, Phys. Rev. Lett. 109 (2012) 012001 [arXiv:1203.4051] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    N. Hartland, LHC data and the proton strangeness, arXiv:1205.3508 [INSPIRE].
  27. [27]
    S. Alekhin, Extraction of parton distributions and α s from DIS data within the Bayesian treatment of systematic errors, Eur. Phys. J. C 10 (1999) 395 [hep-ph/9611213] [INSPIRE].ADSGoogle Scholar
  28. [28]
    F. De Lorenzi, Parton distribution function sensitivity studies using electroweak processes at LHCb, arXiv:1011.4260 [INSPIRE].
  29. [29]
    F. De Lorenzi, Parton distribution function studies and a measurement of Drell-Yan produced muon pairs at LHCb, Ph.D. Thesis, University College Dublin, Dublin Ireland (2011), CERN-THESIS-2011-237.
  30. [30]
    J. Pumplin et al., Collider inclusive jet data and the gluon distribution, Phys. Rev. D 80 (2009) 014019 [arXiv:0904.2424] [INSPIRE].ADSGoogle Scholar
  31. [31]
    S. Forte, Parton distributions at the dawn of the LHC, Acta Phys. Polon. B 41 (2010) 2859 [arXiv:1011.5247] [INSPIRE].Google Scholar
  32. [32]
    NNPDF collaboration, R.D. Ball et al., Reweighting NNPDFs: the W lepton asymmetry, Nucl. Phys. B 849 (2011) 112 [Erratum ibid. B 854 (2012) 926] [arXiv:1012.0836] [INSPIRE].
  33. [33]
    NNPDF collaboration, R.D. Ball et al., Reweighting and unweighting of parton distributions and the LHC W lepton asymmetry data, Nucl. Phys. B 855 (2012) 608 [arXiv:1108.1758] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    CMS collaboration, Measurement of the muon charge asymmetry in inclusive W production in pp collisions at \( \sqrt {s} = {7} \) TeV, CMS PAS EWK-11-005 (2011).
  36. [36]
    CMS collaboration, Measurement of the electron charge asymmetry in inclusive W production in pp collisions at \( \sqrt {s} = {7} \) TeV, CMS PAS SMP-12-001 (2012).
  37. [37]
    LHCb collaboration, R. Aaij et al., Inclusive W and Z production in the forward region at \( \sqrt {s} = {7} \) TeV, JHEP 06 (2012) 058 [arXiv:1204.1620] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    R.S. Thorne, A.D. Martin, W.J. Stirling and G. Watt, The effects of combined HERA and recent Tevatron Wℓν charge asymmetry data on the MSTW PDFs, PoS(DIS 2010)052 [arXiv:1006.2753] [INSPIRE].
  39. [39]
    A. De Roeck and R.S. Thorne, Structure functions, Prog. Part. Nucl. Phys. 66 (2011) 727 [arXiv:1103.0555] [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© SISSA 2012

Authors and Affiliations

  1. 1.Theory Group, Physics Department, CERNGeneva 23Switzerland
  2. 2.Department of Physics and AstronomyUniversity College LondonLondonU.K.

Personalised recommendations