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Extraction of parton distributions and $α_s$ from DIS data within the Bayesian treatment of systematic errors

Sergey Alekhin

TL;DR

This paper demonstrates a Bayesian framework to propagate full experimental systematic uncertainties, including point-to-point correlations, into parton distributions extracted from DIS data. Using a NLO QCD global fit to BCDMS, NMC, H1, and ZEUS data with a detailed error model, the authors obtain PDFs at Q0^2 = 9 GeV^2 and a robust α_s(M_Z) = 0.1146(75% C.L.). The gluon distribution is found to be softer at moderate x than in analyses incorporating prompt-photon data, and the resulting PDFs include 75% confidence bands reflecting experimental uncertainties and model choices. The work highlights the value of Bayesian error treatment for reliable PDF uncertainties and cross-section predictions.

Abstract

We have performed the NLO QCD global fit of BCDMS, NMC, H1 and ZEUS data with full account of point-to-point correlations using the Bayesian approach to the treatment of systematic errors. Parton distributions in the proton associated with experimental uncertainties, including both statistical and systematic ones were obtained. The gluon distribution in the wide region of $x$ was determined and it turned out to be softer than in the global analysis using prompt photon data. We also obtained the robust estimate of $α_s(M_Z) = 0.1146\pm0.0036 (75% C.L.)$ based on Chebyshev's inequality, which is compatible with the earlier determination of $α_s$ from DIS data, but with less dependence on high twist effects.

Extraction of parton distributions and $α_s$ from DIS data within the Bayesian treatment of systematic errors

TL;DR

This paper demonstrates a Bayesian framework to propagate full experimental systematic uncertainties, including point-to-point correlations, into parton distributions extracted from DIS data. Using a NLO QCD global fit to BCDMS, NMC, H1, and ZEUS data with a detailed error model, the authors obtain PDFs at Q0^2 = 9 GeV^2 and a robust α_s(M_Z) = 0.1146(75% C.L.). The gluon distribution is found to be softer at moderate x than in analyses incorporating prompt-photon data, and the resulting PDFs include 75% confidence bands reflecting experimental uncertainties and model choices. The work highlights the value of Bayesian error treatment for reliable PDF uncertainties and cross-section predictions.

Abstract

We have performed the NLO QCD global fit of BCDMS, NMC, H1 and ZEUS data with full account of point-to-point correlations using the Bayesian approach to the treatment of systematic errors. Parton distributions in the proton associated with experimental uncertainties, including both statistical and systematic ones were obtained. The gluon distribution in the wide region of was determined and it turned out to be softer than in the global analysis using prompt photon data. We also obtained the robust estimate of based on Chebyshev's inequality, which is compatible with the earlier determination of from DIS data, but with less dependence on high twist effects.

Paper Structure

This paper contains 12 sections, 15 equations, 9 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical and experimental input
  3. Data used in the fit
  4. Probability model of the data
  5. QCD input
  6. Corrections to the basic formula and data
  7. Target mass correction
  8. Reduction to the common $R=\sigma_L/\sigma_T$
  9. Fermi motion correction in deuterium
  10. Results
  11. Conclusion
  12. Acknowledgements

Figures (9)

  • Figure 1: $R=\sigma_L/\sigma_T$ calculated using our resulting PDFs (solid line) and the band of $R^{1990}_{SLAC}$ [22] (dashed lines) at $Q^2=9~GeV^2$.
  • Figure 2: The description of BCDMS data with our PDFs. The data and curves are scaled by factor $1.2^{11-i}$, where $i$ runs from 1 for the highest x bin to 11 for the lowest one.
  • Figure 3: The same as in Fig.2 for the NMC data ($i$ runs from 1 to 12). For the presentation purposes we pictured combined energy data with convenient binning.
  • Figure 4: The description of H1 data with our PDFs. The data and curves are shifted by $5.1-0.3i$, where $i$ runs from 1 for the highest x bin to 16 for the lowest one.
  • Figure 5: The description of ZEUS data with our PDFs. The data and curves are shifted by $4.5-0.3i$, where $i$ runs from 1 for the highest x bin to 14 for the lowest one.
  • ...and 4 more figures