Uncertainties of predictions from parton distribution functions. I. The Lagrange multiplier method

2001/01/31 by D. Stump, Daniel R. Stump, J. Pumplin +7 · 9 citations
Physics and Astronomy · #Distribution function #High-Energy Particle Collisions Research #Lagrange multiplier #Large Hadron Collider #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Statistical physics #Tevatron #hep-ph

paper · pdf · doi:10.1103/physrevd.65.014012

published as Phys.Rev.D65:014012,2001 · 36 pages, 12 figures, LaTeX; CERN preprint number added. Tables in Appendix C have been corrected; the calculation of W production at the LHC has been replaced by one with fixed normalization factors

arxiv created 2001/02/05 · openalex publication_date 2001/12/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We apply the Lagrange multiplier method to study the uncertainties of physical predictions due to the uncertainties of parton distribution functions (PDF's), using the cross section \ensuremathσ_W for W production at a hadron collider as an archetypal example. An effective \ensuremathχ² function based on the CTEQ global QCD analysis is used to generate a series of PDF's, each of which represents the best fit to the global data for some specified value of \ensuremathσ_W. By analyzing the likelihood of these ``alterative hypotheses,'' using available information on errors from the individual experiments, we estimate that the fractional uncertainty of \ensuremathσ_W due to current experimental input to the PDF analysis is approximately \ifmmode±\else\textpm\fi4% at the Fermilab Tevatron, and \ifmmode±\else\textpm\fi8--10% at the CERN Large Hadron Collider. We give sets of PDF's corresponding to these up and down variations of \ensuremathσ_W. We also present similar results on Z production at the colliders. Our method can be applied to any combination of physical variables in precision QCD phenomenology, and it can be used to generate benchmarks for testing the accuracy of approximate methods based on the error matrix.

Citations

• Field Theories for Learning Probability Distributions
• Uncertainties of predictions from parton distribution functions. II. The Hessian method
• Review of Particle Physics

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