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Parton Distribution Function Uncertainties

Walter T. Giele, Stephane A. Keller, David A. Kosower

TL;DR

This paper introduces a quantitative framework for parton distribution function (PDF) uncertainties by representing them as a density over the PDF functional space. It develops an optimized Monte Carlo approach that integrates theory priors, experimental response functions, and detector systematics to produce ensembles of PDFs whose spread encodes uncertainties and can propagate to observables. The method is applied to proton F2 data and an alpha_S benchmark, yielding multiple optimized PDF sets (based on an MRST-like parameterization) and revealing tensions among experiments and between DIS data and Tevatron jet results. The authors discuss limitations of the current parameterization and outline future directions to broaden the approach, including nuclear effects and more flexible functional forms, with implications for hadron collider phenomenology.

Abstract

We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density measure over the functional space of parton distribution functions. This leads to a convenient method of propagating the parton distribution function uncertainties to new observables, now expressing the uncertainty as a density in the prediction of the observable. New measurements can easily be included in the optimized sets as added weight functions to the density measure. Using the optimized method nowhere in the analysis compromises have to be made with regard to the treatment of the uncertainties.

Parton Distribution Function Uncertainties

TL;DR

This paper introduces a quantitative framework for parton distribution function (PDF) uncertainties by representing them as a density over the PDF functional space. It develops an optimized Monte Carlo approach that integrates theory priors, experimental response functions, and detector systematics to produce ensembles of PDFs whose spread encodes uncertainties and can propagate to observables. The method is applied to proton F2 data and an alpha_S benchmark, yielding multiple optimized PDF sets (based on an MRST-like parameterization) and revealing tensions among experiments and between DIS data and Tevatron jet results. The authors discuss limitations of the current parameterization and outline future directions to broaden the approach, including nuclear effects and more flexible functional forms, with implications for hadron collider phenomenology.

Abstract

We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density measure over the functional space of parton distribution functions. This leads to a convenient method of propagating the parton distribution function uncertainties to new observables, now expressing the uncertainty as a density in the prediction of the observable. New measurements can easily be included in the optimized sets as added weight functions to the density measure. Using the optimized method nowhere in the analysis compromises have to be made with regard to the treatment of the uncertainties.

Paper Structure

This paper contains 11 sections, 19 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The Method
  3. The Model Priors
  4. The Experimental Response Function
  5. The Optimized Monte Carlo Approach
  6. Comparison Methodology
  7. The Optimized Sets
  8. The Parameterization Choice
  9. The $F_2^{proton}$ and $\alpha_S$ Data Optimized Sets
  10. Some PDF set Results
  11. Conclusions and Outlook

Figures (3)

  • Figure 1: The H1-MRST set parameter distributions (histograms) together with the gaussian approximation (red curve) and the central MRST fit result MRST (blue bar). In addition the log-likelyhood $\Delta L^2$ distribution (histogram) and the $\chi^2$ probability distribution approximation (red curve) is shown. Note that the last 5 parameters are the detector model parameters of H1 H1 together with the prior probability distribution for this parameter (green curve). The green curve for the $\alpha_S$ result is the LEP value alphas
  • Figure 2: The squared renormalization/factorization scale distribution of the optimized sets. The horizontal axis is the squared ratio of the scale and the momentum transfer.
  • Figure 3: The ratio of the optimized PDF sets (blue) and CTEQ5M (green) over MRS99 at a scale of 10 GeV. The dashed red curves are the two MRS99 sets with $\alpha_S$$(M_Z)$ values of 0.1125 and 0.1225. The left column is the charged summed combination of PDF's , while the right column ratio of the gluon PDF .