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Study of the Uncertainty of the Gluon Distribution

J. Huston, S. Kuhlmann, H. L. Lai, F. Olness, J. F. Owens, D. E. Soper, W. K. Tung

TL;DR

This study quantifies the uncertainty in the proton's gluon distribution, which dominates many QCD predictions for hadron colliders. By performing a global QCD analysis around the CTEQ4M gluon parameterization and systematically varying key gluon parameters (including an additional medium-x term) while refitting to DIS and Drell–Yan data, the authors derive uncertainty bands for gluon–gluon and gluon–quark luminosities across x and Q^2. They find that uncertainties are modest at small-to-medium x but grow rapidly at large x, with about 7–10% uncertainty for x<0.15 at Q>100 GeV and up to ~60% in the 0.3–0.4 √τ range, underscoring the need for better large-x data. The results provide practical, energy-agnostic uncertainty benchmarks for Tevatron and LHC predictions and clarify the limitations of using direct photon or jet data to constrain the gluon under current theory and data conditions.

Abstract

The uncertainty in the calculation of many important new processes at the Tevatron and LHC is dominated by that concerning the gluon distribution function. We investigate the uncertainty in the gluon distribution of the proton by systematically varying the gluon parameters in the global QCD analysis of parton distributions. The results depend critically on the parton momentum fraction x and the QCD scale Q^2. The uncertainties are presented for integrated gluon-gluon and gluon-quark luminosities for both the Tevatron and LHC as a function of sqrt(tau)=sqrt(x1x2)=sqrt(shat/s), the most relevant quantity for new particle production. The uncertainties are reasonably small, except for large x.

Study of the Uncertainty of the Gluon Distribution

TL;DR

This study quantifies the uncertainty in the proton's gluon distribution, which dominates many QCD predictions for hadron colliders. By performing a global QCD analysis around the CTEQ4M gluon parameterization and systematically varying key gluon parameters (including an additional medium-x term) while refitting to DIS and Drell–Yan data, the authors derive uncertainty bands for gluon–gluon and gluon–quark luminosities across x and Q^2. They find that uncertainties are modest at small-to-medium x but grow rapidly at large x, with about 7–10% uncertainty for x<0.15 at Q>100 GeV and up to ~60% in the 0.3–0.4 √τ range, underscoring the need for better large-x data. The results provide practical, energy-agnostic uncertainty benchmarks for Tevatron and LHC predictions and clarify the limitations of using direct photon or jet data to constrain the gluon under current theory and data conditions.

Abstract

The uncertainty in the calculation of many important new processes at the Tevatron and LHC is dominated by that concerning the gluon distribution function. We investigate the uncertainty in the gluon distribution of the proton by systematically varying the gluon parameters in the global QCD analysis of parton distributions. The results depend critically on the parton momentum fraction x and the QCD scale Q^2. The uncertainties are presented for integrated gluon-gluon and gluon-quark luminosities for both the Tevatron and LHC as a function of sqrt(tau)=sqrt(x1x2)=sqrt(shat/s), the most relevant quantity for new particle production. The uncertainties are reasonably small, except for large x.

Paper Structure

This paper contains 7 sections, 2 equations, 7 figures, 2 tables.

Table of Contents

  1. Constraints Based on the Momentum Sum Rule
  2. Scanning the Gluon Parameters
  3. Uncertainty on the gluon-gluon luminosity function
  4. Uncertainty on the gluon-quark luminosity function
  5. Summary of gluon-gluon and gluon-quark uncertainties
  6. Comments on Other Data Sets
  7. Conclusions

Figures (7)

  • Figure 1: The gluon momentum fraction distribution is shown for Q=5 GeV and for Q=100 GeV.
  • Figure 2: The total $\chi^2$ is shown from the $A_2$ parameter scan is shown.
  • Figure 3: One example of a gluon distribution that causes clear disagreements with data is shown. Upper left is the ratio of the gluon distribution to CTEQ4M. The other three plots show the ratio of QCD predictions for three of the data sets, using the trial gluon distribution. Also indicated on these three plots are the typical data uncertainty, and the change in $\chi^2$ for this set of data.
  • Figure 4: The ratio of gluon distributions compared to CTEQ4M is shown. On top is for Q=5 GeV, and on bottom is Q=100 GeV. These are the examples that cause clear disagreements with some DIS+Drell-Yan data sets (see text).
  • Figure 5: The ratio of gluon distributions compared to CTEQ4M is shown. On top is for Q=5 GeV, and on bottom is Q=100 GeV. These are the examples that are consistent with DIS+Drell-Yan data sets (see text).
  • ...and 2 more figures