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Parametrisation scale invariance of Parton Distribution Function fits

Ivan A. Godino, Eva D. Z. Groenendijk, Tanjona R. Rabemananjara

TL;DR

Problem addressed: whether PDFs from global fits depend on the input scale $Q_0$. Approach: perform fits with $Q_0 \in {1.0,1.25,1.5,1.65}$ GeV within the NNPDF4.0 framework, below the charm threshold, and compare fit quality, PDFs at $Q=1.65$ GeV, and the small- and large-$x$ exponents. Findings: results show consistency of the experimental chi^2, PDFs at $Q=1.65$ GeV within uncertainties across all $Q_0$, slight low-scale differences in the gluon disappear at higher scales, and invariant asymptotic exponents. Significance: confirms the scale-invariance of pQCD evolution in practical PDF determinations and demonstrates the robustness and flexibility of the NNPDF approach for global analyses.

Abstract

In global PDF analyses, parton distribution functions (PDFs) are parametrised at a fixed input scale $Q_0$ and evolved to higher scales using the DGLAP equations. Since QCD evolution is fully determined within perturbation theory, the fitted PDFs should, in principle, be independent of the arbitrary choice of $Q_0$. In this work, we test this within the NNPDF framework by performing a series of fits at different starting scales, namely $Q_0 \in {1.0, 1.25, 1.5, 1.65}$ GeV. We find that the resulting PDFs are consistent within uncertainties and the fit quality remains stable across this range, therefore confirming the invariance of PDF determinations with respect to the choice of starting scale.

Parametrisation scale invariance of Parton Distribution Function fits

TL;DR

Problem addressed: whether PDFs from global fits depend on the input scale . Approach: perform fits with GeV within the NNPDF4.0 framework, below the charm threshold, and compare fit quality, PDFs at GeV, and the small- and large- exponents. Findings: results show consistency of the experimental chi^2, PDFs at GeV within uncertainties across all , slight low-scale differences in the gluon disappear at higher scales, and invariant asymptotic exponents. Significance: confirms the scale-invariance of pQCD evolution in practical PDF determinations and demonstrates the robustness and flexibility of the NNPDF approach for global analyses.

Abstract

In global PDF analyses, parton distribution functions (PDFs) are parametrised at a fixed input scale and evolved to higher scales using the DGLAP equations. Since QCD evolution is fully determined within perturbation theory, the fitted PDFs should, in principle, be independent of the arbitrary choice of . In this work, we test this within the NNPDF framework by performing a series of fits at different starting scales, namely GeV. We find that the resulting PDFs are consistent within uncertainties and the fit quality remains stable across this range, therefore confirming the invariance of PDF determinations with respect to the choice of starting scale.

Paper Structure

This paper contains 7 sections, 3 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Method
  3. Results
  4. Fit quality for different starting scales
  5. PDF comparison
  6. Asymptotic exponents
  7. Conclusion

Figures (3)

  • Figure 1: The effect of choosing a different parametrisation scale for fitting the up, down and strange quark PDF and the gluon PDF. The comparison is between parametrisation scales of $1.0, 1.25, 1.5$ and $1.65$ GeV. All PDFs are shown at the scale $Q=1.65$ GeV.
  • Figure 2: The distance of the central values of the evolution basis PDFs with $Q_0=1.0$ (left) and $Q_0=1.25$ (right) from the ones with $Q_0=1.65$ GeV.
  • Figure 3: The small- and large-$x$ asymptotic exponents for the $V$ and $\Sigma$ PDFs fitted at different starting scales $Q_0 \in \{1.0,1.5,1.65\}$. The exponents are computed at the scale $Q=1.65$ GeV.