Parametrisation scale invariance of Parton Distribution Function fits

TL;DR

This paper investigates whether the choice of initial scale in parton distribution function fits affects the results, confirming that PDFs are invariant under different starting scales within uncertainties.

Contribution

It demonstrates the scale invariance of PDF fits by performing multiple fits at different initial scales and showing consistent results.

Findings

PDF results are consistent across different initial scales.

Fit quality remains stable regardless of the starting scale.

Confirms theoretical expectation of scale invariance in PDF fits.

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.