DGLAP evolution of parton distributions at approximate N$^3$LO

TL;DR

This paper advances the precision of parton distribution functions by implementing approximate N$^3$LO DGLAP evolution, estimating uncertainties, and integrating it into the NNPDF framework for improved QCD predictions.

Contribution

It constructs a parametrisation of N$^3$LO splitting functions, estimates related uncertainties, and incorporates this into an open-source evolution code within the NNPDF framework.

Findings

aN$^3$LO splitting functions closely match exact results

The implementation enables more precise PDF evolution

Quantified impact of higher order uncertainties on PDFs

Abstract

We present recent progress towards a global determination of parton distribution functions (PDFs) at approximate N$^3$LO (aN$^3$LO) accuracy within the NNPDF framework. We construct a parametrisation of the $\mathcal{O}(\alpha_s^4)$ QCD splitting functions and anomalous dimensions reproducing all known exact results, estimate the associated missing and incomplete higher order uncertainties (MHOU and IHOU, respectively), and implement it in the open-source DGLAP code EKO enabling PDFs to be evolved at aN$^3$LO accuracy in the NNPDF fitting framework. We compare aN$^3$LO calculation of splitting functions with the results of lower perturbative orders and quantify the impact of the various sources of theoretical uncertainties.