A Benchmarking of QCD Evolution at Approximate $N^3LO$

TL;DR

This paper benchmarks various implementations of QCD evolution at approximate N^3LO order in the coupling, comparing their effects on toy PDFs to assess consistency and accuracy across different global PDF fitting groups.

Contribution

It provides a detailed comparison of different approximate N^3LO QCD evolution implementations in public PDF fitting frameworks, highlighting their agreement and differences.

Findings

Consistent evolution results across different implementations

Identification of small discrepancies at N^3LO approximation level

Enhanced understanding of QCD evolution uncertainties at high order

Abstract

We present a detailed benchmarking of different treatments of the QCD evolution of unpolarized PDFs at approximate $N^3LO$ ($aN^3LO$) order in the QCD coupling. Namely, the implementations in the public $aN^3LO$ releases of the MSHT and NNPDF global PDF fitters, as well as that of the theoretical FHMRUVV collaboration are compared. This follows the same procedure as in previous benchmarking exercises at lower order, that is by considering the impact of this evolution on a set of simple toy PDFs.