Open Access

DGLAP evolution at $N^{3} LO$ with the candia algorithm

Department of Physics, Kennesaw State University, Kennesaw, Georgia 30144, USA

^*Contact author: champso1@students.kennesaw.edu
^†Contact author: mguzzi@kennesaw.edu

Phys. Rev. D 113, 074008 – Published 6 April, 2026

DOI: https://doi.org/10.1103/p6vv-8zph

Abstract

We present a generalization of the $x$ -space candia algorithm to next-to-next-to-next-to-leading order ( $N^{3} LO$ ) accuracy in quantum chromodynamics (QCD) for solving the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations for unpolarized parton densities in the nucleon. The algorithm is based on logarithmic expansions of the solution and can be extended to all orders in QCD. An expansion equivalent to the exact solution of the DGLAP equation at $N^{3} LO$ is presented in the non-singlet sector. Results for approximate $N^{3} LO$ parton distribution functions, evolved using the most recent approximations to the $N^{3} LO$ DGLAP splitting functions, are provided for benchmarking. The new version of the code, candia-v2, is publicly available [github, candia-v2, (2025).].

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Phys. Rev. D 113, 074008– Published 6 April, 2026

Vol. 113, Iss. 7 — 1 April 2026

Received 11 January 2026
Accepted 13 March 2026

DOI: https://doi.org/10.1103/p6vv-8zph

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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DGLAP evolution at $N^{3} LO$ with the candia algorithm

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DGLAP evolution at N3LO with the candia algorithm

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DGLAP evolution at $N^{3} LO$ with the candia algorithm