DGLAP evolution at N$^3$LO with the $\texttt{Candia}$ algorithm

TL;DR

This paper extends the Candia algorithm to N$^3$LO accuracy in QCD for solving DGLAP equations, enabling precise evolution of parton densities with a publicly available code for benchmarking and future extensions.

Contribution

The paper introduces a generalized Candia algorithm at N$^3$LO, providing a new method for solving DGLAP equations with higher precision in QCD.

Findings

Provides approximate N$^3$LO PDFs for benchmarking.

Presents an exact solution expansion in the non-singlet sector.

Code version Candia-v2 is publicly available.

Abstract

We present a generalization of the $x$-space $\texttt{Candia}$ algorithm to next-to-next-to-next-to-leading order (N$^3$LO) accuracy in Quantum Chromodynamics (QCD) for solving the 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 PDFs, evolved using the most recent approximations to the N$^3$LO DGLAP splitting functions, are provided for benchmarking. The new version of the code, $\texttt{Candia-v2}$, is publicly available at https://github.com/champso1/candia-v2.