Short-flow-time expansion of non-singlet twist-two operators at next-to-next-to-leading order QCD

TL;DR

This paper computes the matching coefficients for the first six non-singlet PDF moments at NNLO in QCD within the gradient-flow formalism, facilitating more accurate lattice QCD determinations of PDFs.

Contribution

It provides the first NNLO calculation of short-flow-time expansion coefficients for non-singlet twist-two operators in the gradient-flow scheme.

Findings

Matching coefficients computed up to NNLO

Enhanced precision for lattice QCD PDF moments

Facilitates direct determination of PDFs from lattice data

Abstract

The gradient-flow formalism provides a framework for the direct determination of moments of parton distribution functions (PDFs) from lattice QCD calculations. Their conversion from the gradient-flow scheme to $\overline{\text{MS}}$ requires the matching coefficients of the short-flow-time expansion, which can be computed perturbatively. We determine these coefficients for the first six non-singlet PDF moments up to next-to-next-to-leading order in the strong coupling.