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

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 $$\overline{\text {MS}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mtext>MS</mml:mtext> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> 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.