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

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.