Gradient flow for parton distribution functions: first application to the pion

Parton distribution functions (PDFs) are central to precision QCD phenomenology. Their Mellin moments can be computed on the lattice, but direct determinations using local operators, besides $⟨x⟩$, face severe challenges from reduced hypercubic symmetry, limiting results to the lowest moments. A recently proposed method resolves these issues using gradient flow. We demonstrate the efficacy of this method by computing ratios of flavor non-singlet pion PDF moments up to $⟨x^5⟩$, on four lattice spacings at $m_{\pi }\simeq 411$ MeV. The moments and reconstructed PDF agree quantitatively with recent phenomenological extractions.