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Gradient Flow for Parton Distribution Functions: First Application to the Pion

Anthony Francis1, Patrick Fritzsch2, Robert V. Harlander3, Rohith Karur4,5, Jangho Kim6, Jonas T. Kohnen3, Giovanni Pederiva7,8, Dimitra A. Pefkou4,5,*, Antonio Rago9 et al.

Andrea Shindler3,5,4,†, André Walker-Loud5,4, and Savvas Zafeiropoulos10

  • *Contact author: dpefkou@berkeley.edu
  • †Contact author: shindler@physik.rwth-aachen.de
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Phys. Rev. Lett. 136, 171903 – Published 29 April, 2026

DOI: https://doi.org/10.1103/z3wr-zk8n

Abstract

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 nonsinglet pion PDF moments up to ⟨x5⟩ on four lattice spacings at mπ≃411  MeV. The moments and reconstructed PDF agree quantitatively with recent phenomenological extractions.

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Moments of parton distribution functions of the pion from lattice QCD using gradient flow

Anthony Francis, Patrick Fritzsch, Rohith Karur, Jangho Kim, Giovanni Pederiva, Dimitra A. Pefkou, Antonio Rago, Andrea Shindler, André Walker-Loud, and Savvas Zafeiropoulos
Phys. Rev. D 113, 074520 (2026)

Article Text

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Outline

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Phys. Rev. Lett. 136, 171903– Published 29 April, 2026
  • Received 13 November 2025
  • Revised 2 March 2026
  • Accepted 20 March 2026
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