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

Anthony Francis; Patrick Fritzsch; Robert V. Harlander; Rohith Karur; Jangho Kim; Jonas T. Kohnen; Giovanni Pederiva; Dimitra A. Pefkou; Antonio Rago; Andrea Shindler; André Walker-Loud; Savvas Zafeiropoulos

doi:10.1103/z3wr-zk8n

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

Anthony Francis
, Patrick Fritzsch
, Robert V. Harlander
, Rohith Karur
, Jangho Kim
, Jonas T. Kohnen
, Giovanni Pederiva
, Dimitra A. Pefkou^*
, Antonio Rago
, Andrea Shindler
, André Walker-Loud
, Savvas Zafeiropoulos

^*Corresponding author for this work

National Chiao Tung University
Trinity College Dublin
RWTH Aachen University
University of California
Seoul National University
Forschungszentrum Jülich
University of Toulon

Research output: Contribution to journal › Journal article › Research › peer-review

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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 m_π≃411 MeV. The moments and reconstructed PDF agree quantitatively with recent phenomenological extractions.

Original language	English
Article number	171903
Journal	Physical Review Letters
Volume	136
Issue number	17
Number of pages	12
ISSN	0031-9007
DOIs	https://doi.org/10.1103/z3wr-zk8n
Publication status	Published - May 2026

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10.1103/z3wr-zk8nLicence: CC BY

Open Access VersionFinal published version, 1.32 MBLicence: CC BY

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@article{4ee1f92353f3453da0f0c684778c88f0,

title = "Gradient Flow for Parton Distribution Functions: First Application to the Pion",

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.",

author = "Anthony Francis and Patrick Fritzsch and Harlander, \{Robert V.\} and Rohith Karur and Jangho Kim and Kohnen, \{Jonas T.\} and Giovanni Pederiva and Pefkou, \{Dimitra A.\} and Antonio Rago and Andrea Shindler and Andr{\'e} Walker-Loud and Savvas Zafeiropoulos",

year = "2026",

month = may,

doi = "10.1103/z3wr-zk8n",

language = "English",

volume = "136",

journal = "Physical Review Letters",

issn = "0031-9007",

publisher = "American Physical Society",

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TY - JOUR

T1 - Gradient Flow for Parton Distribution Functions

T2 - First Application to the Pion

AU - Francis, Anthony

AU - Fritzsch, Patrick

AU - Harlander, Robert V.

AU - Karur, Rohith

AU - Kim, Jangho

AU - Kohnen, Jonas T.

AU - Pederiva, Giovanni

AU - Pefkou, Dimitra A.

AU - Rago, Antonio

AU - Shindler, Andrea

AU - Walker-Loud, André

AU - Zafeiropoulos, Savvas

PY - 2026/5

Y1 - 2026/5

N2 - 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.

AB - 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.

U2 - 10.1103/z3wr-zk8n

DO - 10.1103/z3wr-zk8n

M3 - Journal article

C2 - 42139470

AN - SCOPUS:105037582550

SN - 0031-9007

VL - 136

JO - Physical Review Letters

JF - Physical Review Letters

IS - 17

M1 - 171903

ER -

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

Abstract

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