Journal Article

FZJ-2026-04484

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Moments of parton distribution functions of the pion from lattice QCD using gradient flow

Francis, A. ; Fritzsch, P. ; Karur, R. ; Kim, J. ; Pederiva, G.FZJ* ; Pefkou, D. A. (Corresponding author) ; Rago, A. ; Shindler, A. (Corresponding author) ; Walker-Loud, A. ; Zafeiropoulos, S.

2026
American Physical Society Ridge, NY, USA

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Please use a persistent id in citations: doi:10.1103/vw4v-nyvw  doi:10.34734/FZJ-2026-04484

Abstract: We present a nonperturbative determination of the pion valence parton distribution function (PDF) moment ratios $\left\langle x^{n-1} \right\rangle / \left\langle x \right\rangle$ up to $n=6$, using the gradient flow in lattice QCD. As a testing ground, we employ SU($3$) isosymmetric gauge configurations generated by the OpenLat initiative with a pseudoscalar mass of $m_π\simeq 411~\text{MeV}$. Our analysis uses four lattice spacings and a nonperturbatively improved action, enabling full control over the continuum extrapolation, and the limit of vanishing flow time, $t\to0$. The flowed ratios exhibit O($a^2$) scaling across the ensembles, and the continuum-extrapolated results, matched to the $\overline {\text{MS}}$ scheme at $μ= 2$ GeV using next-to-next-to-leading order matching coefficients, show only mild residual flow-time dependence. The resulting ratios, computed with a relatively small number of configurations, are consistent with phenomenological expectations for the pion's valence distribution, with statistical uncertainties that are competitive with modern global fits. These findings demonstrate that the gradient flow provides an efficient and systematically improvable method to access partonic quantities from first principles. Future extensions of this work will target lighter pion masses toward the physical point, and applications to nucleon structure such as the proton PDFs and the gluon and sea-quark distributions.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 5111 - Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups (POF4-511) (POF4-511)
2. DFG project G:(GEPRIS)460248186 - PUNCH4NFDI - Teilchen, Universum, Kerne und Hadronen für die NFDI (PUNCH4NFDI) (460248186) (460248186)

Appears in the scientific report 2026

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Database coverage:
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