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Accessing the gluon momentum fraction of nucleons through the gradient flow

Robert Edwards1, Joe Karpie1, Lorenzo Maio2, Christopher J. Monahan3, Kostas Orginos4, David Richards1, Alexandru M. Sturzu4,*, and Savvas Zafeiropoulos5 (HadStruc Collaboration)

  • *Contact author: amsturzu@wm.edu
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Phys. Rev. D 114, 014516 – Published 22 July, 2026

DOI: https://doi.org/10.1103/3cc3-mnbs

Abstract

We calculate the gluon momentum fraction of the nucleon using lattice QCD, with a nonperturbative renormalization technique based on the gradient flow. The gluon momentum fraction is determined on a single Wilson-clover ensemble using Nf=2+1 flavors with pion mass 358 MeV and lattice spacing 0.094 fm. We employ the variational method to reduce excited-state contamination and apply the distillation framework to ensure a large operator basis. To reduce systematic uncertainties, we apply Bayesian model averaging to all fit procedures. We apply matching coefficients to the flow-time dependent lattice results to recover the gluon momentum fraction in the MS¯-scheme at 2 GeV. Our final result is ⟨x⟩g(μ=2  GeV)=0.482(35), where we quote only statistical uncertainties.

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Phys. Rev. D 114, 014516– Published 22 July, 2026
  • Received 16 March 2026
  • Accepted 5 June 2026
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