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Mellin moments of pion and kaon unpolarized PDFs from nonlocal operators in lattice QCD

Joshua Miller1,*, Joseph Torsiello1, Krzysztof Cichy2, Martha Constantinou1,†, and Joseph Delmar1,3

  • *Contact author: joshua.miller0007@temple.edu
  • †Contact author: marthac@temple.edu
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Phys. Rev. D 114, 054508 – Published 23 September, 2026

DOI: https://doi.org/10.1103/fw2x-3hl3

Abstract

We present a first-principles lattice-QCD determination of Mellin moments of the unpolarized pion and kaon parton distribution functions using matrix elements of boosted mesons coupled to nonlocal operators containing a straight Wilson line. The calculation is performed on a single Nf=2+1+1 ensemble of maximally twisted-mass fermions with a clover term, with lattice volume 323×64, lattice spacing a=0.0934  fm, and pion mass mπ=260  MeV. Matrix elements are computed for hadron momenta P3=0, 0.41, 0.83, 1.25, 1.66, and 2.07 GeV and analyzed within the short-distance factorization framework. We investigate how the extracted moments depend on the truncation of the operator-product expansion, the coordinate-space fit window, and the perturbative accuracy of the Wilson coefficients, comparing next-to-leading-order and next-to-next-to-leading-order results. We also perform an RG-improved analysis as a consistency check of the perturbative treatment. Our final results are obtained from combined fits in (P3,z) space at next-to-next-to-leading order and are quoted at μ=2  GeV. We also study the SU(3) symmetry-breaking effect and reconstruct the valence parton distribution functions from the moments.

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Phys. Rev. D 114, 054508– Published 23 September, 2026
  • Received 2 July 2026
  • Accepted 1 September 2026
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