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Kaon gluon parton distribution and momentum fraction from 2+1+1 lattice QCD with high statistics

Alex NieMiera1,2,*, William Good1,2, and Huey-Wen Lin1

  • *Contact author: niemiera@msu.edu
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Phys. Rev. D 112, 074504 – Published 14 October, 2025

DOI: https://doi.org/10.1103/89mq-gx33

Abstract

We present a high-statistics lattice-QCD determination of the kaon gluon parton distribution function and gluon momentum fraction. We use clover valence fermion action to take 1,296,640 kaon-correlator measurements on a highly improved staggered quark ensemble with a≈0.12  fm and 310-MeV pion mass generated by the MILC Collaboration. A detailed investigation into the impact of gauge-link smearing on the gluonic matrix elements indicates that five steps of hypercubic smearing offer an effective balance between signal quality and preservation of long-distance physics. We report a nonperturbatively renormalized kaon gluon momentum fraction of ⟨x⟩gMS¯,K=0.557(18)stat(24)NPR(56)mixing at μ=2  GeV in the MS¯ scheme. Using reduced pseudo-Ioffe-time-distribution matrix elements and pseudo-parton-distribution-function (PDF) matching, we extract the kaon gluon PDF and compare with the prediction from the Dyson-Schwinger equation and with the pion PDF obtained from the same ensemble.

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References (39)

  1. P. Achenbach et al., The present and future of QCD, Nucl. Phys. A1047, 122874 (2024).
  2. J. Arrington et al., Revealing the structure of light pseudoscalar mesons at the electron–ion collider, J. Phys. G 48, 075106 (2021).
  3. Arlene C. Aguilar et al., Pion and kaon structure at the electron-ion collider, Eur. Phys. J. A 55, 190 (2019).
  4. Xiangdong Ji, Parton physics on a euclidean lattice, Phys. Rev. Lett. 110, 262002 (2013).
  5. Ian Balitsky, Wayne Morris, and Anatoly Radyushkin, Gluon pseudo-distributions at short distances: Forward case, Phys. Lett. B 808, 135621 (2020).
  6. Jian-Hui Zhang, Luchang Jin, Huey-Wen Lin, Andreas Schäfer, Peng Sun, Yi-Bo Yang, Rui Zhang, Yong Zhao, and Jiunn-Wei Chen, Kaon distribution amplitude from lattice QCD and the flavor SU(3) symmetry, Nucl. Phys. B 939, 429 (2019).
  7. Rui Zhang, Carson Honkala, Huey-Wen Lin, and Jiunn-Wei Chen, Pion and kaon distribution amplitudes in the continuum limit, Phys. Rev. D 102, 094519 (2020).
  8. Jun Hua et al., Pion and kaon distribution amplitudes from lattice QCD, Phys. Rev. Lett. 129, 132001 (2022).
  9. Ian Cloet, Xiang Gao, Swagato Mukherjee, Sergey Syritsyn, Nikhil Karthik, Peter Petreczky, Rui Zhang, and Yong Zhao, Lattice QCD calculation of x-dependent meson distribution amplitudes at physical pion mass with threshold logarithm resummation, Phys. Rev. D 110, 114502 (2024).
  10. Huey-Wen Lin, Jiunn-Wei Chen, Zhouyou Fan, Jian-Hui Zhang, and Rui Zhang, Valence-quark distribution of the kaon and pion from lattice QCD, Phys. Rev. D 103, 014516 (2021).
  11. Constantia Alexandrou, Simone Bacchio, Ian Cloet, Martha Constantinou, Kyriakos Hadjiyiannakou, Giannis Koutsou, and Colin Lauer, Mellin moments ⟨x⟩ and ⟨x2⟩ for the pion and kaon from lattice QCD, Phys. Rev. D 103, 014508 (2021).
  12. Constantia Alexandrou, Simone Bacchio, Ian Cloët, Martha Constantinou, Kyriakos Hadjiyiannakou, Giannis Koutsou, and Colin Lauer, Pion and kaon ⟨x3⟩ from lattice QCD and PDF reconstruction from Mellin moments, Phys. Rev. D 104, 054504 (2021).
  13. Constantia Alexandrou et al., Quark and gluon momentum fractions in the pion and in the kaon, Phys. Rev. Lett. 134, 131902 (2025).
  14. Alejandro Salas-Chavira, Zhouyou Fan, and Huey-Wen Lin, First glimpse into the kaon gluon parton distribution using lattice QCD, Phys. Rev. D 106, 094510 (2022).
  15. E. Follana, Q. Mason, C. Davies, K. Hornbostel, G. P. Lepage, J. Shigemitsu, H. Trottier, and K. Wong, Highly improved staggered quarks on the lattice, with applications to charm physics, Phys. Rev. D 75, 054502 (2007).
  16. A. Bazavov et al., Lattice QCD ensembles with four flavors of highly improved staggered quarks, Phys. Rev. D 87, 054505 (2013).
  17. Gunnar S. Bali, Bernhard Lang, Bernhard U. Musch, and Andreas Schäfer, Novel quark smearing for hadrons with high momenta in lattice QCD, Phys. Rev. D 93, 094515 (2016).
  18. P. E. Shanahan and W. Detmold, Gluon gravitational form factors of the nucleon and the pion from lattice QCD, Phys. Rev. D 99, 014511 (2019).
  19. Constantia Alexandrou et al., Quark and gluon momentum fractions in the pion from Nf=2+1+1 lattice QCD, Phys. Rev. Lett. 127, 252001 (2021).
  20. Zhouyou Fan, Huey-Wen Lin, and Matthew Zeilbeck, Nonperturbatively renormalized nucleon gluon momentum fraction in the continuum limit of Nf=2+1+1 lattice QCD, Phys. Rev. D 107, 034505 (2023).
  21. Daniel C. Hackett, Patrick R. Oare, Dimitra A. Pefkou, and Phiala E. Shanahan, Gravitational form factors of the pion from lattice QCD, Phys. Rev. D 108, 114504 (2023).
  22. William Good, Kinza Hasan, Allison Chevis, and Huey-Wen Lin, Gluon moment and parton distribution function of the pion from Nf=2+1+1 lattice QCD, Phys. Rev. D 109, 114509 (2024).
  23. Tanjib Khan et al., Unpolarized gluon distribution in the nucleon from lattice quantum chromodynamics, Phys. Rev. D 104, 094516 (2021).
  24. Zhouyou Fan, William Good, and Huey-Wen Lin, Gluon parton distribution of the nucleon from (2+1+1)-flavor lattice QCD in the physical-continuum limit, Phys. Rev. D 108, 014508 (2023).
  25. Joseph Delmar, Constantia Alexandrou, Krzysztof Cichy, Martha Constantinou, and Kyriakos Hadjiyiannakou, Gluon PDF of the proton using twisted mass fermions, Phys. Rev. D 108, 094515 (2023).
  26. Martin Lüscher, Properties and uses of the Wilson flow in lattice QCD, J. High Energy Phys. 08 (2010) 071; 03 (2014) 92.
  27. Anna Hasenfratz and Francesco Knechtli, Flavor symmetry and the static potential with hypercubic blocking, Phys. Rev. D 64, 034504 (2001).
  28. Colin Morningstar and Mike J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69, 054501 (2004).
  29. William Good and Huey-Wen Lin, How gluon pseudo-PDF matrix elements depend on gauge smearing, Proc. Sci., LATTICE2023 (2024) 330.
  30. Zhouyou Fan and Huey-Wen Lin, Gluon parton distribution of the pion from lattice QCD, Phys. Lett. B 823, 136778 (2021).
  31. William Good, Kinza Hasan, and Huey-Wen Lin, Toward the first gluon parton distribution from the LaMET, J. Phys. G 52, 035105 (2025).
  32. Huey-Wen Lin, Mapping parton distributions of hadrons with lattice QCD, Prog. Part. Nucl. Phys. 144, 104177 (2025).
  33. Constantia Alexandrou, Martha Constantinou, Kyriakos Hadjiyiannakou, Karl Jansen, Haralambos Panagopoulos, and Christian Wiese, Gluon momentum fraction of the nucleon from lattice QCD, Phys. Rev. D 96, 054503 (2017).
  34. Zhu-Fang Cui, Minghui Ding, Fei Gao, Khépani Raya, Daniele Binosi, Lei Chang, Craig D Roberts, Jose Rodríguez-Quintero, and Sebastian M. Schmidt, Kaon and pion parton distributions, Eur. Phys. J. C 80, 1064 (2020).
  35. Wayne Henry Morris III, Investigating gluonic operators in coordinate space, Ph.D. thesis, Old Dominion University, 2022.
  36. P. C. Barry, N. Sato, W. Melnitchouk, and Chueng-Ryong Ji, First Monte Carlo global QCD analysis of pion parton distributions, Phys. Rev. Lett. 121, 152001 (2018).
  37. P. C. Barry, Chueng-Ryong Ji, N. Sato, and W. Melnitchouk, Global QCD analysis of pion parton distributions with threshold resummation, Phys. Rev. Lett. 127, 232001 (2021).
  38. William Good, Fei Yao, and Huey-Wen Lin, First nucleon gluon PDF from large momentum effective theory, arXiv:2505.13321.
  39. Robert G. Edwards and Balint Joo, The Chroma software system for lattice QCD, Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).

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Phys. Rev. D 112, 074504– Published 14 October, 2025
  • Received 9 July 2025
  • Accepted 22 August 2025
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