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Strange and flavor-singlet axial form factors of the nucleon from lattice QCD

Alessandro Barone1,*, Dalibor Djukanovic2,3, Georg von Hippel1, Harvey B. Meyer1,2,4, Konstantin Ottnad1,5, and Hartmut Wittig1,2

  • *Contact author: abarone@uni-mainz.de
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Phys. Rev. D 114, 034520 – Published 27 August, 2026

DOI: https://doi.org/10.1103/dgcm-4yz4

Abstract

The singlet axial form factor of the nucleon provides essential input for a complete understanding of the nucleon axial structure. Together with the isovector and isoscalar octet channels, in the forward limit it forms the basis for a full flavor decomposition of the proton spin. In this work we present a lattice QCD determination of the singlet axial form factor GAu+d+s(Q2) and related strange contribution GAs(Q2) using a set of Nf=2+1 gauge ensembles generated by the Coordinated Lattice Simulations effort with O(a)-improved Wilson fermions, with a full error budget for the extrapolation to the chiral, continuum and infinite-volume limits. Particular focus is placed on the treatment of the disconnected contributions, which constitute the crucial element for the extraction of the strange component. Together with determinations of the isovector and isoscalar octet axial form factors, this work provides a comprehensive lattice QCD determination of the nucleon axial structure across different flavor channels.

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References (67)

  1. X.-D. Ji, Phys. Rev. Lett. 78, 610 (1997).
  2. V. Y. Alexakhin et al. (COMPASS Collaboration), Phys. Lett. B 647, 8 (2007).
  3. C. A. Aidala, S. D. Bass, D. Hasch, and G. K. Mallot, Rev. Mod. Phys. 85, 655 (2013).
  4. R. Acciarri et al. (DUNE Collaboration), arXiv:1512.06148.
  5. K. Abe et al. (Hyper-Kamiokande Collaboration), arXiv:1805.04163.
  6. D. Becker et al., Eur. Phys. J. A 54, 208 (2018).
  7. V. Papavassiliou, AIP Conf. Proc. 1222, 186 (2010).
  8. T. Miceli, V. Papavassiliou, S. Pate, and K. Woodruff (MicroBooNE Collaboration), Phys. Procedia 61, 495 (2015).
  9. K. S. Kim, K.-S. Choi, M.-K. Cheoun, W. Y. So, and H. Moon, Phys. Rev. C 100, 034604 (2019).
  10. G. S. Bali, L. Barca, S. Collins, M. Gruber, M. Löffler, A. Schäfer, W. Söldner, P. Wein, S. Weishäupl, and T. Wurm (RQCD Collaboration), J. High Energy Phys. 05 (2020) 126.
  11. N. Hasan, J. Green, S. Meinel, M. Engelhardt, S. Krieg, J. Negele, A. Pochinsky, and S. Syritsyn, Phys. Rev. D 99, 114505 (2019).
  12. C. Alexandrou et al., Phys. Rev. D 103, 034509 (2021).
  13. R. Gupta, Y.-C. Jang, H.-W. Lin, B. Yoon, and T. Bhattacharya, Phys. Rev. D 96, 114503 (2017).
  14. D. Djukanovic, G. von Hippel, J. Koponen, H. B. Meyer, K. Ottnad, T. Schulz, and H. Wittig, Phys. Rev. D 106, 074503 (2022).
  15. Y.-C. Jang, R. Gupta, B. Yoon, and T. Bhattacharya, Phys. Rev. Lett. 124, 072002 (2020).
  16. O. Tomalak, R. Gupta, and T. Bhattacharya, Phys. Rev. D 108, 074514 (2023).
  17. Y.-C. Jang, R. Gupta, T. Bhattacharya, B. Yoon, and H.-W. Lin (Precision Neutron Decay Matrix Elements (PNDME) Collaboration), Phys. Rev. D 109, 014503 (2024).
  18. A. S. Meyer, arXiv:2601.02676.
  19. J. Green, N. Hasan, S. Meinel, M. Engelhardt, S. Krieg, J. Laeuchli, J. Negele, K. Orginos, A. Pochinsky, and S. Syritsyn, Phys. Rev. D 95, 114502 (2017).
  20. C. Alexandrou, S. Bacchio, M. Constantinou, K. Hadjiyiannakou, K. Jansen, and G. Koutsou, Phys. Rev. D 104, 074503 (2021).
  21. J. Liang, Y.-B. Yang, T. Draper, M. Gong, and K.-F. Liu, Phys. Rev. D 98, 074505 (2018).
  22. H.-W. Lin, R. Gupta, B. Yoon, Y.-C. Jang, and T. Bhattacharya, Phys. Rev. D 98, 094512 (2018).
  23. S. Park, T. Bhattacharya, R. Gupta, Y.-C. Jang, B. Joo, H.-W. Lin, and B. Yoon, Proc. Sci. LATTICE2019 (2020) 136.
  24. C. Alexandrou, S. Bacchio, J. Finkenrath, C. Iona, G. Koutsou, Y. Li, and G. Spanoudes, Phys. Rev. D 111, 054505 (2025).
  25. A. Barone, D. Djukanovic, G. von Hippel, J. Koponen, H. B. Meyer, K. Ottnad, and H. Wittig, Proc. Sci. LATTICE2024 (2025) 334.
  26. A. Barone, D. Djukanovic, G. von Hippel, J. Koponen, H. B. Meyer, K. Ottnad, and H. Wittig, Phys. Rev. D 112, 014503 (2025).
  27. M. Bruno et al., J. High Energy Phys. 02 (2015) 043.
  28. B. Sheikholeslami and R. Wohlert, Nucl. Phys. B259, 572 (1985).
  29. M. Luscher and P. Weisz, Commun. Math. Phys. 98, 433 (1985); 98, 433(E) (1985).
  30. D. Mohler and S. Schaefer, Phys. Rev. D 102, 074506 (2020).
  31. S. Kuberski, Comput. Phys. Commun. 300, 109173 (2024).
  32. B. Strassberger et al., Proc. Sci. LATTICE2021 (2022) 135.
  33. G. S. Bali, S. Collins, P. Georg, D. Jenkins, P. Korcyl, A. Schäfer, E. E. Scholz, J. Simeth, W. Söldner, and S. Weishäupl (RQCD Collaboration), J. High Energy Phys. 05 (2023) 035 [arXiv:2211.03744].
  34. S. Gusken, U. Low, K. H. Mutter, R. Sommer, A. Patel, and K. Schilling, Phys. Lett. B 227, 266 (1989).
  35. M. Albanese et al. (APE Collaboration), Phys. Lett. B 192, 163 (1987).
  36. A. Agadjanov, D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad, and H. Wittig, Phys. Rev. Lett. 131, 261902 (2023).
  37. M. Cè, A. Gérardin, G. von Hippel, H. B. Meyer, K. Miura, K. Ottnad, A. Risch, T. San José, J. Wilhelm, and H. Wittig, J. High Energy Phys. 08 (2022) 220.
  38. J. Bulava, M. Della Morte, J. Heitger, and C. Wittemeier (ALPHA Collaboration), Nucl. Phys. B896, 555 (2015).
  39. G. S. Bali, V. Braun, S. Collins, A. Schäfer, and J. Simeth (RQCD Collaboration), J. High Energy Phys. 08 (2021) 137.
  40. M. Dalla Brida, T. Korzec, S. Sint, and P. Vilaseca, Eur. Phys. J. C 79, 23 (2019).
  41. G. S. Bali, S. Collins, S. Heybrock, M. Löffler, R. Rödl, W. Söldner, and S. Weishäupl (RQCD Collaboration), Phys. Rev. D 108, 034512 (2023).
  42. T. Bhattacharya, R. Gupta, W. Lee, S. R. Sharpe, and J. M. S. Wu, Phys. Rev. D 73, 034504 (2006).
  43. L. Maiani, G. Martinelli, M. L. Paciello, and B. Taglienti, Nucl. Phys. B293, 420 (1987).
  44. S. Capitani, M. Della Morte, G. von Hippel, B. Jager, A. Juttner, B. Knippschild, H. B. Meyer, and H. Wittig, Phys. Rev. D 86, 074502 (2012).
  45. D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad, M. Salg, and H. Wittig, Phys. Rev. D 109, 094510 (2024).
  46. S. R. Beane and M. J. Savage, Phys. Rev. D 70, 074029 (2004).
  47. Z. B. Hall et al., Phys. Rev. C 113, 055206 (2026).
  48. W. I. Jay and E. T. Neil, Phys. Rev. D 103, 114502 (2021).
  49. H. Akaike, IEEE Trans. Autom. Control 19, 716 (1974).
  50. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG), Phys. Rev. D 113, 014508 (2026).
  51. D. Djukanovic, H. Meyer, K. Ottnad, G. von Hippel, J. Wilhelm, and H. Wittig, Proc. Sci. LATTICE2019 (2019) 158. [arXiv:1911.01177].
  52. J. Ashman et al. (European Muon Collaboration), Phys. Lett. B 206, 364 (1988).
  53. J. Ashman et al. (European Muon Collaboration), Nucl. Phys. B328, 1 (1989).
  54. www.gauss-centre.eu.
  55. www.hlrs.de.
  56. R. G. Edwards and B. Joo (SciDAC, LHPC, and UKQCD Collaborations), Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).
  57. M. Luscher and S. Schaefer, Comput. Phys. Commun. 184, 519 (2013).
  58. D. Djukanovic, Comput. Phys. Commun. 247, 106950 (2020).
  59. T. Harris, G. von Hippel, P. Junnarkar, H. B. Meyer, K. Ottnad, J. Wilhelm, H. Wittig, and L. Wrang, Phys. Rev. D 100, 034513 (2019).
  60. J. Wilhelm, The strangeness form factors of the nucleon from lattice QCD, Ph.D. thesis, Johannes Gutenberg University Mainz, 2020.
  61. G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa, and A. Vladikas, Nucl. Phys. B445, 81 (1995).
  62. M. Gockeler, R. Horsley, H. Oelrich, H. Perlt, D. Petters, P. E. L. Rakow, A. Schafer, G. Schierholz, and A. Schiller, Nucl. Phys. B544, 699 (1999).
  63. S. J. Brodsky, G. P. Lepage, and P. B. Mackenzie, Phys. Rev. D 28, 228 (1983).
  64. G. P. Lepage and P. B. Mackenzie, Phys. Rev. D 48, 2250 (1993).
  65. S. A. Larin, Phys. Lett. B 303, 113 (1993).
  66. S. A. Larin and J. A. M. Vermaseren, Phys. Lett. B 303, 334 (1993).
  67. M. Dalla Brida, R. Höllwieser, F. Knechtli, T. Korzec, A. Ramos, S. Sint, and R. Sommer, Nature (London) 652, 328 (2026).

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Phys. Rev. D 114, 034520– Published 27 August, 2026
  • Received 22 May 2026
  • Accepted 30 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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