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  • Letter
  • Open Access

Current-enhanced excited states in lattice QCD three-point functions

Lorenzo Barca*

  • *Contact author: lorenzo.barca@desy.de

Phys. Rev. D 112, L091503 – Published 24 November, 2025

DOI: https://doi.org/10.1103/69yc-d74z

Abstract

Excited-state contamination remains one of the leading sources of systematic uncertainty in the precise determination of hadron structure observables from lattice QCD. In this letter, we present a general argument, inspired by meson dominance ideas and implemented through the variational method, to identify which excited states are enhanced by the choice of the inserted current and kinematics. The argument is supported by numerical evidence across multiple hadronic channels and provides both a conceptual understanding and practical guidance to account for excited-state effects in hadron three-point function analyses.

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References (50)

  1. D. C. Hackett and M. L. Wagman, Block Lanczos algorithm for lattice QCD spectroscopy and matrix elements, Phys. Rev. D 112, 014514 (2025).
  2. J. J. Sakurai, Theory of strong interactions, Ann. Phys. (N.Y.) 11, 1 (1960).
  3. J. J. Sakurai, Currents and Mesons (University of Chicago Press, Chicago, 1969).
  4. N. M. Kroll, T. D. Lee, and B. Zumino, Neutral vector mesons and the hadronic electromagnetic current, Phys. Rev. 157, 1376 (1967).
  5. R. J. Oakes and J. J. Sakurai, Spectral-function sum rules, omega- phi mixing, and lepton-pair decays of vector mesons, Phys. Rev. Lett. 19, 1266 (1967).
  6. M. Gell-Mann and F. Zachariasen, Form-factors and vector mesons, Phys. Rev. 124, 953 (1961).
  7. U. G. Meissner, Low-energy hadron physics from effective chiral Lagrangians with vector mesons, Phys. Rep. 161, 213 (1988).
  8. S. Weinberg, Precise relations between the spectra of vector and axial vector mesons, Phys. Rev. Lett. 18, 507 (1967).
  9. S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial vector current, Phys. Rev. 137, B1022 (1965).
  10. S. L. Adler, Consistency conditions on the strong interactions implied by a partially conserved axial-vector current. II, Phys. Rev. 139, B1638 (1965).
  11. G. Altarelli, N. Cabibbo, and L. Maiani, The sigma term and low-energy pi-n scattering, Nucl. Phys. B34, 621 (1971).
  12. V. Bernard, N. Kaiser, and U.-G. Meissner, Chiral dynamics in nucleons and nuclei, Int. J. Mod. Phys. E 04, 193 (1995).
  13. B. Blossier, M. Della Morte, G. von Hippel, T. Mendes, and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, J. High Energy Phys. 04 (2009) 094.
  14. C. J. Shultz, J. J. Dudek, and R. G. Edwards, Excited meson radiative transitions from lattice QCD using variationally optimized operators, Phys. Rev. D 91, 114501 (2015).
  15. J. Bulava, M. Donnellan, and R. Sommer, On the computation of hadron-to-hadron transition matrix elements in lattice QCD, J. High Energy Phys. 01 (2012) 140.
  16. See Supplemental Material at http://link.aps.org/supplemental/10.1103/69yc-d74z for a sketch of the quark-line connected and disconnected diagrams, and results on nucleon-vector matrix elements with nucleon and nucleon-vector interpolating operators. The Supplemental Material includes Ref. [17] for the construction of Nρ operators.
  17. S. Prelovsek, U. Skerbis, and C. B. Lang, Lattice operators for scattering of particles with spin, J. High Energy Phys. 01 (2017) 129.
  18. L. Barca, G. Bali, and S. Collins, Nucleon sigma terms with a variational analysis from lattice QCD, Phys. Rev. D 111, L031505 (2025).
  19. M. Bruno et al., Simulation of QCD with Nf = 2 + 1 flavors of non-perturbatively improved Wilson fermions, J. High Energy Phys. 02 (2015) 043.
  20. C. Alexandrou, G. Koutsou, Y. Li, M. Petschlies, and F. Pittler, Investigation of pion-nucleon contributions to nucleon matrix elements, Phys. Rev. D 110, 094514 (2024).
  21. K.-F. Liu, Parton degrees of freedom in pdfs from the hadronic tensor and large momentum effective theory, Phys. Rev. D 102, 074502 (2020).
  22. L. Barca, G. Bali, and S. Collins, Progress on nucleon transition matrix elements with a lattice QCD variational analysis, Proc. Sci., EuroPLEx2023 (2024) 002.
  23. L. Barca, G. Bali, and S. Collins, Toward N to Nπ matrix elements from lattice QCD, Phys. Rev. D 107, L051505 (2023).
  24. R. A. Briceño, J. J. Dudek, R. G. Edwards, C. J. Shultz, C. E. Thomas, and D. J. Wilson, The ππ→πγ⋆ amplitude and the resonant ρ→πγ⋆ transition from lattice QCD, Phys. Rev. D 93, 114508 (2016); 105, 079902(E) (2022).
  25. A. Radhakrishnan, J. J. Dudek, and R. G. Edwards, Radiative decay of the resonant K* and the γK→Kπ amplitude from lattice QCD, Phys. Rev. D 106, 114513 (2022).
  26. F. G. Ortega-Gama, J. J. Dudek, and R. G. Edwards, Timelike meson form factors beyond the elastic region from lattice QCD, Phys. Rev. D 110, 094505 (2024).
  27. L. Leskovec, S. Meinel, M. Petschlies, J. Negele, S. Paul, and A. Pochinsky, B→ρℓν− resonance form factors from B→ππℓν− in lattice QCD, Phys. Rev. Lett. 134, 161901 (2025).
  28. Y. Aoki, K.-I. Ishikawa, Y. Kuramashi, S. Sasaki, K. Sato, E. Shintani, R. Tsuji, H. Watanabe, and T. Yamazaki, Method for high-precision determination of the nucleon axial structure using lattice QCD: Removing πN-state contamination, Phys. Rev. D 112, 074510 (2025).
  29. R. Tsuji, Y. Aoki, K.-I. Ishikawa, Y. Kuramashi, S. Sasaki, K. Sato, E. Shintani, H. Watanabe, and T. Yamazaki, Investigating the axial structure of the nucleon based on large-volume lattice QCD at the physical point, arXiv:2505.10998.
  30. O. Bar, Nucleon-pion-state contribution to nucleon two-point correlation functions, Phys. Rev. D 92, 074504 (2015).
  31. O. Bar, Nπ-state contamination in lattice calculations of the nucleon axial form factors, Phys. Rev. D 99, 054506 (2019).
  32. G. S. Bali, L. Barca, S. Collins, M. Gruber, M. Löffler, A. Schäfer, W. Söldner, P. Wein, S. Weishäupl, and T. Wurm, Nucleon axial structure from lattice QCD, J. High Energy Phys. 05 (2020) 126.
  33. R. Gupta, S. Park, M. Hoferichter, E. Mereghetti, B. Yoon, and T. Bhattacharya, Pion–nucleon sigma term from lattice QCD, Phys. Rev. Lett. 127, 242002 (2021).
  34. O. Bar, A. Broll, and R. Sommer, Bπ excited-state contamination in lattice calculations of B-meson correlation functions, Eur. Phys. J. C 83, 757 (2023).
  35. Y.-Chull Jang, R. Gupta, B. Yoon, and T. Bhattacharya, Axial vector form factors from lattice QCD that satisfy the PCAC relation, Phys. Rev. Lett. 124, 072002 (2020).
  36. J. Liang, Y.-B. Yang, K.-F. Liu, A. Alexandru, T. Draper, and R. S. Sufian, Lattice calculation of nucleon isovector axial charge with improved currents, Phys. Rev. D 96, 034519 (2017).
  37. L. Liu, T. Chen, T. Draper, J. Liang, K.-F. Liu, G. Wang, and Y.-B. Yang, Nucleon isovector scalar charge from overlap fermions, Phys. Rev. D 104, 094503 (2021).
  38. A. Agadjanov, D. Djukanovic, G. von Hippel, H. B. Meyer, K. Ottnad, and H. Wittig, Nucleon sigma terms with Nf=2+1 flavors of O(a)-improved Wilson fermions, Phys. Rev. Lett. 131, 261902 (2023).
  39. R. Gupta, Y.-C. Jang, H.-W. Lin, B. Yoon, and T. Bhattacharya, Axial-vector form factors of the nucleon from lattice QCD, Phys. Rev. D 96, 114503 (2017).
  40. G. S. Bali, S. Collins, M. Gruber, A. Schäfer, P. Wein, and T. Wurm, Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors, Phys. Lett. B 789, 666 (2019).
  41. B. C. Tiburzi, Chiral corrections to nucleon two- and three-point correlation functions, Phys. Rev. D 91, 094510 (2015).
  42. M. T. Hansen and H. B. Meyer, On the effect of excited states in lattice calculations of the nucleon axial charge, Nucl. Phys. B923, 558 (2017).
  43. Z. B. Hall et al., Signs of non-monotonic finite-volume corrections to gA, arXiv:2503.09891.
  44. Particle Data Group, Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
  45. O. Bar, Nπ-state contamination in lattice calculations of the nucleon pseudoscalar form factor, Phys. Rev. D 100, 054507 (2019).
  46. C. Alexandrou, S. Bacchio, J. Finkenrath, C. Iona, G. Koutsou, Y. Li, and G. Spanoudes, Nucleon charges and σ-terms in lattice QCD, Phys. Rev. D 111, 054505 (2025).
  47. L. Barca, G. Bali, S. Collins, and M. Rodekamp (to be published).
  48. S. Park, R. Gupta, B. Yoon, S. Mondal, T. Bhattacharya, Y.-C. Jang, B. Joó, and F. Winter., Precision nucleon charges and form factors using (2+1)-flavor lattice QCD, Nucl. Phys. B, Proc. Suppl. 105, 054505 (2022).
  49. A. Bazavov et al., Bs→Kℓν decay from lattice QCD, Phys. Rev. D 100, 034501 (2019).
  50. R. G. Edwards and B. Joo, The chroma software system for lattice QCD, Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).

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