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Anatomy of finite-volume effects on the hadronic vacuum polarization contribution to the muon g−2

Sakura Itatani1,*, Hidenori Fukaya2,†, and Shoji Hashimoto1,3,‡

  • *Contact author: itasaku@post.kek.jp
  • †Contact author: hfukaya@het.phys.sci.osaka-u.ac.jp
  • ‡Contact author: shoji.hashimoto@kek.jp
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Phys. Rev. D 111, 114507 – Published 13 June, 2025

DOI: https://doi.org/10.1103/2swb-krdz

Abstract

The low-energy spectrum relevant to the lattice calculation of the hadronic vacuum polarization contribution to muon anomalous magnetic moment aμHVP,LO is dominantly given by two-pion states satisfying Lüscher’s finite-volume quantization condition. Finite-volume effects from those states may exhibit power-law dependence on the volume, contrary to an exponential suppression as suggested by chiral effective theory. Employing the finite-volume state decomposition of Euclidean correlators, we systematically investigate the volume dependence and identify the different volume scalings depending on the volume and Euclidean-time region. Using phenomenological inputs for ππ phase shift and the timelike pion form factor, we obtain an estimate for the finite-volume effects on aμHVP,LO, which is consistent with previous works. Numerical results are given for the “window” observables of aμ.

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References (41)

  1. S. Borsanyi et al., Leading hadronic contribution to the muon magnetic moment from lattice QCD, Nature (London) 593, 51 (2021).
  2. D. P. Aguillard et al. (Muon g−2 Collaboration), Measurement of the positive muon anomalous magnetic moment to 0.20 ppm, Phys. Rev. Lett. 131, 161802 (2023).
  3. C. Aubin, T. Blum, P. Chau, M. Golterman, S. Peris, and C. Tu, Finite-volume effects in the muon anomalous magnetic moment on the lattice, Phys. Rev. D 93, 054508 (2016).
  4. J. Bijnens and J. Relefors, Vector two-point functions in finite volume using partially quenched chiral perturbation theory at two loops, J. High Energy Phys. 12 (2017) 114.
  5. C. Aubin, T. Blum, M. Golterman, and S. Peris, Application of effective field theory to finite-volume effects in aμHVP, Phys. Rev. D 102, 094511 (2020).
  6. C. Aubin, T. Blum, M. Golterman, and S. Peris, Muon anomalous magnetic moment with staggered fermions: Is the lattice spacing small enough?, Phys. Rev. D 106, 054503 (2022).
  7. M. T. Hansen and A. Patella, Finite-volume effects in (g−2)μHVP,LO, Phys. Rev. Lett. 123, 172001 (2019).
  8. M. T. Hansen and A. Patella, Finite-volume and thermal effects in the leading-HVP contribution to muonic (g−2), J. High Energy Phys. 10 (2020) 029.
  9. M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
  10. L. Lellouch and M. Lüscher, Weak transition matrix elements from finite volume correlation functions, Commun. Math. Phys. 219, 31 (2001).
  11. C. J. D. Lin, G. Martinelli, C. T. Sachrajda, and M. Testa, K→ππ decays in a finite volume, Nucl. Phys. B619, 467 (2001).
  12. H. B. Meyer, Lattice QCD and the timelike pion form factor, Phys. Rev. Lett. 107, 072002 (2011).
  13. D. Bernecker and H. B. Meyer, Vector correlators in lattice QCD: Methods and applications, Eur. Phys. J. A 47, 148 (2011).
  14. G. J. Gounaris and J. J. Sakurai, Finite width corrections to the vector meson dominance prediction for ρ→e+e−, Phys. Rev. Lett. 21, 244 (1968).
  15. A. Francis, B. Jaeger, H. B. Meyer, and H. Wittig, A new representation of the Adler function for lattice QCD, Phys. Rev. D 88, 054502 (2013).
  16. X. Feng, S. Aoki, S. Hashimoto, and T. Kaneko, Timelike pion form factor in lattice QCD, Phys. Rev. D 91, 054504 (2015).
  17. D. Giusti, F. Sanfilippo, and S. Simula, Light-quark contribution to the leading hadronic vacuum polarization term of the muon g−2 from twisted-mass fermions, Phys. Rev. D 98, 114504 (2018).
  18. Cè, Marco et al., Window observable for the hadronic vacuum polarization contribution to the muon g-2 from lattice QCD, Phys. Rev. D 106, 114502 (2022).
  19. A. Bazavov et al. (Fermilab Lattice, HPQCD, and MILC Collaborations), Light-quark connected intermediate-window contributions to the muon g-2 hadronic vacuum polarization from lattice QCD, Phys. Rev. D 107, 114514 (2023).
  20. T. Blum, P. A. Boyle, V. Gülpers, T. Izubuchi, L. Jin, C. Jung, A. Jüttner, C. Lehner, A. Portelli, and J. T. Tsang (RBC and UKQCD Collaborations), Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 121, 022003 (2018).
  21. T. Aoyama et al., The anomalous magnetic moment of the muon in the standard model, Phys. Rep. 887, 1 (2020).
  22. A. Boccaletti et al., High precision calculation of the hadronic vacuum polarisation contribution to the muon anomaly, arXiv:2407.10913.
  23. C. Lehner and A. S. Meyer, Consistency of hadronic vacuum polarization between lattice QCD and the R-ratio, Phys. Rev. D 101, 074515 (2020).
  24. G. Wang, T. Draper, K.-F. Liu, and Y.-B. Yang (χQCD Collaboration), Muon g-2 with overlap valence fermions, Phys. Rev. D 107, 034513 (2023).
  25. T. Blum et al. (RBC and UKQCD Collaborations), Update of Euclidean windows of the hadronic vacuum polarization, Phys. Rev. D 108, 054507 (2023).
  26. T. Blum et al., The long-distance window of the hadronic vacuum polarization for the muon g-2, Phys. Rev. Lett. 134, 201901 (2025).
  27. A. Bazavov et al., Hadronic vacuum polarization for the muon g−2 from lattice QCD: Long-distance and full light-quark connected contribution, arXiv:2412.18491.
  28. T. Blum, Lattice calculation of the lowest order hadronic contribution to the muon anomalous magnetic moment, Phys. Rev. Lett. 91, 052001 (2003).
  29. X. Wang, Asymptotics of the q-theta function, Commun. Math. Anal. 7, 50 (2009), https://userweb.ucs.louisiana.edu/~xxw6637/papers/CMA2009.pdf.
  30. M. Luscher, Signatures of unstable particles in finite volume, Nucl. Phys. B364, 237 (1991).
  31. G. Colangelo, M. Hoferichter, and P. Stoffer, Two-pion contribution to hadronic vacuum polarization, J. High Energy Phys. 02 (2019) 006.
  32. G. Colangelo, M. Hoferichter, B. Kubis, and P. Stoffer, Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization, J. High Energy Phys. 10 (2022) 032.
  33. V. M. Aul’chenko et al., Measurement of the e+e−→π+π− cross section with the CMD-2 detector in the 370–520-MeV c.m. energy range, JETP Lett. 84, 413 (2006).
  34. R. R. Akhmetshin et al. (CMD-2 Collaboration), High-statistics measurement of the pion form factor in the ρ-meson energy range with the CMD-2 detector, Phys. Lett. B 648, 28 (2007).
  35. M. N. Achasov et al., Update of the e+e−→π+π− cross-section measured by SND detector in the energy region 400<s<1000MeV, J. Exp. Theor. Phys. 103, 380 (2006).
  36. F. Ambrosino et al. (KLOE Collaboration), Measurement of σ(e+e−→π+π−) from threshold to 0.85  GeV2 using initial state radiation with the KLOE detector, Phys. Lett. B 700, 102 (2011).
  37. J. P. Lees et al. (BABAR Collaboration), Precise measurement of the e+e−→π+π−(γ) cross section with the initial-state radiation method at BABAR, Phys. Rev. D 86, 032013 (2012).
  38. P. Estabrooks and A. D. Martin, ππ phase shift analysis below the K anti-K threshold, Nucl. Phys. B79, 301 (1974).
  39. S. D. Protopopescu, M. Alston-Garnjost, A. Barbaro-Galtieri, S. M. Flatte, J. H. Friedman, T. A. Lasinski, G. R. Lynch, M. S. Rabin, and F. T. Solmitz, ππ partial wave analysis from reactions π+p→π+π−Δ++ and π+p→K+K−Δ++ at 7.1GeV/c, Phys. Rev. D 7, 1279 (1973).
  40. M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to α(mZ2), Eur. Phys. J. C 80, 241 (2020); 80, 410(E) (2020).
  41. A. Keshavarzi, D. Nomura, and T. Teubner, g−2 of charged leptons, α(MZ2), and the hyperfine splitting of muonium, Phys. Rev. D 101, 014029 (2020).

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Phys. Rev. D 111, 114507– Published 13 June, 2025
  • Received 14 January 2025
  • Accepted 27 May 2025
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