Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Inclusive semileptonic decays from lattice QCD: Analysis of systematic effects

Ryan Kellermann* and Zhi Hu

Alessandro Barone

Ahmed Elgaziari

Shoji Hashimoto and Takashi Kaneko

Andreas Jüttner

  • *Contact author: kelry@post.kek.jp

Phys. Rev. D 112, 014501 – Published 1 July, 2025

DOI: https://doi.org/10.1103/kltp-1p1f

Abstract

Lattice QCD calculations of inclusive semileptonic decay rates involve new types of systematic effects, such as truncation errors in the estimation of energy integrals, or finite-volume effects for multibody final states. We investigate them for the lattice data of Ds→Xsℓν decays, obtained using Möbius domain-wall fermions. Separating the ground-state and excited-state contributions results in better control over these systematic effects. With the Chebyshev polynomial approximation, the truncation error is under control, while the finite-volume effects are estimated using a model to describe two-body final states.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (51)

  1. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG), FLAG review 2021, Eur. Phys. J. C 82, 869 (2022).
  2. T. Kaneko, Heavy flavor physics from lattice QCD, Proc. Sci. LATTICE2022 (2023) 238 [arXiv:2304.01618].
  3. M. Fael, M. Prim, and K. K. Vos, Inclusive B→Xcℓν¯ℓ and B→Xuℓν¯ℓ decays: Current status and future prospects, Eur. Phys. J. Spec. Top. 233, 325 (2024).
  4. G. Finauri and P. Gambino, The q2 moments in inclusive semileptonic B decays, J. High Energy Phys. 02 (2024) 206.
  5. S. Hashimoto, Inclusive semi-leptonic B meson decay structure functions from lattice QCD, Prog. Theor. Exp. Phys. 2017, 053B03 (2017).
  6. M. T. Hansen, H. B. Meyer, and D. Robaina, From deep inelastic scattering to heavy-flavor semileptonic decays: Total rates into multihadron final states from lattice QCD, Phys. Rev. D 96, 094513 (2017).
  7. P. Gambino and S. Hashimoto, Inclusive semileptonic decays from lattice QCD, Phys. Rev. Lett. 125, 032001 (2020).
  8. P. Gambino, S. Hashimoto, S. Mächler, M. Panero, F. Sanfilippo, S. Simula, A. Smecca, and N. Tantalo, Lattice QCD study of inclusive semileptonic decays of heavy mesons, J. High Energy Phys. 07 (2022) 083.
  9. A. Barone, S. Hashimoto, A. Jüttner, T. Kaneko, and R. Kellermann, Approaches to inclusive semileptonic B(s)-meson decays from Lattice QCD, J. High Energy Phys. 07 (2023) 145.
  10. A. Evangelista, R. Frezzotti, N. Tantalo, G. Gagliardi, F. Sanfilippo, S. Simula, and V. Lubicz (Extended Twisted Mass Collaboration), Inclusive hadronic decay rate of the τ lepton from lattice QCD, Phys. Rev. D 108, 074513 (2023).
  11. C. Alexandrou et al. (Extended Twisted Mass Collaboration), Inclusive hadronic decay rate of the τ lepton from lattice QCD: The u¯s flavor channel and the Cabibbo angle, Phys. Rev. Lett. 132, 261901 (2024).
  12. H. Fukaya, S. Hashimoto, T. Kaneko, and H. Ohki, Towards fully nonperturbative computations of inelastic ℓN scattering cross sections from lattice QCD, Phys. Rev. D 102, 114516 (2020).
  13. A. Barone, A. Jüttner, S. Hashimoto, T. Kaneko, and R. Kellermann, Inclusive semi-leptonic B(s) mesons decay at the physical b quark mass, Proc. Sci. LATTICE2022 (2023) 403 [arXiv:2211.15623].
  14. R. Kellermann, A. Barone, S. Hashimoto, A. Jüttner, and T. Kaneko, Inclusive semi-leptonic decays of charmed mesons with Möbius domain wall fermions, Proc. Sci. LATTICE2022 (2023) 414 [arXiv:2211.16830].
  15. A. Barone, S. Hashimoto, A. Jüttner, T. Kaneko, and R. Kellermann, Chebyshev and Backus-Gilbert reconstruction for inclusive semileptonic B(s)-meson decays from lattice QCD, Proc. Sci. LATTICE2023 (2024) 236 [arXiv:2312.17401].
  16. R. Kellermann, A. Barone, S. Hashimoto, and A. Jüttnerc, and T. Kanekoa, Studies on finite-volume effects in the inclusive semileptonic decays of charmed mesons, Proc. Sci. LATTICE2023 (2024) 272 [arXiv:2312.16442].
  17. R. Kellermann, A. Barone, A. Elgaziari, S. Hashimoto, Z. Hu, A. Jüttnerc, and T. Kaneko, Systematic effects in the lattice calculation of inclusive semileptonic decays, Proc. Sci. LATTICE2024 (2025) 245 [arXiv:2411.18058].
  18. J. C. A. Barata and K. Fredenhagen, Particle scattering in Euclidean lattice field theories, Commun. Math. Phys. 138, 507 (1991).
  19. G. Bailas, S. Hashimoto, and T. Ishikawa, Reconstruction of smeared spectral function from Euclidean correlation functions, Prog. Theor. Exp. Phys. 2020, 043B07 (2020).
  20. M. Hansen, A. Lupo, and N. Tantalo, Extraction of spectral densities from lattice correlators, Phys. Rev. D 99, 094508 (2019).
  21. A. De Santis and C. F. Groß, Lattice calculation of the Ds↦Xℓν¯ℓ inclusive decay rate: An overview, Proc. Sci. LATTICE2024 (2025) 238 [arXiv:2502.15519].
  22. We ignore the disconnected strange-quark-loop diagram in this work. The ss¯ pseudoscalar state is called ηs instead of η or η′.

  23. M. Luscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104, 177 (1986).
  24. M. Luscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105, 153 (1986).
  25. Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B406, 90 (1993).
  26. V. Furman and Y. Shamir, Axial symmetries in lattice QCD with Kaplan fermions, Nucl. Phys. B439, 54 (1995).
  27. R. C. Brower, H. Neff, and K. Orginos, The Möbius domain wall fermion algorithm, Comput. Phys. Commun. 220, 1 (2017).
  28. B. Colquhoun, S. Hashimoto, T. Kaneko, and J. Koponen (JLQCD Collaboration), Form factors of B→πℓν and a determination of |Vub| with Möbius domain-wall fermions, Phys. Rev. D 106, 054502 (2022).
  29. Y. Aoki, B. Colquhoun, H. Fukaya, S. Hashimoto, T. Kaneko, R. Kellermann, J. Koponen, and E. Kou (JLQCD Collaboration), B→D*ℓνℓ semileptonic form factors from lattice QCD with Möbius domain-wall quarks, Phys. Rev. D 109, 074503 (2024).
  30. S. Borsanyi et al. (BMW Collaboration), High-precision scale setting in lattice QCD, J. High Energy Phys. 09 (2012) 010.
  31. C. Morningstar and M. J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69, 054501 (2004).
  32. M. Tomii, G. Cossu, B. Fahy, H. Fukaya, S. Hashimoto, T. Kaneko, and J. Noaki (JLQCD Collaboration), Renormalization of domain-wall bilinear operators with short-distance current correlators, Phys. Rev. D 94, 054504 (2016).
  33. P. A. Boyle (UKQCD Collaboration), Conserved currents for mobius domain wall fermions, Proc. Sci. LATTICE2014 (2015) 087.
  34. K. Nakayama, B. Fahy, and S. Hashimoto, Short-distance charmonium correlator on the lattice with Möbius domain-wall fermion and a determination of charm quark mass, Phys. Rev. D 94, 054507 (2016).
  35. P. Boyle, A. Yamaguchi, G. Cossu, and A. Portelli, grid: A next generation data parallel c++ QCD library, Proc. Sci. LATTICE2015 (2016) 023 [arXiv:1512.03487].
  36. A. Yamaguchi, P. Boyle, G. Cossu, G. Filaci, C. Lehner, and A. Portelli, grid: OneCode and FourAPIs, Proc. Sci. LATTICE2021 (2022) 035 [arXiv:2203.06777].
  37. A. Portelli, R. Abott, N. Asmussen, A. Barone, P. Boyle, and F. E. et al., aportelli/hadrons: hadrons v1.3, Zenodo, 10.5281/zenodo.8023716 (2022).
  38. P. Lepage and C. Gohlke, gplepage/lsqfit: lsqfit version 13.2.4, Zenodo, 10.5281/zenodo.14837295 (2025).
  39. G. P. Lepage, B. Clark, C. T. H. Davies, K. Hornbostel, P. B. Mackenzie, C. Morningstar, and H. Trottier (HPQCD Collaboration), Constrained curve fitting, Nucl. Phys. B, Proc. Suppl. 106, 12 (2002).
  40. P. Lepage, gplepage/corrfitter: corrfitter version 8.2, Zenodo, 10.5281/zenodo.5733391 (2021).
  41. P. Lepage, C. Gohlke, and D. Hackett, gplepage/gvar: gvar version 13.1.1, Zenodo, 10.5281/zenodo.15132844 (2025).
  42. A. K. Leibovich, Z. Ligeti, I. W. Stewart, and M. B. Wise, Semileptonic B decays to excited charmed mesons, Phys. Rev. D 57, 308 (1998).
  43. B. Fahy, G. Cossu, and S. Hashimoto, Approaching the bottom using fine lattices with domain-wall fermions, Proc. Sci. LATTICE2016 (2016) 118 [arXiv:1702.02303].
  44. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  45. T. Kaneko, B. Colquhoun, H. Fukaya, and S. Hashimoto (JLQCD Collaboration), D meson semileptonic form factors in Nf=3 QCD with Möbius domain-wall quarks, EPJ Web Conf. 175, 13007 (2018).
  46. G. Backus and F. Gilbert, The resolving power of gross earth data, Geophys. J. R. Astron. Soc. 16, 169 (1968).
  47. We note that the KK¯ states are always heavier than ϕ in our setup, where the light-quark mass is heavier than physical, and the form factor does not diverge even at zero relative momentum. When the ϕ meson can decay to KK¯, we have to introduce a width to circumvent the divergence.

  48. V⊥V⊥ is included in the simultaneous fit to better constraint the ground-state ϕ meson, see Eqs. (58) and (62).

  49. M. Ablikim et al. (BESIII Collaboration), Measurement of the absolute branching fraction of inclusive semielectronic Ds+ decays, Phys. Rev. D 104, 012003 (2021).
  50. Z. Hu, A. Barone, A. Elgaziari, S. Hashimoto, A. Jüttner, T. Kaneko, and R. Kellermann, Study on the P-wave form factors contributing to Bs to Ds inclusive semileptonic decays from lattice simulations, Proc. Sci. LATTICE2024 (2025) 241 [arXiv:2501.19284].
  51. A. Weiße, G. Wellein, A. Alvermann, and H. Fehske, The kernel polynomial method, Rev. Mod. Phys. 78, 275 (2006).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation