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Inclusive Semileptonic Decays of the Ds Meson: Lattice QCD Confronts Experiments

Alessandro De Santis1,2, Antonio Evangelista3, Roberto Frezzotti3, Giuseppe Gagliardi4,5, Paolo Gambino6, Marco Garofalo7, Christiane Franziska Groß7, Bartosz Kostrzewa7, Vittorio Lubicz4,5 et al.

Francesca Margari3, Marco Panero6,8, Francesco Sanfilippo5, Silvano Simula5, Antonio Smecca9, Nazario Tantalo3, and Carsten Urbach7

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Phys. Rev. Lett. 135, 121901 – Published 15 September, 2025

DOI: https://doi.org/10.1103/snc6-cpz6

Abstract

We present the results of a first-principles theoretical study of the inclusive semileptonic decays of the Ds meson. We performed a state-of-the-art lattice QCD calculation by taking into account all sources of systematic errors. A detailed discussion of our lattice calculation, demonstrating that inclusive semileptonic decays can nowadays be studied on the lattice at a phenomenologically relevant level of accuracy, is the subject of a companion paper [A. De Santis et al., Inclusive semileptonic decays of the Ds meson: A first-principles lattice QCD calculation, Phys. Rev. D 112, 054503 (2025)]. Here, we focus on the phenomenological implications of our results. Using the current best estimates of the relevant Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, our theoretical predictions for the decay rate and for the first two lepton-energy moments are in very good agreement with the corresponding experimental measurements. We also argue that, while the inclusive Ds channel is not yet competitive with the exclusive channels in the |Vcs| determination, the situation can be significantly improved in the near future.

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Inclusive semileptonic decays of the Ds meson: A first-principles lattice QCD calculation

Alessandro De Santis, Antonio Evangelista, Roberto Frezzotti, Giuseppe Gagliardi, Paolo Gambino, Marco Garofalo, Christiane Franziska Groß, Bartosz Kostrzewa, Vittorio Lubicz, Francesca Margari, Marco Panero, Francesco Sanfilippo, Silvano Simula, Antonio Smecca, Nazario Tantalo, and Carsten Urbach
Phys. Rev. D 112, 054503 (2025)

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References (68)

  1. N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10, 531 (1963).
  2. M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49, 652 (1973).
  3. J. P. Lees et al. (BABAR Collaboration), Evidence for an excess of B¯→D(*)τ−ν¯τ decays, Phys. Rev. Lett. 109, 101802 (2012).
  4. J. P. Lees et al. (BABAR Collaboration), Measurement of an excess of B¯→D(*)τ−ν¯τ decays and implications for charged Higgs bosons, Phys. Rev. D 88, 072012 (2013).
  5. R. Aaij et al. (LHCb Collaboration), Measurement of form-factor-independent observables in the decay B0→K*0μ+μ−, Phys. Rev. Lett. 111, 191801 (2013).
  6. R. Aaij et al. (LHCb Collaboration), Test of lepton universality using B+→K+ℓ+ℓ− decays, Phys. Rev. Lett. 113, 151601 (2014).
  7. R. Aaij et al. (LHCb Collaboration), Angular analysis and differential branching fraction of the decay Bs0→ϕμ+μ−, J. High Energy Phys. 09 (2015) 179.
  8. M. Huschle et al. (Belle Collaboration), Measurement of the branching ratio of B¯→D(*)τ−ν¯τ relative to B¯→D(*)ℓ−ν¯ℓ decays with hadronic tagging at Belle, Phys. Rev. D 92, 072014 (2015).
  9. S. Bifani, S. Descotes-Genon, A. Romero Vidal, and M.-H. Schune, Review of lepton universality tests in B decays, J. Phys. G 46, 023001 (2019).
  10. R. Aaij et al. (LHCb Collaboration), Test of lepton universality in beauty-quark decays, Nat. Phys. 18, 277 (2022); 19, 1517(A) (2023).
  11. G. W. Bennett et al. (Muon g−2 Collaboration), Final report of the muon E821 anomalous magnetic moment measurement at BNL, Phys. Rev. D 73, 072003 (2006).
  12. B. Abi et al. (Muon g−2 Collaboration), Measurement of the positive muon anomalous magnetic moment to 0.46 ppm, Phys. Rev. Lett. 126, 141801 (2021).
  13. 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).
  14. S. Banerjee et al. (Heavy Flavor Averaging Group (HFLAV) Collaboration), Averages of b-hadron, c-hadron, and τ-lepton properties as of 2023, arXiv:2411.18639.
  15. S. Borsanyi et al. (BMW Collaboration), Ab initio calculation of the neutron-proton mass difference, Science 347, 1452 (2015).
  16. R. Abbott et al. (RBC and UKQCD Collaborations), Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model, Phys. Rev. D 102, 054509 (2020).
  17. R. Aliberti et al., The anomalous magnetic moment of the muon in the standard model: An update, arXiv:2505.21476.
  18. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG) Collaboration), FLAG review 2024, arXiv:2411.04268.
  19. S. Hashimoto, Inclusive semi-leptonic B meson decay structure functions from lattice QCD, Prog. Theor. Exp. Phys. 2017, 053B03 (2017).
  20. 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).
  21. M. Hansen, A. Lupo, and N. Tantalo, Extraction of spectral densities from lattice correlators, Phys. Rev. D 99, 094508 (2019).
  22. J. Bulava and M. T. Hansen, Scattering amplitudes from finite-volume spectral functions, Phys. Rev. D 100, 034521 (2019).
  23. J. Bulava, M. T. Hansen, M. W. Hansen, A. Patella, and N. Tantalo, Inclusive rates from smeared spectral densities in the two-dimensional O(3) non-linear σ-model, J. High Energy Phys. 07 (2022) 034.
  24. P. Gambino and S. Hashimoto, Inclusive semileptonic decays from lattice QCD, Phys. Rev. Lett. 125, 032001 (2020).
  25. M. Asakawa, T. Hatsuda, and Y. Nakahara, Maximum entropy analysis of the spectral functions in lattice QCD, Prog. Part. Nucl. Phys. 46, 459 (2001).
  26. H. B. Meyer, Transport properties of the quark-gluon plasma: A lattice QCD perspective, Eur. Phys. J. A 47, 86 (2011).
  27. Y. Burnier and A. Rothkopf, Bayesian approach to spectral function reconstruction for euclidean quantum field theories, Phys. Rev. Lett. 111, 182003 (2013).
  28. A. Rothkopf, Heavy quarkonium in extreme conditions, Phys. Rep. 858, 1 (2020).
  29. L. Kades, J. M. Pawlowski, A. Rothkopf, M. Scherzer, J. M. Urban, S. J. Wetzel, N. Wink, and F. P. G. Ziegler, Spectral reconstruction with deep neural networks, Phys. Rev. D 102, 096001 (2020).
  30. G. Bailas, S. Hashimoto, and T. Ishikawa, Reconstruction of smeared spectral function from Euclidean correlation functions, Prog. Theor. Exp. Phys. 2020, 043B07 (2020).
  31. J. Horak, J. M. Pawlowski, J. Rodríguez-Quintero, J. Turnwald, J. M. Urban, N. Wink, and S. Zafeiropoulos, Reconstructing QCD spectral functions with Gaussian processes, Phys. Rev. D 105, 036014 (2022).
  32. T. Bergamaschi, W. I. Jay, and P. R. Oare, Hadronic structure, conformal maps, and analytic continuation, Phys. Rev. D 108, 074516 (2023).
  33. 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.
  34. G. Backus and F. Gilbert, The resolving power of gross Earth data, Geophys. J. Int. 16, 169 (1968).

  35. After Ref. [33], also another lattice group started to face the same challenge [36, 37, 38, 39, 40, 41, 42]. See also Ref. [43], which appeared after the completion of this work, for a study at fixed lattice spacing and unphysical pion mass of the same process.

  36. 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].
  37. 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].
  38. 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.
  39. R. Kellermann, A. Barone, S. Hashimoto, A. Jüttner, and T. Kaneko, Studies on finite-volume effects in the inclusive semileptonic decays of charmed mesons, Proc. Sci. LATTICE2023 (2024) 272 [arXiv:2312.16442].
  40. 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].
  41. R. Kellermann, A. Barone, S. Hashimoto, A. Jüttner, and T. Kaneko, Updates on inclusive charmed and bottomed meson decays from the lattice, in 12th International Workshop on the CKM Unitarity Triangle (2024), arXiv:2405.06152.
  42. S. Hashimoto, Towards the understanding of the inclusive vs exclusive puzzles in the—Vcb—determinations, Proc. Sci. EuroPLEx2023 (2024) 012 [arXiv:2406.04579].
  43. R. Kellermann, Z. Hu, A. Barone, A. Elgaziari, S. Hashimoto, T. Kaneko, and A. Jüttner, Inclusive semileptonic decays from lattice QCD: Analysis of systematic effects, Phys. Rev. D 112, 014501 (2025).
  44. A. De Santis et al., companion paper, Inclusive semileptonic decays of the Ds meson: A first-principles lattice QCD calculation, Phys. Rev. D 112, 054503 (2025).
  45. D. M. Asner et al. (CLEO Collaboration), Measurement of absolute branching fractions of inclusive semileptonic decays of charm and charmed-strange mesons, Phys. Rev. D 81, 052007 (2010).
  46. M. Ablikim et al. (BESIII Collaboration), Measurement of the absolute branching fraction of inclusive semielectronic Ds+ decays, Phys. Rev. D 104, 012003 (2021).
  47. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  48. A. Sirlin, Large mW, mZ behavior of the O(α) corrections to semileptonic processes mediated by W, Nucl. Phys. B196, 83 (1982).
  49. D. Bigi, M. Bordone, P. Gambino, U. Haisch, and A. Piccione, QED effects in inclusive semi-leptonic B decays, J. High Energy Phys. 11 (2023) 163; 03 (2025) 078(E).

  50. QED threshold corrections are different in the u¯s channel. However, in [44] we show that Γu¯s is negligible at the current level of accuracy.

  51. C. Alexandrou et al., Simulating twisted mass fermions at physical light, strange and charm quark masses, Phys. Rev. D 98, 054518 (2018).
  52. G. Bergner, P. Dimopoulos, J. Finkenrath, E. Fiorenza, R. Frezzotti, M. Garofalo, B. Kostrzewa, F. Sanfilippo, S. Simula, and U. Wenger (Extended Twisted Mass Collaboration), Quark masses and decay constants in Nf=2+1+1 isoQCD with Wilson clover twisted mass fermions, Proc. Sci. LATTICE2019 (2020) 181 [arXiv:2001.09116].
  53. C. Alexandrou et al. (Extended Twisted Mass Collaboration), Ratio of kaon and pion leptonic decay constants with Nf=2+1+1 Wilson-clover twisted-mass fermions, Phys. Rev. D 104, 074520 (2021).
  54. J. Finkenrath et al., Twisted mass gauge ensembles at physical values of the light, strange and charm quark masses, Proc. Sci. LATTICE2021 (2022) 284 [arXiv:2201.02551].
  55. R. Frezzotti, P. A. Grassi, S. Sint, and P. Weisz (Alpha Collaboration), Lattice QCD with a chirally twisted mass term, J. High Energy Phys. 08 (2001) 058.
  56. R. Frezzotti and G. C. Rossi, Twisted mass lattice QCD with mass nondegenerate quarks, Nucl. Phys. B, Proc. Suppl. 128, 193 (2004).
  57. R. Frezzotti and G. C. Rossi, Chirally improving Wilson fermions. II. Four-quark operators, J. High Energy Phys. 10 (2004) 070.
  58. P. Gambino and J. F. Kamenik, Lepton energy moments in semileptonic charm decays, Nucl. Phys. B840, 424 (2010).
  59. F. Bernlochner, A. Gilman, S. Malde, M. Prim, K. K. Vos, and G. Wilkinson, Charming Darwin: The evolution of QCD parameters across different species, J. High Energy Phys. 05 (2025) 061.
  60. J. Hietala, D. Cronin-Hennessy, T. Pedlar, and I. Shipsey, Exclusive Ds semileptonic branching fraction measurements, Phys. Rev. D 92, 012009 (2015).
  61. M. Ablikim et al. (BESIII Collaboration), First measurement of the form factors in Ds+→K0e+νe and Ds+→K*0e+νe decays, Phys. Rev. Lett. 122, 061801 (2019).
  62. www.gauss-centre.eu
  63. Jülich Supercomputing Centre, JUWELS cluster and booster: Exascale pathfinder with modular supercomputing architecture at Juelich Supercomputing Centre, J. Large-Scale Res. Facil. 7 (2021), 10.17815/jlsrf-7-183
  64. https://prace-ri.eu/
  65. https://www.lumi-supercomputer.eu/lumi-consortium/
  66. https://csc.fi/en/
  67. https://www.supercomputing-icsc.it/en/icsc-home/
  68. A. De Santis, A. Evangelista, R. Frezzotti, G. Gigliardi, P. Gambino, M. Garofalo, C. F. Groß, B. Kostrzewa, V. Lubicz, F. Margari, M. Panero, F. Sanfilippo, S. Simula, A. Smecca, N. Tantalo, and C. Urbach, Supplementary data for “Inclusive semileptonic decays of the Ds meson”, V1, 2025, https://doi.org/10.60507/FK2/VQFYKW.

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Phys. Rev. Lett. 135, 121901– Published 15 September, 2025
  • Received 24 April 2025
  • Revised 25 July 2025
  • Accepted 18 August 2025
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