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An updated muon-decay correction factor shrinks theory error on the Fermi constant by an order of magnitude.

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load-bearing objection Clean, usable update of Δq and G_F that finally makes theory error negligible next to the MuLan lifetime.

arxiv 2607.02657 v1 pith:LH3EII7A submitted 2026-07-02 hep-ph

Muon lifetime and Fermi constant: an update

Alexander Eberhart , Matteo Fael , Alexander Keshavarzi , Daisuke Nomura , Kay Sch\"onwald , Matthias Steinhauser , Thomas Teubner , Aidan Wright This is my paper
classification hep-ph
keywords muon lifetimeFermi constantQED correctionshadronic vacuum polarizationdispersion relationselectroweak precision
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The Fermi constant is extracted from the measured muon lifetime once radiative and mass corrections are known. This paper recomputes those corrections, called Δq, through order α³ in QED and with modern dispersive hadronic input. The result is Δq = (−4 384 678 ± 34)×10⁻⁹, ten times more precise than the previous O(α²) value. Combined with the experimental lifetime and muon mass it yields G_F = 1.166 378 59(59)×10⁻⁵ GeV⁻². Theory is no longer the limiting factor: further gains require better measurements of the muon lifetime and mass.

Core claim

The authors obtain Δq = (−4 384 678 ± 34)×10⁻⁹ by combining exact fermionic O(α³) QED terms, an improved expansion of the bosonic piece, and a dispersive hadronic contribution that accounts for present tensions in e⁺e⁻ data. This reduces the theory uncertainty attached to Δq by an order of magnitude relative to the previous O(α²) determination and produces the updated Fermi constant G_F = 1.166 378 59(59)×10⁻⁵ GeV⁻².

What carries the argument

The correction factor Δq that multiplies the tree-level muon-decay rate, expanded as a series in α-bar(m_μ)/π with separate mass-independent, mass-dependent, fermionic, bosonic and hadronic pieces.

Load-bearing premise

The size of the still-unknown hadronic correction at order α³ is guessed by simple analogy with the closed-muon-loop term and assigned a 100 percent uncertainty.

What would settle it

A direct dispersive or lattice evaluation of the O(α³) hadronic piece that differs from (27 ± 27)×10⁻⁹ by more than the quoted error, or a new muon-lifetime measurement whose central value shifts G_F outside the present (59) uncertainty.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 4 minor

Summary. The manuscript updates the theoretical prediction for the muon lifetime within the Fermi theory by computing the correction factor Δq through O(α³) QED (including exact fermionic pieces and an improved expansion for the bosonic contribution) together with a modern dispersive evaluation of the O(α²) hadronic vacuum-polarization contribution that accounts for the CMD-3 tension. The result is Δq = (−4 384 678 ± 34) × 10^{-9}, which is then combined with the experimental muon lifetime and mass to extract G_F = 1.166 378 59(59) × 10^{-5} GeV^{-2}. Uncertainties are broken down by source and shown to be dominated by experiment.

Significance. If correct, the work reduces the theory uncertainty on Δq by an order of magnitude relative to the previous O(α²) determination, rendering the residual theory error on G_F negligible compared with the present experimental lifetime uncertainty (0.5 ppm) and even the muon-mass uncertainty. This supplies a cleaner baseline for electroweak precision fits and global SM analyses. Strengths include the transparent use of published high-order analytic results, a conservative averaging procedure for the hadronic R-ratio tension, and a clear quadrature error budget that isolates the remaining theory pieces.

minor comments (4)
  1. Section III (after Eq. 15): the O(α³) hadronic estimate is obtained purely by analogy with the closed-muon-loop term and assigned a flat 100 % uncertainty. While the choice is conservative and sub-dominant, a short additional sentence comparing the relative sizes of the corresponding diagrams in a_μ (or citing the lattice/dispersive literature for those diagrams) would make the argument more self-contained.
  2. Eq. (10) and surrounding text: the bosonic coefficient is taken from the C_F³ piece of a QCD calculation extrapolated in δ. The comparison with the exact b → u result is helpful; stating explicitly that the dominant color structures absent in QED do not affect the quoted uncertainty would remove any residual ambiguity.
  3. Eqs. (13)–(14): the four uncertainty components (st, sy, rad, corr) are clearly defined, but a one-line reminder of how the “corr” term is constructed (reference to the KNTW covariance treatment) would aid readers who have not followed the companion papers.
  4. Throughout: a few typographical inconsistencies remain (e.g., spacing in author names with umlauts, occasional missing thin spaces in numerical results such as 4 384 678). These are purely cosmetic.

Circularity Check

0 steps flagged

No significant circularity; Δq is assembled from independent QED diagram evaluations plus external e^{+}e^{-} data, and G_F is extracted from measured τ_μ.

full rationale

The central quantity Δq is obtained by summing explicit QED coefficients (massless and mass-dependent pieces through O(α^{3}), fermionic and bosonic) that originate in Feynman-diagram calculations, together with a dispersion integral of the experimental R-ratio. The O(α^{3}) bosonic piece is an extrapolation of a prior expansion (with a quantified truncation error), and the O(α^{3}) hadronic piece is a conservative analogy to the closed-muon-loop term; neither is fitted to the target. G_F is then solved for from the defining relation that uses the experimental muon lifetime and mass. Self-citations point to earlier independent computations or data compilations that remain externally checkable; none of them define the present result by construction, import an unverified uniqueness theorem, or rename a fit as a prediction. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The calculation rests on standard QED Feynman rules, the Fermi effective theory matched to the SM, and the optical theorem that converts the hadronic R-ratio into a vacuum-polarization integral. No free parameters are fitted to the muon lifetime itself; all numerical inputs (α, lepton masses, R(s)) are taken from external measurements or previous calculations. The only ad-hoc modeling choice is the 100 % uncertainty assigned to the unknown O(α³) hadronic piece.

axioms (4)
  • domain assumption The muon decay rate in the Fermi theory is given by Eq. (1) with all pure electroweak matching effects absorbed into the definition of G_F.
    Standard definition used since Sirlin (1980); invoked in the Introduction and Eq. (1).
  • domain assumption The hadronic vacuum polarization contribution is exactly the dispersion integral (12) over the experimental R-ratio.
    Optical theorem + analyticity; used throughout Section III.
  • domain assumption The bosonic O(α³) coefficient can be obtained by taking the C_F³ color factor of the QCD b→c calculation and extrapolating the mass-ratio expansion to δ=1.
    Justified by the known mapping between QED and the abelian part of QCD; residual extrapolation uncertainty is quantified in Eq. (10).
  • ad hoc to paper Unknown O(α³) hadronic corrections are of the same size as the closed-muon-loop term and carry 100 % relative uncertainty.
    Explicit modeling choice stated after Eq. (15); no independent calculation is available.

pith-pipeline@v1.1.0-grok45 · 17879 in / 2490 out tokens · 24530 ms · 2026-07-12T07:53:33.136774+00:00 · methodology

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read the original abstract

We present an updated prediction for the lifetime of the muon including a detailed analysis of all relevant uncertainties. Our prediction includes QED corrections up to order $\alpha^3$ and state-of-the-art hadronic contributions based on dispersive methods. Radiative corrections and finite-electron-mass effects are parametrized by the correction factor $\Delta q$ in $\tau_\mu^{-1}=G_F^2m_\mu^5(1+\Delta q)/(192\pi^3)$, for which we obtain $\Delta q=(-4\, 384\, 678 \pm 34)\times 10^{-9}$. This reduces the uncertainty associated with $\Delta q$ by an order of magnitude compared to the previous prediction at order $\alpha^2$. We use our results to provide an updated value of the Fermi coupling constant, $G_F=1.166\,378\, 59 \, (59) \times 10^{-5} \, \mathrm{GeV}^{-2}$. Further improvements will require better measurements of the muon lifetime and mass.

discussion (0)

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Reference graph

Works this paper leans on

115 extracted references · 89 linked inside Pith

  1. [1]

    Tishchenkoet al.(MuLan), Phys

    V. Tishchenkoet al.(MuLan), Phys. Rev. D87, 052003 (2013), arXiv:1211.0960 [hep-ex]

    Pith/arXiv arXiv 2013

  2. [2]

    Sirlin, Phys

    A. Sirlin, Phys. Rev. D22, 971 (1980)

    1980

  3. [3]

    Ferroglia, G

    A. Ferroglia, G. Ossola, and A. Sirlin, Nucl. Phys. B 560, 23 (1999), arXiv:hep-ph/9905442

    Pith/arXiv arXiv 1999

  4. [4]

    Ferroglia, C

    A. Ferroglia, C. Greub, A. Sirlin, and Z. Zhang, Phys. Rev. D88, 033012 (2013), arXiv:1307.6900 [hep-ph]

    Pith/arXiv arXiv 2013

  5. [5]

    M. Fael, L. Mercolli, and M. Passera, Phys. Rev. D88, 093011 (2013), arXiv:1310.1081 [hep-ph]

    Pith/arXiv arXiv 2013

  6. [6]

    Kinoshita and A

    T. Kinoshita and A. Sirlin, Phys. Rev.113, 1652 (1959)

    1959

  7. [7]

    van Ritbergen and R

    T. van Ritbergen and R. G. Stuart, Phys. Rev. Lett. 82, 488 (1999), arXiv:hep-ph/9808283

    Pith/arXiv arXiv 1999

  8. [8]

    Steinhauser and T

    M. Steinhauser and T. Seidensticker, Phys. Lett. B467, 271 (1999), arXiv:hep-ph/9909436

    Pith/arXiv arXiv 1999

  9. [9]

    M. Fael, K. Sch¨ onwald, and M. Steinhauser, Phys. Rev. D104, 016003 (2021), arXiv:2011.13654 [hep-ph]

    Pith/arXiv arXiv 2021

  10. [10]

    Fael and J

    M. Fael and J. Usovitsch, Phys. Rev. D108, 114026 (2023), arXiv:2310.03685 [hep-ph]

    Pith/arXiv arXiv 2023

  11. [11]

    van Ritbergen and R

    T. van Ritbergen and R. G. Stuart, Phys. Lett. B437, 201 (1998), arXiv:hep-ph/9802341

    Pith/arXiv arXiv 1998

  12. [12]

    Alibertiet al., Phys

    R. Alibertiet al., Phys. Rept.1143, 1 (2025), arXiv:2505.21476 [hep-ph]

    Pith/arXiv arXiv 2025

  13. [13]

    Aoyama, M

    T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett.109, 111808 (2012), arXiv:1205.5370 [hep-ph]

    Pith/arXiv arXiv 2012

  14. [14]

    Volkov, Phys

    S. Volkov, Phys. Rev. D100, 096004 (2019), arXiv:1909.08015 [hep-ph]

    Pith/arXiv arXiv 2019

  15. [15]

    Volkov, Phys

    S. Volkov, Phys. Rev. D110, 036001 (2024), arXiv:2404.00649 [hep-ph]

    Pith/arXiv arXiv 2024

  16. [16]

    Aoyama, M

    T. Aoyama, M. Hayakawa, A. Hirayama, and M. Nio, Phys. Rev. D111, L031902 (2025), arXiv:2412.06473 [hep-ph]

    Pith/arXiv arXiv 2025

  17. [17]

    R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. M¨ uller, Science360, 191 (2018), arXiv:1812.04130 [physics.atom-ph]

    Pith/arXiv arXiv 2018

  18. [18]

    Morel, Z

    L. Morel, Z. Yao, P. Clad´ e, and S. Guellati-Kh´ elifa, Na- ture588, 61 (2020)

    2020

  19. [19]

    X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, Phys. Rev. Lett.130, 071801 (2023), arXiv:2209.13084 [physics.atom-ph]

    Pith/arXiv arXiv 2023

  20. [20]

    Czarnecki, W

    A. Czarnecki, W. J. Marciano, and A. Vainshtein, Phys. Rev. D67, 073006 (2003), [Erratum: Phys. Rev. D73, 119901 (2006)], arXiv:hep-ph/0212229 [hep-ph]

    Pith/arXiv arXiv 2003

  21. [21]

    Gnendiger, D

    C. Gnendiger, D. St¨ ockinger, and H. St¨ ockinger-Kim, Phys. Rev. D88, 053005 (2013), arXiv:1306.5546 [hep- ph]

    Pith/arXiv arXiv 2013

  22. [22]

    L¨ udtke, M

    J. L¨ udtke, M. Procura, and P. Stoffer, JHEP04, 130, arXiv:2410.11946 [hep-ph]

    Pith/arXiv arXiv

  23. [23]

    Hoferichter, J

    M. Hoferichter, J. L¨ udtke, L. Naterop, M. Procura, and P. Stoffer, Phys. Rev. Lett.134, 201801 (2025), arXiv:2503.04883 [hep-ph]

    Pith/arXiv arXiv 2025

  24. [24]

    T. Blum, P. A. Boyle, V. G¨ ulpers, T. Izubuchi, L. Jin, C. Jung, A. J¨ uttner, C. Lehner, A. Portelli, and J. T. Tsang (RBC, UKQCD), Phys. Rev. Lett.121, 022003 (2018), arXiv:1801.07224 [hep-lat]

    Pith/arXiv arXiv 2018

  25. [25]

    Giusti, V

    D. Giusti, V. Lubicz, G. Martinelli, F. Sanfilippo, and S. Simula (ETM), Phys. Rev. D99, 114502 (2019), arXiv:1901.10462 [hep-lat]

    Pith/arXiv arXiv 2019

  26. [26]

    Bors´ anyiet al., Nature593, 51 (2021), arXiv:2002.12347 [hep-lat]

    S. Bors´ anyiet al., Nature593, 51 (2021), arXiv:2002.12347 [hep-lat]

    Pith/arXiv arXiv 2021

  27. [27]

    Lehner and A

    C. Lehner and A. S. Meyer, Phys. Rev. D101, 074515 (2020), arXiv:2003.04177 [hep-lat]

    Pith/arXiv arXiv 2020

  28. [28]

    G. Wang, T. Draper, K.-F. Liu, and Y.-B. Yang (χQCD), Phys. Rev. D107, 034513 (2023), arXiv:2204.01280 [hep-lat]

    Pith/arXiv arXiv 2023

  29. [29]

    Aubin, T

    C. Aubin, T. Blum, M. Golterman, and S. Peris, Phys. Rev. D106, 054503 (2022), arXiv:2204.12256 [hep-lat]

    Pith/arXiv arXiv 2022

  30. [30]

    C` eet al., Phys

    M. C` eet al., Phys. Rev. D106, 114502 (2022), arXiv:2206.06582 [hep-lat]

    Pith/arXiv arXiv 2022

  31. [31]

    Alexandrouet al.(ETM), Phys

    C. Alexandrouet al.(ETM), Phys. Rev. D107, 074506 (2023), arXiv:2206.15084 [hep-lat]

    Pith/arXiv arXiv 2023

  32. [32]

    Blumet al.(RBC, UKQCD), Phys

    T. Blumet al.(RBC, UKQCD), Phys. Rev. D108, 054507 (2023), arXiv:2301.08696 [hep-lat]

    Pith/arXiv arXiv 2023

  33. [33]

    Kuberski, M

    S. Kuberski, M. C` e, G. von Hippel, H. B. Meyer, K. Ottnad, A. Risch, and H. Wittig, JHEP03, 172, arXiv:2401.11895 [hep-lat]

    Pith/arXiv arXiv

  34. [34]

    Boccalettiet al., (2024), arXiv:2407.10913 [hep-lat]

    A. Boccalettiet al., (2024), arXiv:2407.10913 [hep-lat]

    Pith/arXiv arXiv 2024

  35. [35]

    Spiegel and C

    S. Spiegel and C. Lehner, Phys. Rev. D111, 114517 (2025), arXiv:2410.17053 [hep-lat]

    Pith/arXiv arXiv 2025

  36. [36]

    Blumet al.(RBC, UKQCD), Phys

    T. Blumet al.(RBC, UKQCD), Phys. Rev. Lett.134, 201901 (2025), arXiv:2410.20590 [hep-lat]

    Pith/arXiv arXiv 2025

  37. [37]

    Djukanovic, G

    D. Djukanovic, G. von Hippel, S. Kuberski, H. B. Meyer, N. Miller, K. Ottnad, J. Parrino, A. Risch, and H. Wit- tig, JHEP04, 098, arXiv:2411.07969 [hep-lat]. 6

    Pith/arXiv arXiv

  38. [38]

    Alexandrouet al.(ETM), Phys

    C. Alexandrouet al.(ETM), Phys. Rev. D111, 054502 (2025), arXiv:2411.08852 [hep-lat]

    Pith/arXiv arXiv 2025

  39. [39]

    Bazavovet al.(Fermilab Lattice, HPQCD, MILC), Phys

    A. Bazavovet al.(Fermilab Lattice, HPQCD, MILC), Phys. Rev. D111, 094508 (2025), arXiv:2411.09656 [hep-lat]

    Pith/arXiv arXiv 2025

  40. [40]

    Bazavovet al.(Fermilab Lattice, HPQCD, MILC), Phys

    A. Bazavovet al.(Fermilab Lattice, HPQCD, MILC), Phys. Rev. Lett.135, 011901 (2025), arXiv:2412.18491 [hep-lat]

    Pith/arXiv arXiv 2025

  41. [41]

    Keshavarzi, D

    A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D101, 014029 (2020), arXiv:1911.00367 [hep-ph]

    Pith/arXiv arXiv 2020

  42. [42]

    Di Luzio, A

    L. Di Luzio, A. Keshavarzi, A. Masiero, and P. Paradisi, Phys. Rev. Lett.134, 011902 (2025), arXiv:2408.01123 [hep-ph]

    Pith/arXiv arXiv 2025

  43. [43]

    A. Kurz, T. Liu, P. Marquard, and M. Steinhauser, Phys. Lett. B734, 144 (2014), arXiv:1403.6400 [hep- ph]

    Pith/arXiv arXiv 2014

  44. [44]

    Colangelo, M

    G. Colangelo, M. Hoferichter, M. Procura, and P. Stof- fer, JHEP09, 074, arXiv:1506.01386 [hep-ph]

    Pith/arXiv arXiv

  45. [45]

    Masjuan and P

    P. Masjuan and P. S´ anchez-Puertas, Phys. Rev. D95, 054026 (2017), arXiv:1701.05829 [hep-ph]

    Pith/arXiv arXiv 2017

  46. [46]

    Colangelo, M

    G. Colangelo, M. Hoferichter, M. Procura, and P. Stof- fer, JHEP04, 161, arXiv:1702.07347 [hep-ph]

    Pith/arXiv arXiv

  47. [47]

    Hoferichter, B.-L

    M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, and S. P. Schneider, JHEP10, 141, arXiv:1808.04823 [hep- ph]

    Pith/arXiv arXiv

  48. [48]

    Eichmann, C

    G. Eichmann, C. S. Fischer, E. Weil, and R. Williams, Phys. Lett. B797, 134855 (2019), [Erratum: Phys. Lett. B799, 135029 (2019)], arXiv:1903.10844 [hep-ph]

    Pith/arXiv arXiv 2019

  49. [49]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, and A. Rodr´ ıguez-S´ anchez, Phys. Lett. B798, 134994 (2019), arXiv:1908.03331 [hep-ph]

    Pith/arXiv arXiv 2019

  50. [50]

    Leutgeb and A

    J. Leutgeb and A. Rebhan, Phys. Rev. D101, 114015 (2020), arXiv:1912.01596 [hep-ph]

    Pith/arXiv arXiv 2020

  51. [51]

    Cappiello, O

    L. Cappiello, O. Cat` a, G. D’Ambrosio, D. Grey- nat, and A. Iyer, Phys. Rev. D102, 016009 (2020), arXiv:1912.02779 [hep-ph]

    Pith/arXiv arXiv 2020

  52. [52]

    Masjuan, P

    P. Masjuan, P. Roig, and P. S´ anchez-Puertas, J. Phys. G49, 015002 (2022), arXiv:2005.11761 [hep-ph]

    Pith/arXiv arXiv 2022

  53. [53]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, L. Laub, and A. Rodr´ ıguez-S´ anchez, JHEP10, 203, arXiv:2008.13487 [hep-ph]

    Pith/arXiv arXiv 2008

  54. [54]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, L. Laub, and A. Rodr´ ıguez-S´ anchez, JHEP04, 240, arXiv:2101.09169 [hep-ph]

    Pith/arXiv arXiv

  55. [55]

    Danilkin, M

    I. Danilkin, M. Hoferichter, and P. Stoffer, Phys. Lett. B820, 136502 (2021), arXiv:2105.01666 [hep-ph]

    Pith/arXiv arXiv 2021

  56. [56]

    Stamen, D

    D. Stamen, D. Hariharan, M. Hoferichter, B. Ku- bis, and P. Stoffer, Eur. Phys. J. C82, 432 (2022), arXiv:2202.11106 [hep-ph]

    Pith/arXiv arXiv 2022

  57. [57]

    Leutgeb, J

    J. Leutgeb, J. Mager, and A. Rebhan, Phys. Rev. D 107, 054021 (2023), arXiv:2211.16562 [hep-ph]

    Pith/arXiv arXiv 2023

  58. [58]

    Hoferichter, B

    M. Hoferichter, B. Kubis, and M. Zanke, JHEP08, 209, arXiv:2307.14413 [hep-ph]

    Pith/arXiv arXiv

  59. [59]

    Hoferichter, P

    M. Hoferichter, P. Stoffer, and M. Zillinger, JHEP04, 092, arXiv:2402.14060 [hep-ph]

    Pith/arXiv arXiv

  60. [60]

    E. J. Estrada, S. Gonz` alez-Sol´ ıs, A. Guevara, and P. Roig, JHEP12, 203, arXiv:2409.10503 [hep-ph]

    Pith/arXiv arXiv

  61. [61]

    Deineka, I

    O. Deineka, I. Danilkin, and M. Vanderhaeghen, Phys. Rev. D111, 034009 (2025), arXiv:2410.12894 [hep-ph]

    Pith/arXiv arXiv 2025

  62. [62]

    Eichmann, C

    G. Eichmann, C. S. Fischer, T. Haeuser, and O. Regen- felder, Eur. Phys. J. C85, 445 (2025), arXiv:2411.05652 [hep-ph]

    Pith/arXiv arXiv 2025

  63. [63]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, and A. Rodr´ ıguez-S´ anchez, JHEP03, 094, arXiv:2411.09578 [hep-ph]

    Pith/arXiv arXiv

  64. [64]

    Hoferichter, P

    M. Hoferichter, P. Stoffer, and M. Zillinger, JHEP02, 121, arXiv:2412.00178 [hep-ph]

    Pith/arXiv arXiv

  65. [65]

    S. Holz, M. Hoferichter, B.-L. Hoid, and B. Kubis, JHEP 04, 147, arXiv:2412.16281 [hep-ph]

    Pith/arXiv arXiv

  66. [66]

    Cappiello, J

    L. Cappiello, J. Leutgeb, J. Mager, and A. Rebhan, JHEP07, 033, arXiv:2501.09699 [hep-ph]

    Pith/arXiv arXiv

  67. [67]

    Colangelo, M

    G. Colangelo, M. Hoferichter, A. Nyffeler, M. Passera, and P. Stoffer, Phys. Lett. B735, 90 (2014), arXiv:1403.7512 [hep-ph]

    Pith/arXiv arXiv 2014

  68. [68]

    T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin, C. Jung, and C. Lehner, Phys. Rev. Lett.124, 132002 (2020), arXiv:1911.08123 [hep-lat]

    Pith/arXiv arXiv 2020

  69. [69]

    E.-H. Chao, R. J. Hudspith, A. G´ erardin, J. R. Green, H. B. Meyer, and K. Ottnad, Eur. Phys. J. C81, 651 (2021), arXiv:2104.02632 [hep-lat]

    Pith/arXiv arXiv 2021

  70. [70]

    E.-H. Chao, R. J. Hudspith, A. G´ erardin, J. R. Green, and H. B. Meyer, Eur. Phys. J. C82, 664 (2022), arXiv:2204.08844 [hep-lat]

    Pith/arXiv arXiv 2022

  71. [71]

    T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin, C. Jung, C. Lehner, and C. Tu (RBC, UKQCD), Phys. Rev. D111, 014501 (2025), arXiv:2304.04423 [hep-lat]

    Pith/arXiv arXiv 2025

  72. [72]

    Fodor, A

    Z. Fodor, A. G´ erardin, L. Lellouch, K. K. Szab´ o, B. C. Toth, and C. Zimmermann, Phys. Rev. D111, 114509 (2025), arXiv:2411.11719 [hep-lat]

    Pith/arXiv arXiv 2025

  73. [73]

    P. J. Mohr, D. B. Newell, B. N. Taylor, and E. Tiesinga, Rev. Mod. Phys.97, 025002 (2025), arXiv:2409.03787 [hep-ph]

    Pith/arXiv arXiv 2025

  74. [74]

    Navaset al.(Particle Data Group), Phys

    S. Navaset al.(Particle Data Group), Phys. Rev. D 110, 030001 (2024)

    2024

  75. [75]

    P. A. Baikov, K. G. Chetyrkin, J. H. Kuhn, and C. Sturm, Nucl. Phys. B867, 182 (2013), arXiv:1207.2199 [hep-ph]

    Pith/arXiv arXiv 2013

  76. [76]

    Nir, Phys

    Y. Nir, Phys. Lett. B221, 184 (1989)

    1989

  77. [77]

    van Ritbergen and R

    T. van Ritbergen and R. G. Stuart, Nucl. Phys. B564, 343 (2000), arXiv:hep-ph/9904240

    Pith/arXiv arXiv 2000

  78. [78]

    Pak and A

    A. Pak and A. Czarnecki, Phys. Rev. Lett.100, 241807 (2008), arXiv:0803.0960 [hep-ph]

    Pith/arXiv arXiv 2008

  79. [79]

    L. Chen, X. ChenX, X. Guan, and Y.-Q. Ma, Heavy- to-light Structure Functions atO(α 3 s) in QCD (2026), arXiv:2602.11879 [hep-ph]

    arXiv 2026

  80. [80]

    L. Chen, X. Chen, X. Guan, and Y.-Q. Ma, Triple Differential Heavy-to-light Semi-leptonic Decays at Next-to-Next-to-Next-to-Leading Order in QCD (2026), arXiv:2602.11537 [hep-ph]

    arXiv 2026

Showing first 80 references.