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B→Xcℓν¯ decay as a probe of complex conjugate poles

Jinglong Zhu1,* and Hiroyuki Umeeda1,2,3,†

  • *Contact author: zhujl23@mails.jlu.edu.cn
  • †Contact author: umeeda@jlu.edu.cn
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Phys. Rev. D 112, 014006 – Published 2 July, 2025

DOI: https://doi.org/10.1103/ky9k-mmxd

Abstract

In this work, nontrivial analytic structure of the quark propagator is discussed for B-meson inclusive decays. Attributed to invalidity of the standard Källén-Lehman spectral representation, complex conjugate poles alter the evaluation of decay rates, which lead to violation of quark-hadron duality. As phenomenological observables, widths in B→Xcℓν¯ decay as well as the lifetime of the Bd0 meson are discussed. In the presence of the mentioned nonanalytical contributions, the possibility for resolving the |Vcb| puzzle is addressed. It is demonstrated that there exists a parameter region, which explains |Vcb| and Bd0-meson lifetime simultaneously within 1σ via the complex conjugate poles from a charm quark.

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References (60)

  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. M. Bordone, B. Capdevila, and P. Gambino, Three loop calculations and inclusive Vcb, Phys. Lett. B 822, 136679 (2021).
  4. F. Bernlochner, M. Fael, K. Olschewsky, E. Persson, R. van Tonder, K. K. Vos, and M. Welsch, First extraction of inclusive Vcb from q2 moments, J. High Energy Phys. 10 (2022) 068.
  5. G. Finauri and P. Gambino, The q2 moments in inclusive semileptonic B decays, J. High Energy Phys. 02 (2024) 206.
  6. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG), FLAG review 2021, Eur. Phys. J. C 82, 869 (2022).
  7. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  8. A. Crivellin and S. Pokorski, Can the differences in the determinations of Vub and Vcb be explained by new physics?, Phys. Rev. Lett. 114, 011802 (2015).
  9. J. P. Lees et al. (BABAR Collaboration, Model-independent extraction of form factors and |Vcb| in B¯→Dℓ−ν¯ℓ with hadronic tagging at BABAR, Phys. Rev. D 110, 032018 (2024).
  10. K. G. Wilson, Nonlagrangian models of current algebra, Phys. Rev. 179, 1499 (1969).
  11. J. Chay, H. Georgi, and B. Grinstein, Lepton energy distributions in heavy meson decays from QCD, Phys. Lett. B 247, 399 (1990).
  12. I. I. Y. Bigi, M. A. Shifman, N. G. Uraltsev, and A. I. Vainshtein, QCD predictions for lepton spectra in inclusive heavy flavor decays, Phys. Rev. Lett. 71, 496 (1993).
  13. A. V. Manohar and M. B. Wise, Inclusive semileptonic B and polarized Λb decays from QCD, Phys. Rev. D 49, 1310 (1994).
  14. B. Blok, L. Koyrakh, M. A. Shifman, and A. I. Vainshtein, Differential distributions in semileptonic decays of the heavy flavors in QCD, Phys. Rev. D 49, 3356 (1994); 50, 3572(E) (1994).
  15. E. D. Bloom and F. J. Gilman, Scaling, duality, and the behavior of resonances in inelastic electron-proton scattering, Phys. Rev. Lett. 25, 1140 (1970).
  16. E. D. Bloom and F. J. Gilman, Scaling and the behavior of nucleon resonances in inelastic electron-nucleon scattering, Phys. Rev. D 4, 2901 (1971).
  17. E. C. Poggio, H. R. Quinn, and S. Weinberg, Smearing the quark model, Phys. Rev. D 13, 1958 (1976).
  18. M. A. Shifman, Quark hadron duality, in Proceedings of the 8th International Symposium on Heavy Flavor Physics (World Scientific, Singapore, 2000), Vol. 3, pp. 1447–1494, arXiv:hep-ph/0009131.
  19. J. Chay and S.-J. Rey, Instanton contribution to B→Xueν¯ decay, Z. Phys. C 68, 431 (1995).
  20. J. Chay and S.-J. Rey, Instanton contribution to B→Xsγ decay, Z. Phys. C 68, 425 (1995).
  21. A. F. Falk and A. Kyatkin, Instantons and the endpoint of the lepton energy spectrum in charmless semileptonic B decays, Phys. Rev. D 52, 5049 (1995).
  22. B. Chibisov, R. D. Dikeman, M. A. Shifman, and N. Uraltsev, Operator product expansion, heavy quarks, QCD duality and its violations, Int. J. Mod. Phys. A 12, 2075 (1997).
  23. H. Umeeda, Is the right-handed current contribution to B→Xulν decays corrected by the nontrivial vacuum in QCD?, Phys. Rev. D 106, 114034 (2022).
  24. P. Colangelo, C. A. Dominguez, and G. Nardulli, Violations of local duality in the heavy quark sector, Phys. Lett. B 409, 417 (1997).
  25. B. Grinstein and R. F. Lebed, Explicit quark—hadron duality in heavy—light meson weak decays in the ’t Hooft model, Phys. Rev. D 57, 1366 (1998).
  26. I. I. Y. Bigi, M. A. Shifman, N. Uraltsev, and A. I. Vainshtein, Heavy flavor decays, OPE and duality in two-dimensional ’t Hooft model, Phys. Rev. D 59, 054011 (1999).
  27. B. Grinstein and R. F. Lebed, Quark hadron duality in the ’t Hooft model for meson weak decays: Different quark diagram topologies, Phys. Rev. D 59, 054022 (1999).
  28. I. I. Y. Bigi and N. Uraltsev, Heavy quark expansion and preasymptotic corrections to decay widths in the ’t Hooft model, Phys. Rev. D 60, 114034 (1999).
  29. I. I. Y. Bigi and N. Uraltsev, Pauli interference in the ’t Hooft model: Heavy quark expansion and quark hadron duality, Phys. Lett. B 457, 163 (1999).
  30. R. F. Lebed and N. G. Uraltsev, Precision studies of duality in the ’t Hooft model, Phys. Rev. D 62, 094011 (2000).
  31. B. Grinstein, Global duality in heavy flavor decays in the ’t Hooft model, Phys. Rev. D 64, 094004 (2001).
  32. B. Grinstein, Global duality in heavy flavor hadronic decays, Phys. Lett. B 529, 99 (2002).
  33. J. Mondejar, A. Pineda, and J. Rojo, Heavy meson semileptonic differential decay rate in two dimensions in the large Nc, J. High Energy Phys. 09 (2006) 060.
  34. H. Umezawa and S. Kamefuchi, The vacuum in quantum electrodynamics, Prog. Theor. Phys. 6, 543 (1951).
  35. G. Källén, On the definition of the renormalization constants in quantum electrodynamics, Helv. Phys. Acta 25, 417 (1952).
  36. H. Lehmann, On the Properties of propagation functions and renormalization contants of quantized fields, Nuovo Cimento 11, 342 (1954).
  37. D. Binosi and R.-A. Tripolt, Spectral functions of confined particles, Phys. Lett. B 801, 135171 (2020).
  38. Z. Zhu, K. Raya, and L. Chang, Extracting a model quark propagator’s spectral density, Phys. Rev. D 103, 034005 (2021).
  39. L. Schlessinger, Use of analyticity in the calculation of nonrelativistic scattering amplitudes, Phys. Rev. 167, 1411 (1968).
  40. D. Zwanziger, Local and renormalizable action from the gribov horizon, Nucl. Phys. B323, 513 (1989).
  41. V. N. Gribov, Quantization of nonAbelian gauge theories, Nucl. Phys. B139, 1 (1978).
  42. Y. Hayashi and K.-I. Kondo, Complex poles and spectral function of Yang-Mills theory, Phys. Rev. D 99, 074001 (2019).
  43. Y. Hayashi and K.-I. Kondo, Complex poles and spectral functions of Landau gauge QCD and QCD-like theories, Phys. Rev. D 101, 074044 (2020).
  44. Y. Hayashi and K.-I. Kondo, Reconstructing confined particles with complex singularities, Phys. Rev. D 103, L111504 (2021).
  45. Y. Hayashi and K.-I. Kondo, Reconstructing propagators of confined particles in the presence of complex singularities, Phys. Rev. D 104, 074024 (2021).
  46. H. Georgi, An effective field theory for heavy quarks at low-energies, Phys. Lett. B 240, 447 (1990).
  47. E. Eichten and B. R. Hill, An effective field theory for the calculation of matrix elements involving heavy quarks, Phys. Lett. B 234, 511 (1990).
  48. E. Eichten and B. R. Hill, Static effective field theory: 1/m corrections, Phys. Lett. B 243, 427 (1990).
  49. T. Mannel, W. Roberts, and Z. Ryzak, A derivation of the heavy quark effective Lagrangian from QCD, Nucl. Phys. B368, 204 (1992).
  50. I. Bigi, M. Shifman, N. G. Uraltsev, and A. Vainshtein, Sum rules for heavy flavor transitions in the small velocity limit, Phys. Rev. D 52, 196 (1995).
  51. G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996).
  52. A. F. Falk, Z. Ligeti, M. Neubert, and Y. Nir, Heavy quark expansion for the inclusive decay B¯→τν¯X, Phys. Lett. B 326, 145 (1994).
  53. S. M. Dorkin, L. P. Kaptari, T. Hilger, and B. Kampfer, Analytical properties of the quark propagator from a truncated Dyson-Schwinger equation in complex Euclidean space, Phys. Rev. C 89, 034005 (2014).
  54. C. G. Boyd, B. Grinstein, and R. F. Lebed, Model-independent extraction of |Vcb| using dispersion relations, Phys. Lett. B 353, 306 (1995).
  55. I. Caprini, L. Lellouch, and M. Neubert, Dispersive bounds on the shape of B¯→D(*)ℓν¯ form factors, Nucl. Phys. B530, 153 (1998).
  56. S. Iguro and R. Watanabe, Bayesian fit analysis to full distribution data of B¯→D(*)ℓν¯:|Vcb| determination and new physics constraints, J. High Energy Phys. 08 (2020) 006.
  57. M. Jung and D. M. Straub, Constraining new physics in b→cℓν transitions, J. High Energy Phys. 01 (2019) 009.
  58. A. Lenz, M. L. Piscopo, and A. V. Rusov, Disintegration of beauty: A precision study, J. High Energy Phys. 01 (2023) 004.
  59. Y. S. Amhis et al. (HFLAV Collaboration), Averages of b-hadron, c-hadron, and τ-lepton properties as of 2021, Phys. Rev. D 107, 052008 (2023).
  60. E. V. Shuryak, The role of instantons in quantum chromodynamics. 1. Physical vacuum, Nucl. Phys. B203, 93 (1982).

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Phys. Rev. D 112, 014006– Published 2 July, 2025
  • Received 20 November 2024
  • Accepted 18 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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