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Study of the two-body nonleptonic Bc(2S) weak decays with the QCD factorization approach

Na Wang1,*, Yueling Yang2,†, and Junfeng Sun2,‡

  • *Contact author: wangna@haut.edu.cn
  • †Contact author: yangyueling@htu.edu.cn
  • ‡Contact author: sunjunfeng@htu.edu.cn

Phys. Rev. D 112, 076029 – Published 23 October, 2025

DOI: https://doi.org/10.1103/f56z-g713

Abstract

Inspired by the promising prospect of the Bc(2S) meson at the coming HL-LHC experiments, the nonleptonic Bc(2S) meson weak decays induced by both the b and c decays are investigated with the quantum chromodynamics (QCD) factorization approach. It is found that branching ratios for the color- and Cabibbo-Kobayashi-Maskawa (CKM)-favored Bc(2S)→Bsρ, Bsπ decays can reach up to O(10−9), which might be measurable. The Bc(2S) decays into the final states containing one charmonium are highly suppressed by the CKM factors, and have significantly small branching ratios, O(10−12) and less, which might be outside the future measurement capability. This paper provides a ready reference for the future experimental study on the hadronic Bc(2S) weak decays.

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References (88)

  1. S. Navas, C. Amsler, T. Gutsche et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  2. C. Chang and Y. Chen, The Bc and B¯c mesons accessible to experiments by Z0 bosons decay, Phys. Lett. B 284, 127 (1992).
  3. C. Chang and Y. Chen, Production of Bc or B¯c meson associated with two heavy quark jets in Z0 boson decay, Phys. Rev. D 46, 3845 (1992); 50, 6013(E) (1994).
  4. Z. Yang, X. Wu, L. Deng, J. Zhang, and G. Chen, Production of the P-wave excited Bc-states through the Z0 boson decays, Eur. Phys. J. C 71, 1563 (2011).
  5. Z. Yang, X. Wu, G. Chen, Q. Liao, and J. Zhang, Bc meson production around the Z0 peak at a high luminosity e+e− collider, Phys. Rev. D 85, 094015 (2012).
  6. Z. Zhang, X. Zheng, and X. Wu, Production of the Bc meson at the CEPC, Eur. Phys. J. C 82, 246 (2022).
  7. X. Zhan, X. Wu, and X. Zheng, Photoproduction of the Bc meson at future e+e− colliders, Phys. Rev. D 106, 094036 (2022).
  8. K. Kołodziej, A. Leike, and R. Rückl, Production mechanisms for Bc mesons in photon-photon collisions, Phys. Lett. B 348, 219 (1995).
  9. V. Kiselev, A. Likhoded, and M. Shevlyagin, Bc and bb¯cc¯ at the Z0-boson pole, Z. Phys. C 63, 77 (1994).
  10. A. Berezhnoy, A. Likhoded, and M. Shevlyagin, Photonic production of Bc-mesons, Phys. Lett. B 342, 351 (1995).
  11. A. Berezhnoy, V. Kiselev, and A. Likhoded, Photonic production of P-wave states of Bc mesons, Phys. Lett. B 381, 341 (1996).
  12. A. Berezhnoy, A. Likhoded, A. Onishchenko, and S. Poslavsky, Next-to-leading order QCD corrections to paired Bc production in e+e− annihilation, Nucl. Phys. B915, 224 (2017).
  13. A. Karyasov, A. Martynenko, and F. Martynenko, Relativistic corrections to the pair Bc-meson production in e+e− annihilation, Nucl. Phys. B911, 36 (2016).
  14. C. Qiao, L. Sun, and R. Zhu, The NLO QCD corrections to Bc meson production in Z0 decays, J. High Energy Phys. 08 (2011) 131.
  15. J. Jiang, L. Chen, and C. Qiao, QCD NLO corrections to inclusive Bc* production in Z0 decays, Phys. Rev. D 91, 034033 (2015).
  16. Z. Chen, H. Yang, and C. Qiao, NLO QCD corrections to Bc-pair production in photon-photon collisions, Phys. Rev. D 102, 016011 (2020).
  17. Y. Wei, R. Li, D. Luo, C. Lü, and Y. Shen, Exclusive production of Bc mesons in e+e− colliders, Chin. Phys. C 42, 083107 (2018).
  18. C. Qiao, L. Sun, D. Yang, and R. Zhu, W boson inclusive decays to quarkonium and Bc(*) meson at the LHC, Eur. Phys. J. C 71, 1766 (2011).
  19. Z. Chen, H. Yang, and C. Qiao, NLO QCD corrections to inclusive charmonium and Bc meson production in W+ decays, Phys. Rev. D 101, 036009 (2020).
  20. X. Zhang, C. Chang, X. Wu, J. Zeng, and X. Huang, Next-to-leading order QCD corrections to the production of Bc and Bc* through W+-boson decays, Phys. Rev. D 101, 034029 (2020).
  21. J. Jiang and C. Qiao, Bc production in Higgs boson decays, Phys. Rev. D 93, 054031 (2016).
  22. Q. Liao, Y. Deng, Y. Yu, G. Wang, and G. Xie, Heavy P-wave quarkonium production via Higgs decays, Phys. Rev. D 98, 036014 (2018).
  23. Q. Liao and J. Jiang, Excited heavy quarkonium production in Higgs boson decays, Phys. Rev. D 100, 053002 (2019).
  24. I. Belov, A. Berezhnoy, A. Dorokhov, A. K. Likhoded, A. P. Martynenko, and F. A. Martynenko, Higgs boson decay to paired Bc: Relativistic and one-loop corrections, Nucl. Phys. A1015, 122285 (2021).
  25. X. Zheng, X. Wu, X. Zhan, G. Wang, and H. Li, Higgs boson decays to Bc meson in the fragmentation-function approach, Phys. Rev. D 107, 074005 (2023).
  26. C. Qiao, C. Li, and K. Chao, Top quark decays into heavy quark mesons, Phys. Rev. D 54, 5606 (1996).
  27. P. Sun, L. Sun, and C. Qiao, Next-to-leading order corrections to top quark decays to heavy quarkonia, Phys. Rev. D 81, 114035 (2010).
  28. C. Chang, J. Wang, and X. Wu, Production of Bc or B¯c meson and its excited states via t¯-quark or t-quark decays, Phys. Rev. D 77, 014022 (2008).
  29. J. Niu, L. Guo, H. Ma, and S. Wang, Heavy quarkonium production through the top quark rare decays via the channels involving flavor changing neutral currents, Eur. Phys. J. C 78, 657 (2018).
  30. C. Chang and Y. Chen, Hadronic production of the Bc meson at TeV energies, Phys. Rev. D 48, 4086 (1993).
  31. N. Brambilla, M. Krämer, R. Mussa et al. (Quarkonium Working Group), Heavy quarkonium physics, CERN Yellow Report, CERN-2005-005, The Quarkonium Working Group, 2005.
  32. C. Chang and X. Wu, Uncertainties in estimating Bc hadronic production and comparisons of the production at Tevatron and LHC, Eur. Phys. J. C 38, 267 (2004).
  33. G. Chen, C. Chang, and X. Wu, Bc(*)-meson production via the proton-nucleus and the nucleus-nucleus collision modes at the colliders RHIC and LHC, Phys. Rev. D 97, 114022 (2018).
  34. Y. Gao, J. He, P. Robbe, M. Schune, and Z. Yang, Experimental prospects of the Bc studies of the LHCb experiment, Chin. Phys. Lett. 27, 061302 (2010).
  35. https://home.cern/resources/faqs/high-luminosity-lhc
  36. A. Sirunyan et al. (CMS Collaboration), Measurement of Bc(2S)+ and Bc*(2S)+ cross section ratios in proton-proton collisions at s=13  TeV, Phys. Rev. D 102, 092007 (2020).
  37. G. Aad et al. (ATLAS Collaboration), Observation of an excited Bc± meson state with the ATLAS detector, Phys. Rev. Lett. 113, 212004 (2014).
  38. A. Sirunyan et al. (CMS Collaboration), Observation of two excited Bc+ states and measurement of the Bc+(2S) mass in pp collisions at s=13  TeV, Phys. Rev. Lett. 122, 132001 (2019).
  39. R. Aaij et al. (LHCb Collaboration), Observation of an excited Bc+ state, Phys. Rev. Lett. 122, 232001 (2019).
  40. E. Eichten and C. Quigg, Mesons with beauty and charm: Spectroscopy, Phys. Rev. D 49, 5845 (1994).
  41. L. Fulcher, Phenomenological predictions of the properties of the Bc system, Phys. Rev. D 60, 074006 (1999).
  42. S. Godfrey, Spectroscopy of Bc mesons in the relativized quark model, Phys. Rev. D 70, 054017 (2004).
  43. I. Asghar, F. Akram, B. Masud, and M. Sultan, Properties of excited charmed-bottom mesons, Phys. Rev. D 100, 096002 (2019).
  44. B. Martín-González, P. Ortega, D. Entem, F. Fernández, and J. Segovia, Toward the discovery of novel Bc states: Radiative and hadronic transitions, Phys. Rev. D 106, 054009 (2022).
  45. X. Li, Y. Li, F. Wang, and X. Liu, Spectroscopic survey of higher-lying states of Bc meson family, Eur. Phys. J. C 83, 1080 (2023).
  46. M. Lusignoli and M. Masetti, Bc decays, Z. Phys. C 51, 549 (1991).
  47. C. Chang and Y. Chen, Decays of the Bc meson, Phys. Rev. D 49, 3399 (1994).
  48. I. Bigi, Inclusive Bc decays as a QCD lab, Phys. Lett. B 371, 105 (1996).
  49. J. Sun, G. Xue, Y. Yang, G. Lu, and D. Du, Study of Bc−→J/ψπ−, ηcπ− decays with QCD factorization, Phys. Rev. D 77, 074013 (2008).
  50. J. Sun, Y. Yang, W. Du, and H. Ma, Study of Bc→B(*)P, BV decays with QCD factorization, Phys. Rev. D 77, 114004 (2008).
  51. J. Sun, N, Wang, Q. Chang, and Y. Yang, Bc→BP, BV decays with the QCD factorization approach, Adv. High Energy Phys. 2015, 104378 (2015).
  52. Y. Yang, J. Sun, and N. Wang, Study of Bc→KK decay with perturbative QCD approach, Phys. Rev. D 81, 074012 (2010).
  53. J. Sun, Y. Yang, Q. Chang, and G. Lu, Phenomenological study of the Bc→BP, BV decays with perturbative QCD approach, Phys. Rev. D 89, 114019 (2014).
  54. J. Sun, Y. Yang, and G. Lu, Study of the Bc→Bsπ decay with the perturbative QCD approach, Sci. China Phys. Mech. Astron. 57, 1891 (2014).
  55. Z. Xiao and X. Liu, The two-body hadronic decays of Bc meson in the perturbative QCD approach: A short review, Chin. Sci. Bull. 59, 3748 (2014).
  56. M. Beneke, G. Buchalla, M. Neubert, and C. Sachrajda, QCD factorization for B→ππ decays: Strong phases and CP violation in the heavy quark limit, Phys. Rev. Lett. 83, 1914 (1999).
  57. M. Beneke, G. Buchalla, M. Neubert, and C. Sachrajda, QCD factorization for exclusive nonleptonic B meson decays: General arguments and the case of heavy light final states, Nucl. Phys. B591, 313 (2000).
  58. M. Beneke, G. Buchalla, M. Neubert, and C. Sachrajda, QCD factorization in B→πK, ππ decays and extraction of Wolfenstein parameters, Nucl. Phys. B606, 245 (2001).
  59. D. Du, D. Yang, and G. Zhu, Analysis of the decays B→ππ and πK with QCD factorization in the heavy quark limit, Phys. Lett. B 488, 46 (2000).
  60. D. Du, D. Yang, and G. Zhu, Infrared divergence and twist-3 distribution amplitudes in QCD factorization for B→PP, Phys. Lett. B 509, 263 (2001).
  61. D. Du, D. Yang, and G. Zhu, QCD factorization for B→PP, Phys. Rev. D 64, 014036 (2001).
  62. G. Buchalla, A. Buras, and M. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996).
  63. G. Lepage and S. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22, 2157 (1980).
  64. P. Ball, V. Braun, and A. Lenz, Higher-twist distribution amplitudes of the K meson in QCD, J. High Energy Phys. 05 (2006) 004.
  65. P. Ball and G. Jones, Twist-3 distribution amplitudes of K* and ϕ mesons, J. High Energy Phys. 03 (2007) 069.
  66. T. Huber, S. Kŕankl, and X. Li, Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization, J. High Energy Phys. 09 (2016) 112.
  67. M. Beneke, T. Huber, and X. Li, NNLO vertex corrections to non-leptonic B decays: Tree amplitudes, Nucl. Phys. B832, 109 (2010).
  68. Th. Feldmann, P. Kroll, and B. Stech, Mixing and decay constants of pseudoscalar mesons, Phys. Rev. D 58, 114006 (1998).
  69. M. Wirbel, B. Stech, and M Bauer, Exclusive semileptonic decays of heavy mesons, Z. Phys. C 29, 637 (1985).
  70. Y. Yang, J. Sun, Y. Guo, Q. Li, J. Huang, and Q. Chang, Study of ϒ(nS)→BcP decays with perturbative QCD approach, Phys. Lett. B 751, 171 (2015).
  71. J. Sun, Y. Yang, Q. Li, H. Li, Q. Chang, and J. Huang, The ϒ(nS)→BcDs, BcDd decays with perturbative QCD approach, Phys. Lett. B 752, 322 (2016).
  72. J. Sun, L. Chen, N. Wang, J. Huang, Y. Yang, and Q. Chang, Study on ϒ(nS)→BcM decays, J. Phys. G 42, 105005 (2015).
  73. J. Sun, Y. Yang, J. Huang, L. Chen, and Q. Chang, Study of the ψ(1S,2S) and ηc(1S,2S) weak decays into DM, Adv. High Energy Phys. 2016, 5071671 (2016).
  74. J. Sun, Y. Yang, N. Wang, J. Huang, and Q. Chang, Study of Bc*→ψ(1S,2S)P, ηc(1S,2S)P weak decays, Phys. Rev. D 95, 036024 (2017).
  75. S. Gershtein, V. Kiselev, A. Likhoded, and A. Tkabladze, Bc spectroscopy, Phys. Rev. D 51, 3613 (1995).
  76. J. Zeng, J. Orden, and W. Roberts, Heavy mesons in a relativistic model, Phys. Rev. D 52, 5229 (1995).
  77. S. Gupta and J. Johnson, Bc spectroscopy in a quantum-chromodynamic Potentkl model, Phys. Rev. D 53, 312 (1996).
  78. D. Ebert, R. Faustov, and V. Galkin, Properties of heavy quarkonia and Bc mesons in the relativistic quark model, Phys. Rev. D 67, 014027 (2003).
  79. D. Ebert, R. Faustov, and V. Galkin, Spectroscopy and Regge trajectories of heavy quarkonia and Bc mesons, Eur. Phys. J. C 71, 1825 (2011).
  80. A. Monteiro, M. Bhat, and K. Kumar, c¯b spectrum and decay properties with coupled channel effects, Phys. Rev. D 95, 054016 (2017).
  81. N. Soni, B. Joshi, R. Shah, H. Chauhan, and J. Pandya, QQ¯ (Q∈{b,c}) spectroscopy using the Cornell potential, Eur. Phys. J. C 78, 592 (2018).
  82. E. Eichten and C. Quigg, Mesons with beauty and charm: New horizons in spectroscopy, Phys. Rev. D 99, 054025 (2019).
  83. Q. Li, M. Liu, L. Lu, Q. Lü, L. Gui, and X. Zhong, Excited bottom-charmed mesons in a nonrelativistic quark model, Phys. Rev. D 99, 096020 (2019).
  84. G. Wang, T. Wang, Q. Li, and C. Chang, The mass spectrum and wave functions of the Bc system, J. High Energy Phys. 05 (2022) 006.
  85. Y. Keum, H. Li, and A. Sanda, Penguin enhancement and B→Kπ decays in perturbative QCD, Phys. Rev. D 63, 054008 (2001).
  86. Y. Yang, L. Lang, X. Zhao, J. Huang, and J. Sun, Reinvestigating the B→PP decays by including the contributions from ϕB2, Phys. Rev. D 103, 056006 (2021).
  87. Y. Yang, X. Zhao, L. Lang, J. Huang, and J. Sun, Reinvestigating B→PV decays by including contributions from ϕB2 with the perturbative QCD approach, Chin. Phys. C 46, 083103 (2022).
  88. Y. Yang, Zhao Lü, S. Jin, and J. Sun, Revisiting Bs→PP and PV decays with contributions from ϕB2 with perturbativen QCD approach, Eur. Phys. J. C 85, 544 (2025).

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