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Systematic analysis of the form factors of Bc to P-wave charmonia and corresponding weak decays

Jie Lu1,2, Dian-Yong Chen1,3,*, Guo-Liang Yu2,†, Zhi-Gang Wang2,‡, and Bin Wu2

  • 1School of Physics, Southeast University, Nanjing 210094, People’s Republic of China
  • 2Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, People’s Republic of China
  • 3Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, People’s Republic of China

  • *Contact author: chendy@seu.edu.cn
  • †Contact author: yuguoliang2011@163.com
  • ‡Contact author: zgwang@aliyun.com

Phys. Rev. D 111, 114037 – Published 30 June, 2025

DOI: https://doi.org/10.1103/s1ym-ph27

Abstract

In this article, the vector, axial vector, and tensor form factors of Bc→χcJ (J=0, 1, 2) and Bc→hc are analyzed within the framework of three-point QCD sum rules. With the calculated vector and axial vector form factors, we directly study the decay widths and branching ratios of semileptonic decays Bc−→χcJlν¯l,hclν¯l (l=e, μ and τ) and analyze the nonleptonic decays Bc−→χcJπ−,χcJK−,χcJρ−,χcJK*−, Bc−→hcπ−,hcK−,hcρ−,hcK*− by using the naive factorization approach. These results can provide more information to understand the properties of Bc meson and P-wave charmonia and to study the heavy quark dynamics.

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References (91)

  1. F. Abe et al. (CDF Collaboration), Phys. Rev. D 58, 112004 (1998).
  2. C.-H. Chang and Y.-Q. Chen, Phys. Rev. D 49, 3399 (1994).
  3. C.-H. Chang, J.-P. Cheng, and C.-D. Lu, Phys. Lett. B 425, 166 (1998).
  4. Y.-N. Gao, J. He, P. Robbe, M.-H. Schune, and Z.-W. Yang, Chin. Phys. Lett. 27, 061302 (2010).
  5. A. Lytle, B. Colquhoun, C. Davies, J. Koponen, and C. McNeile (HPQCD Collaboration), Proc. Sci. LATTICE2016 (2016) 281 [arXiv:1611.01987].
  6. J. Harrison, C. T. H. Davies, and A. Lytle (HPQCD Collaboration), Phys. Rev. D 102, 094518 (2020).
  7. P. Colangelo, G. Nardulli, and N. Paver, Z. Phys. C 57, 43 (1993).
  8. V. V. Kiselev, A. E. Kovalsky, and A. K. Likhoded, Nucl. Phys. B585, 353 (2000).
  9. K. Azizi, H. Sundu, and M. Bayar, Phys. Rev. D 79, 116001 (2009).
  10. K. Azizi, Y. Sarac, and H. Sundu, Eur. Phys. J. C 73, 2638 (2013).
  11. B. Wu, G.-L. Yu, J. Lu, and Z.-G. Wang, Phys. Lett. B 859, 139118 (2024).
  12. T. Huang and F. Zuo, Eur. Phys. J. C 51, 833 (2007).
  13. Y.-M. Wang and C.-D. Lu, Phys. Rev. D 77, 054003 (2008).
  14. D. Leljak, B. Melic, and M. Patra, J. High Energy Phys. 05 (2019) 094.
  15. M. Bordone, A. Khodjamirian, and T. Mannel, J. High Energy Phys. 01 (2023) 032.
  16. V. V. Kiselev, O. N. Pakhomova, and V. A. Saleev, J. Phys. G 28, 595 (2002).
  17. Z. Rui, Phys. Rev. D 97, 033001 (2018).
  18. X. Liu, H.-n. Li, and Z.-J. Xiao, Phys. Rev. D 97, 113001 (2018).
  19. X. Liu, H.-n. Li, and Z.-J. Xiao, Phys. Lett. B 811, 135892 (2020).
  20. M. A. Nobes and R. M. Woloshyn, J. Phys. G 26, 1079 (2000).
  21. M. A. Ivanov, J. G. Korner, and P. Santorelli, Phys. Rev. D 73, 054024 (2006).
  22. D. Ebert, R. N. Faustov, and V. O. Galkin, Phys. Rev. D 82, 034019 (2010).
  23. E. Hernandez, J. Nieves, and J. M. Verde-Velasco, Phys. Rev. D 74, 074008 (2006).
  24. W. Wang, Y.-L. Shen, and C.-D. Lu, Phys. Rev. D 79, 054012 (2009).
  25. X.-X. Wang, W. Wang, and C.-D. Lu, Phys. Rev. D 79, 114018 (2009).
  26. Z.-Q. Zhang, Z.-J. Sun, Y.-C. Zhao, Y.-Y. Yang, and Z.-Y. Zhang, Eur. Phys. J. C 83, 477 (2023).
  27. X.-J. Li, Y.-S. Li, F.-L. Wang, and X. Liu, Eur. Phys. J. C 83, 1080 (2023).
  28. A. Hazra, S. T. Mary, N. Sharma, and R. Dhir, Eur. Phys. J. C 84, 944 (2024).
  29. S. T. Mary, A. Hazra, N. Sharma, and R. Dhir, Eur. Phys. J. C 85, 204 (2025).
  30. C.-F. Qiao, P. Sun, D. Yang, and R.-L. Zhu, Phys. Rev. D 89, 034008 (2014).
  31. R. Zhu, Nucl. Phys. B931, 359 (2018).
  32. R.-Y. Tang, Z.-R. Huang, C.-D. Lü, and R. Zhu, J. Phys. G 49, 115003 (2022).
  33. C.-H. Chang, Y.-Q. Chen, G.-L. Wang, and H.-S. Zong, Phys. Rev. D 65, 014017 (2002).
  34. C.-T. Tran, M. A. Ivanov, J. G. Körner, and P. Santorelli, Phys. Rev. D 97, 054014 (2018).
  35. W. Wei, X. Liu, and S.-L. Zhu, Phys. Rev. D 75, 014013 (2007).
  36. Z.-G. Wang, J. High Energy Phys. 10 (2013) 208.
  37. H.-X. Chen, W. Chen, Q. Mao, A. Hosaka, X. Liu, and S.-L. Zhu, Phys. Rev. D 91, 054034 (2015).
  38. Z.-G. Wang, Eur. Phys. J. C 75, 427 (2015).
  39. H.-X. Chen, Q. Mao, A. Hosaka, X. Liu, and S.-L. Zhu, Phys. Rev. D 94, 114016 (2016).
  40. Y. Zhang, T. Zhong, H.-B. Fu, W. Cheng, and X.-G. Wu, Phys. Rev. D 103, 114024 (2021).
  41. Z.-G. Wang, Nucl. Phys. B985, 115983 (2022).
  42. D. Huang, T. Zhong, H.-B. Fu, Z.-H. Wu, X.-G. Wu, and H. Tong, Eur. Phys. J. C 83, 680 (2023).
  43. N. Su, H.-X. Chen, P. Gubler, and A. Hosaka, Phys. Rev. D 110, 034007 (2024).
  44. Z.-G. Wang, Chin. Phys. C 48, 103104 (2024).
  45. Y.-M. Wang, H. Zou, Z.-T. Wei, X.-Q. Li, and C.-D. Lu, Eur. Phys. J. C 54, 107 (2008).
  46. Y.-M. Wang, H. Zou, Z.-T. Wei, X.-Q. Li, and C.-D. Lu, J. Phys. G 36, 105002 (2009).
  47. Y.-J. Shi, W. Wang, and Z.-X. Zhao, Eur. Phys. J. C 80, 568 (2020).
  48. Y.-Q. Peng and M.-Z. Yang, Commun. Theor. Phys. 72, 095201 (2020).
  49. Z.-X. Zhao, R.-H. Li, Y.-L. Shen, Y.-J. Shi, and Y.-S. Yang, Eur. Phys. J. C 80, 1181 (2020).
  50. Z. Neishabouri, K. Azizi, and H. R. Moshfegh, Phys. Rev. D 110, 014010 (2024).
  51. M. S. Tousi, K. Azizi, and H. R. Moshfegh, Phys. Rev. D 110, 114001 (2024).
  52. J. Lu, G.-L. Yu, Z.-G. Wang, and B. Wu, Phys. Lett. B 852, 138624 (2024).
  53. M. E. Bracco, M. Chiapparini, F. S. Navarra, and M. Nielsen, Prog. Part. Nucl. Phys. 67, 1019 (2012).
  54. Z.-G. Wang, Phys. Rev. D 89, 034017 (2014).
  55. K. Azizi, Y. Sarac, and H. Sundu, Phys. Rev. D 90, 114011 (2014).
  56. K. Azizi, Y. Sarac, and H. Sundu, Nucl. Phys. A943, 159 (2015).
  57. G.-L. Yu, Z.-Y. Li, and Z.-G. Wang, Eur. Phys. J. C 75, 243 (2015).
  58. B. O. Rodrigues, M. E. Bracco, and C. M. Zanetti, Nucl. Phys. A966, 208 (2017).
  59. G.-L. Yu, Z.-G. Wang, and Z.-Y. Li, Eur. Phys. J. C 79, 798 (2019).
  60. J. Lu, G.-L. Yu, and Z.-G. Wang, Eur. Phys. J. A 59, 195 (2023).
  61. J. Lu, G.-L. Yu, Z.-G. Wang, and B. Wu, Eur. Phys. J. C 83, 907 (2023).
  62. Z.-G. Wang, Eur. Phys. J. C 78, 297 (2018).
  63. Z. Dehghan, K. Azizi, and U. Özdem, Phys. Rev. D 108, 094037 (2023).
  64. U. Özdem and K. Azizi, Phys. Rev. D 109, 114019 (2024).
  65. P. Colangelo and A. Khodjamirian, QCD sum rules, a modern perspective, in At the Frontier of Particle Physics (World Scientific, Singapore, 2000), pp. 1495–1576.
  66. M. Wirbel, B. Stech, and M. Bauer, Z. Phys. C 29, 637 (1985).
  67. P. Colangelo, F. De Fazio, N. Losacco, F. Loparco, and M. Novoa-Brunet, Phys. Rev. D 106, 094005 (2022).
  68. M. E. Bracco, F. S. Navarra, and M. Nielsen, Phys. Lett. B 454, 346 (1999).
  69. Z.-G. Wang and Z.-Y. Di, Eur. Phys. J. A 50, 143 (2014).
  70. B. L. Ioffe and A. V. Smilga, Nucl. Phys. B216, 373 (1983).
  71. M. Bauer and B. Stech, Phys. Lett. 152B, 380 (1985).
  72. M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C 34, 103 (1987).
  73. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  74. V. A. Novikov, L. B. Okun, M. A. Shifman, A. I. Vainshtein, M. B. Voloshin, and V. I. Zakharov, Phys. Rep. 41, 1 (1978).
  75. D. Bečirević, G. Duplančić, B. Klajn, B. Melić, and F. Sanfilippo, Nucl. Phys. B883, 306 (2014).
  76. T. M. Aliev, K. Azizi, and M. Savci, Phys. Lett. B 690, 164 (2010).
  77. S. Narison, Phys. Lett. B 693, 559 (2010); 705, 544(E) (2011).
  78. S. Narison, Phys. Lett. B 706, 412 (2012).
  79. S. Narison, Phys. Lett. B 707, 259 (2012).
  80. C. G. Boyd, B. Grinstein, and R. F. Lebed, Phys. Rev. Lett. 74, 4603 (1995).
  81. C. Bourrely, I. Caprini, and L. Lellouch, Phys. Rev. D 79, 013008 (2009); 82, 099902(E) (2010).
  82. Y.-M. Wang and Y.-L. Shen, Nucl. Phys. B898, 563 (2015).
  83. B.-Y. Cui, Y.-K. Huang, Y.-L. Shen, C. Wang, and Y.-M. Wang, J. High Energy Phys. 03 (2023) 140.
  84. Z.-G. Wang, Eur. Phys. J. C 73, 2533 (2013).
  85. G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Rev. Mod. Phys. 68, 1125 (1996).
  86. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 114, 132001 (2015).
  87. N. Losacco, Mod. Phys. Lett. A 38, 2350027 (2023).
  88. M. Beneke, G. Buchalla, M. Neubert, and C. T. Sachrajda, Phys. Rev. Lett. 83, 1914 (1999).
  89. M. Beneke and M. Neubert, Nucl. Phys. B675, 333 (2003).
  90. H.-n. Li and H.-L. Yu, Phys. Rev. D 53, 2480 (1996).
  91. H.-Y. Cheng, H.-n. Li, and K.-C. Yang, Phys. Rev. D 60, 094005 (1999).

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