Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Probing the Color-Octet Mechanism via Dihadron Fragmentation in χb Decays

Zhi-Guo He1, Guanghui Li2,3, Yu-Jie Tian2,3, Xin-Kai Wen2,4,*, and Bin Yan2,5,†

  • *Contact author: xinkaiwen@ihep.ac.cn
  • †Contact author: yanbin@ihep.ac.cn

Phys. Rev. Lett. 137, 131903 – Published 25 September, 2026

DOI: https://doi.org/10.1103/ntf8-k9rh

Abstract

The color-octet (CO) mechanism is a cornerstone of nonrelativistic QCD, yet knowledge of its long-distance matrix elements remains limited, preventing stringent tests of the theory. We demonstrate that the Artru-Collins asymmetry in hadronic decays of the P-wave bottomonium state χb2 provides a direct probe of CO dynamics. At leading order, the asymmetry arises exclusively from the CO decay channel, whereas the color-singlet (CS) contribution affects only the unpolarized rate, so that a nonzero signal constitutes unambiguous evidence of the CO mechanism. This observable provides a novel way to extract the ratio ρ8 between CO and CS matrix elements. Focusing on e+e−→ϒ(2S)→γχb2 at Belle, we show that the asymmetric beam configuration preserves the asymmetry in the laboratory frame and avoids the strong suppression present in the center-of-mass frame. With the Belle II dataset, ρ8 could be determined with sufficient precision to address the long-standing discrepancy between the lattice calculations and phenomenological determinations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (44)

  1. G. P. Lepage, L. Magnea, C. Nakhleh, U. Magnea, and K. Hornbostel, Phys. Rev. D 46, 4052 (1992).
  2. G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D 51, 1125 (1995); 55, 5853(E) (1997).
  3. G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D 46, R1914 (1992).
  4. G. T. Bodwin, D. K. Sinclair, and S. Kim, Phys. Rev. D 65, 054504 (2002).
  5. G. T. Bodwin, D. K. Sinclair, and S. Kim, Phys. Rev. Lett. 77, 2376 (1996).
  6. F. Maltoni, in 5th Workshop on QCD (QCD 2000) (2000), pp. 301–314, arXiv:hep-ph/0007003.
  7. G. T. Bodwin, Int. J. Mod. Phys. A 21, 785 (2006).
  8. G. T. Bodwin, E. Braaten, D. Kang, and J. Lee, Phys. Rev. D 76, 054001 (2007).
  9. R. A. Briere et al. (CLEO Collaboration), Phys. Rev. D 78, 092007 (2008).
  10. N. Brambilla, D. Eiras, A. Pineda, J. Soto, and A. Vairo, Phys. Rev. Lett. 88, 012003 (2002).
  11. N. Brambilla, H. S. Chung, D. Müller, and A. Vairo, J. High Energy Phys. 04 (2020) 095.
  12. H. S. Chung, Phys. Rev. D 109, 054001 (2024).
  13. X. Artru and J. C. Collins, Z. Phys. C 69, 277 (1996).
  14. E. Eichten, S. Godfrey, H. Mahlke, and J. L. Rosner, Rev. Mod. Phys. 80, 1161 (2008).
  15. S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
  16. A. Vossen et al. (Belle Collaboration), Phys. Rev. Lett. 107, 072004 (2011).
  17. J. C. Collins, S. F. Heppelmann, and G. A. Ladinsky, Nucl. Phys. B420, 565 (1994).
  18. J. Collins, Foundations of Perturbative QCD (Cambridge University Press, Cambridge, England, 2011), Vol. 32.
  19. R. L. Jaffe, X.-m. Jin, and J. Tang, Phys. Rev. Lett. 80, 1166 (1998).
  20. R. L. Jaffe, X.-m. Jin, and J.-a. Tang, Phys. Rev. D 57, 5920 (1998).
  21. A. Bianconi, S. Boffi, R. Jakob, and M. Radici, Phys. Rev. D 62, 034008 (2000).
  22. A. Bianconi, S. Boffi, R. Jakob, and M. Radici, Phys. Rev. D 62, 034009 (2000).
  23. A. Bacchetta and M. Radici, Phys. Rev. D 69, 074026 (2004).
  24. A. Bacchetta, F. A. Ceccopieri, A. Mukherjee, and M. Radici, Phys. Rev. D 79, 034029 (2009).
  25. J. Zhou and A. Metz, Phys. Rev. Lett. 106, 172001 (2011).
  26. A. Courtoy, A. Bacchetta, M. Radici, and A. Bianconi, Phys. Rev. D 85, 114023 (2012).
  27. M. Radici, A. Courtoy, A. Bacchetta, and M. Guagnelli, J. High Energy Phys. 05 (2015) 123.
  28. D. Pitonyak, C. Cocuzza, A. Metz, A. Prokudin, and N. Sato, Phys. Rev. Lett. 132, 011902 (2024).
  29. C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl (JAM Collaboration), Phys. Rev. Lett. 132, 091901 (2024).
  30. C. Cocuzza, A. Metz, D. Pitonyak, A. Prokudin, N. Sato, and R. Seidl [Jefferson Lab Angular Momentum (JAM) Collaboration], Phys. Rev. D 109, 034024 (2024).
  31. T. C. Rogers, M. Radici, A. Courtoy, and T. Rainaldi, Phys. Rev. D 111, 056001 (2025).
  32. D. Pitonyak, C. Cocuzza, A. Metz, A. Prokudin, and N. Sato, Phys. Rev. D 113, 038901 (2026).
  33. V. Mahaut, L. Polano, A. Bacchetta, V. Bertone, M. Cerutti, M. Radici, and L. Rossi (MAP Collaboration), J. High Energy Phys. 02 (2026) 051.
  34. T. C. Rogers, T. Rainaldi, M. Radici, and A. Courtoy, Phys. Rev. D 113, 038902 (2026).
  35. L. Yang, Y.-K. Song, and S.-Y. Wei, Phys. Rev. D 111, 054035 (2025).
  36. X.-K. Wen, B. Yan, Z. Yu, and C. P. Yuan, Sci. China Phys. Mech. Astron. 69, 271011 (2026).
  37. X.-K. Wen, B. Yan, Z. Yu, and C. P. Yuan, Phys. Rev. D 112, 053004 (2025).
  38. K. Cheng and B. Yan, Phys. Rev. Lett. 135, 011902 (2025).
  39. Q.-H. Cao, G. Li, X.-K. Wen, and B. Yan, Rep. Prog. Phys. 89, 080501 (2026).
  40. Q.-H. Cao, X.-K. Wen, B. Yan, and S.-T. Zhang, Phys. Rev. Lett. 136, 231901 (2026).
  41. T. Aushev et al., arXiv:1002.5012.
  42. W. Altmannshofer et al. (Belle-II Collaboration), Prog. Theor. Exp. Phys. 2019, 123C01 (2019); 2020, 029201(E) (2020).
  43. Z. Yu and C. P. Yuan, Phys. Rev. Lett. 129, 112001 (2022).
  44. Z.-G. He, G. Li, Y. Liu, Y.-J. Tian, X.-K. Wen, and B. Yan, arXiv:2608.10570.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation