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  • Open Access

Fully Charm-Tetraquark Production at Hadronic Collisions with Gluon Radiation Effects

Yefan Wang* and Ruilin Zhu*

  • *Contact author: rlzhu@njnu.edu.cn
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Phys. Rev. Lett. 137, 131901 – Published 21 September, 2026

DOI: https://doi.org/10.1103/zp4k-2t92

Abstract

We report the first complete next-to-leading order QCD calculation for processes involving fully charm-tetraquark states, revealing that the renormalization constant of the color-singlet four charm quark operator is exactly unity at this order. We have investigated the possible quark configurations of the fully charm tetraquarks and expanded their states in the color symmetry-antisymmetry basis. By applying the transverse momentum dependent factorization formalism, large logarithms induced by soft and collinear gluon radiations are resummed to all orders in the expansion of the strong interaction coupling at the accuracy of next-to-leading logarithm. By combining LHCb data on the total cross section of the exotic hadron X(6900) and CMS measurements of its spin parity, we extracted its nonperturbative but universal long-distance matrix element. The rapidity and transverse momentum distributions of the X(6900) and its spin-zero partners are also predicted, which await further experimental verification.

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References (77)

  1. J. J. Aubert et al. (E598 Collaboration), Phys. Rev. Lett. 33, 1404 (1974).
  2. J. E. Augustin et al. (SLAC-SP-017 Collaboration), Phys. Rev. Lett. 33, 1406 (1974).
  3. G. Goldhaber, F. Pierre, G. S. Abrams, M. S. Alam, A. Boyarski, M. Breidenbach, W. C. Carithers, W. Chinowsky, S. Cooper, R. DeVoe et al., Phys. Rev. Lett. 37, 255 (1976).
  4. LHCb Collaboration, Sci. Bull. 65, 1983 (2020).
  5. G. Aad et al. (ATLAS Collaboration), Phys. Rev. Lett. 131, 151902 (2023).
  6. A. Hayrapetyan et al. (CMS Collaboration), Phys. Rev. Lett. 132, 111901 (2024).
  7. A. Hayrapetyan et al. (CMS Collaboration), Nature (London) 648, 58 (2025).
  8. R. Zhu, Nucl. Phys. B966, 115393 (2021).
  9. F. Zhu, G. Bauer, and K. Yi, Chin. Phys. Lett. 41, 111201 (2024).
  10. J. C. Collins, D. E. Soper, and G. F. Sterman, Nucl. Phys. B250, 199 (1985).
  11. R. Brock et al. (CTEQ Collaboration), Rev. Mod. Phys. 67, 157 (1995).
  12. S. Catani and L. Trentadue, Nucl. Phys. B327, 323 (1989).
  13. S. Camarda, L. Cieri, and G. Ferrera, Phys. Rev. D 104, L111503 (2021).
  14. M. A. Ebert, J. K. L. Michel, I. W. Stewart, and F. J. Tackmann, J. High Energy Phys. 04 (2021) 102.
  15. C. Balazs, J. w. Qiu, and C. P. Yuan, Phys. Lett. B 355, 548 (1995).
  16. P. F. Monni, E. Re, and P. Torrielli, Phys. Rev. Lett. 116, 242001 (2016).
  17. S. Catani, M. Grazzini, and A. Torre, Nucl. Phys. B890, 518 (2014).
  18. E. L. Berger and R. b. Meng, Phys. Rev. D 49, 3248 (1994).
  19. H. X. Zhu, C. S. Li, H. T. Li, D. Y. Shao, and L. L. Yang, Phys. Rev. Lett. 110, 082001 (2013).
  20. W. Bizon, P. F. Monni, E. Re, L. Rottoli, and P. Torrielli, J. High Energy Phys. 02 (2018) 108.
  21. M. A. Ebert and F. J. Tackmann, J. High Energy Phys. 02 (2017) 110.
  22. A. Banfi, H. McAslan, P. F. Monni, and G. Zanderighi, J. High Energy Phys. 05 (2015) 102.
  23. M. Procura, W. J. Waalewijn, and L. Zeune, J. High Energy Phys. 02 (2015) 117.
  24. S. Catani, L. Cieri, D. de Florian, G. Ferrera, and M. Grazzini, Nucl. Phys. B881, 414 (2014).
  25. A. H. Mueller, B. W. Xiao, and F. Yuan, Phys. Rev. D 88, 114010 (2013).
  26. T. Becher and M. Neubert, J. High Energy Phys. 07 (2012) 108.
  27. D. de Florian, G. Ferrera, M. Grazzini, and D. Tommasini, J. High Energy Phys. 06 (2012) 132.
  28. Z. B. Kang, X. Liu, F. Ringer, and H. Xing, J. High Energy Phys. 11 (2017) 068.
  29. S. Mantry and F. Petriello, Phys. Rev. D 81, 093007 (2010).
  30. G. Bozzi, S. Catani, G. Ferrera, D. de Florian, and M. Grazzini, Nucl. Phys. B815, 174 (2009).
  31. A. Banfi, G. P. Salam, and G. Zanderighi, J. High Energy Phys. 03 (2005) 073.
  32. F. Landry, R. Brock, P. M. Nadolsky, and C. P. Yuan, Phys. Rev. D 67, 073016 (2003).
  33. P. Sun, J. Isaacson, C. P. Yuan, and F. Yuan, Int. J. Mod. Phys. A 33, 1841006 (2018).
  34. P. Sun, C. P. Yuan, and F. Yuan, Phys. Rev. D 88, 054008 (2013).
  35. X. Chen, T. Gehrmann, E. W. N. Glover, A. Huss, Y. Li, D. Neill, M. Schulze, I. W. Stewart, and H. X. Zhu, Phys. Lett. B 788, 425 (2019).
  36. A. Kulesza, G. F. Sterman, and W. Vogelsang, Phys. Rev. D 66, 014011 (2002).
  37. P. M. Nadolsky, D. R. Stump, and C. P. Yuan, Phys. Rev. D 61, 014003 (2000); 64, 059903(E) (2001).
  38. F. Landry, R. Brock, G. Ladinsky, and C. P. Yuan, Phys. Rev. D 63, 013004 (2001).
  39. S. Catani, M. L. Mangano, P. Nason, C. Oleari, and W. Vogelsang, J. High Energy Phys. 03 (1999) 025.
  40. E. Laenen, G. Oderda, and G. F. Sterman, Phys. Lett. B 438, 173 (1998).
  41. C. Balazs, E. L. Berger, S. Mrenna, and C. P. Yuan, Phys. Rev. D 57, 6934 (1998).
  42. R. K. Ellis and S. Veseli, Nucl. Phys. B511, 649 (1998).
  43. N. Kidonakis and G. F. Sterman, Nucl. Phys. B505, 321 (1997).
  44. H. Contopanagos, E. Laenen, and G. F. Sterman, Nucl. Phys. B484, 303 (1997).
  45. Q. H. Cao, P. Sun, B. Yan, C. P. Yuan, and F. Yuan, Phys. Rev. D 98, 054032 (2018).
  46. M. Bonvini, S. Forte, M. Ghezzi, and G. Ridolfi, Nucl. Phys. B861, 337 (2012).
  47. M. Beneke, M. Garny, S. Jaskiewicz, J. Strohm, R. Szafron, L. Vernazza, and J. Wang, J. High Energy Phys. 07 (2022) 144.
  48. R. Boussarie et al., arXiv:2304.03302.
  49. See Supplemental Material at http://link.aps.org/supplemental/10.1103/zp4k-2t92 for the matching coefficients and the regular term.
  50. G. T. Bodwin, E. Braaten, and G. P. Lepage, Phys. Rev. D 51, 1125 (1995); 55, 5853(E) (1997).
  51. F. Feng, Y. Huang, Y. Jia, W. L. Sang, D. S. Yang, and J. Y. Zhang, Phys. Rev. D 108, L051501 (2023).
  52. T. Hahn, Comput. Phys. Commun. 140, 418 (2001).
  53. V. Shtabovenko, R. Mertig, and F. Orellana, Comput. Phys. Commun. 256, 107478 (2020).
  54. V. Shtabovenko, R. Mertig, and F. Orellana, Comput. Phys. Commun. 306, 109357 (2025).
  55. F. V. Tkachov, Phys. Lett. 100B, 65 (1981).
  56. K. G. Chetyrkin and F. V. Tkachov, Nucl. Phys. B192, 159 (1981).
  57. J. Klappert, F. Lange, P. Maierhöfer, and J. Usovitsch, Comput. Phys. Commun. 266, 108024 (2021).
  58. V. Shtabovenko, Comput. Phys. Commun. 218, 48 (2017).
  59. H. H. Patel, Comput. Phys. Commun. 197, 276 (2015).
  60. R. Aaij et al. (LHCb Collaboration), J. High Energy Phys. 03 (2024) 088.
  61. Z. G. He, X. B. Jin, and B. A. Kniehl, Phys. Rev. D 111, 094040 (2025).
  62. E. Chapon, D. d’Enterria, B. Ducloue, M. G. Echevarria, P. B. Gossiaux, V. Kartvelishvili, T. Kasemets, J. P. Lansberg, R. McNulty, D. D. Price et al., Prog. Part. Nucl. Phys. 122, 103906 (2022).
  63. R. D. Ball et al. (PDF4LHC Working Group Collaboration), J. Phys. G 49, 080501 (2022).
  64. T. J. Hou, J. Gao, T. J. Hobbs, K. Xie, S. Dulat, M. Guzzi, J. Huston, P. Nadolsky, J. Pumplin, C. Schmidt et al., Phys. Rev. D 103, 014013 (2021).
  65. R. D. Ball et al. (NNPDF Collaboration), J. High Energy Phys. 04 (2015) 040.
  66. A. Buckley, J. Ferrando, S. Lloyd, K. Nordström, B. Page, M. Rüfenacht, M. Schönherr, and G. Watt, Eur. Phys. J. C 75, 132 (2015).
  67. F. G. Celiberto, Phys. Rev. D 112, 074041 (2025).
  68. H. F. Zhang, Y. Q. Ma, and W. L. Sang, Sci. Bull. 70, 1915 (2025).
  69. F. Feng, Y. Huang, Y. Jia, W. L. Sang, X. Xiong, and J. Y. Zhang, Phys. Rev. D 106, 114029 (2022).
  70. W. L. Sang, T. Wang, Y. D. Zhang, and F. Feng, Phys. Rev. D 109, 056016 (2024).
  71. K. Chen, F. X. Liu, Q. Zhao, X. H. Zhong, R. Zhu, and B. S. Zou, arXiv:2412.13455.
  72. I. Belov, A. Giachino, and E. Santopinto, J. High Energy Phys. 01 (2025) 093.
  73. T. Hyodo, Y. R. Liu, M. Oka, K. Sudoh, and S. Yasui, Phys. Lett. B 721, 56 (2013).
  74. M. Jacob and G. C. Wick, Ann. Phys. (N.Y.) 7, 404 (1959).
  75. Z. B. Kang, Y. Q. Ma, J. W. Qiu, and G. Sterman, Phys. Rev. D 90, 034006 (2014).
  76. G. J. Wang, M. Oka, and D. Jido, Phys. Rev. D 108, L071501 (2023).
  77. W. L. Wu, Y. K. Chen, L. Meng, and S. L. Zhu, Phys. Rev. D 109, 054034 (2024).

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Phys. Rev. Lett. 137, 131901– Published 21 September, 2026
  • Received 19 November 2025
  • Revised 5 August 2026
  • Accepted 26 August 2026
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