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  • Letter
  • Open Access

Spin-spin entanglement in diffractive heavy-quark production

Michael Fucilla1 and Yoshitaka Hatta2,3

Phys. Rev. D 113, L031504 – Published 19 February, 2026

DOI: https://doi.org/10.1103/gbk8-z3dd

Abstract

We calculate the spin density matrix of a heavy-quark-antiquark pair (bb¯, cc¯ or ss¯) diffractively produced in deep inelastic scattering and ultraperipheral collisions. We show that the Pomeron exchange leaves characteristic imprints on the entanglement pattern between the quark and the antiquark. For the longitudinally polarized virtual photon, the pair always exhibits maximal entanglement and maximal violation of the Bell-Clauser-Horne-Shimony-Holt inequality. For the transversely polarized photon, the pair is always entangled and Bell violating, reaching maximal entanglement and maximal violation simultaneously when the transverse momentum approximately equals the quark mass.

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References (60)

  1. G. Aad et al. (ATLAS Collaboration), Nature (London) 633, 542 (2024).
  2. A. Hayrapetyan et al. (CMS Collaboration), Rep. Prog. Phys. 87, 117801 (2024).
  3. A. J. Barr, M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Prog. Part. Nucl. Phys. 139, 104134 (2024).
  4. Y. Afik and J. R. M. de Nova, Quantum 6, 820 (2022).
  5. Y. Afik et al., Eur. Phys. J. Plus 140, 855 (2025).
  6. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
  7. C. S. Wu and I. Shaknov, Phys. Rev. 77, 136 (1950).
  8. D. Bohm, Phys. Rev. 85, 166 (1952).
  9. J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).
  10. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
  11. M. Baumgart and B. Tweedie, J. High Energy Phys. 03 (2013) 117.
  12. Y. Afik and J. R. M. de Nova, Eur. Phys. J. Plus 136, 907 (2021).
  13. J. A. Aguilar-Saavedra, Phys. Rev. D 108, 076025 (2023).
  14. T. Han, M. Low, and T. A. Wu, J. High Energy Phys. 07 (2024) 192.
  15. Z. Dong, D. Gonçalves, K. Kong, and A. Navarro, Phys. Rev. D 109, 115023 (2024).
  16. M. Fabbrichesi, R. Floreanini, and G. Panizzo, Phys. Rev. Lett. 127, 161801 (2021).
  17. C. Severi, C. D. E. Boschi, F. Maltoni, and M. Sioli, Eur. Phys. J. C 82, 285 (2022).
  18. M. Galanti, A. Giammanco, Y. Grossman, Y. Kats, E. Stamou, and J. Zupan, J. High Energy Phys. 11 (2015) 067.
  19. S.-J. Lin, M.-J. Liu, D. Y. Shao, and S.-Y. Wei, J. High Energy Phys. 11 (2025) 082.
  20. K. Cheng and B. Yan, Phys. Rev. Lett. 135, 011902 (2025).
  21. Y. Kats and D. Uzan, J. High Energy Phys. 03 (2024) 063.
  22. Y. Afik, Y. Kats, J. R. M. de Nova, A. Soffer, and D. Uzan, Phys. Rev. D 111, L111902 (2025).
  23. STAR Collaboration, arXiv:2506.05499.
  24. R. Abdul Khalek et al., Nucl. Phys. A1026, 122447 (2022).
  25. A. J. Baltz et al., Phys. Rep. 458, 1 (2008).
  26. W. Qi, Z. Guo, and B.-W. Xiao, arXiv:2506.12889.
  27. A. Kovner and M. Lublinsky, Phys. Rev. D 92, 034016 (2015).
  28. R. Peschanski and S. Seki, Phys. Lett. B 758, 89 (2016).
  29. D. E. Kharzeev and E. M. Levin, Phys. Rev. D 95, 114008 (2017).
  30. Y. Liu and I. Zahed, Phys. Rev. D 100, 046005 (2019).
  31. G. S. Ramos and M. V. T. Machado, Phys. Rev. D 102, 034019 (2020).
  32. S. Bhattacharya, R. Boussarie, and Y. Hatta, Phys. Lett. B 859, 139134 (2024).
  33. Y. Guo, X. Liu, F. Yuan, and H. X. Zhu, Research 2025, 0552 (2025).
  34. J. D. Brandenburg, H. Duan, Z. Tu, R. Venugopalan, and Z. Xu, Phys. Rev. Res. 7, 013131 (2025).
  35. Y. Hatta and J. Montgomery, Phys. Rev. D 111, 014024 (2025).
  36. A. Dumitru and E. Kolbusz, Phys. Rev. D 111, 114033 (2025).
  37. S. Agrawal and R. Abir, Phys. Lett. B 868, 139802 (2025).
  38. M. Ouchen and A. Prygarin, Phys. Rev. D 112, 094027 (2025).
  39. M. Hentschinski, H. Jung, and K. Kutak, arXiv:2509.03400.
  40. J. Bartels, H. Lotter, and M. Wüsthoff, Phys. Lett. B 379, 239 (1996); 382, 449(E) (1996).
  41. N. N. Nikolaev, W. Schafer, B. G. Zakharov, and V. R. Zoller, J. Exp. Theor. Phys. 97, 441 (2003).
  42. T. Altinoluk, N. Armesto, G. Beuf, and A. H. Rezaeian, Phys. Lett. B 758, 373 (2016).
  43. Y. Hatta, B.-W. Xiao, and F. Yuan, Phys. Rev. Lett. 116, 202301 (2016).
  44. R. Boussarie, A. V. Grabovsky, L. Szymanowski, and S. Wallon, Phys. Rev. D 100, 074020 (2019).
  45. W. Bernreuther and A. Brandenburg, Phys. Rev. D 49, 4481 (1994).
  46. A. Brandenburg, M. Flesch, and P. Uwer, Phys. Rev. D 59, 14001 (1999).
  47. K. J. Golec-Biernat and M. Wusthoff, Phys. Rev. D 59, 014017 (1998).
  48. M. Jacob and G. C. Wick, Ann. Phys. (N.Y.) 7, 404 (1959).
  49. R. Horodecki, P. Horodecki, and M. Horodecki, Phys. Lett. A 200, 340 (1995).
  50. Y. Hagiwara, Y. Hatta, R. Pasechnik, M. Tasevsky, and O. Teryaev, Phys. Rev. D 96, 034009 (2017).
  51. M. Reinke Pelicer, E. Gräve De Oliveira, and R. Pasechnik, Phys. Rev. D 99, 034016 (2019).
  52. V. P. Gonçalves, G. Sampaio dos Santos, and C. R. Sena, Nucl. Phys. A1000, 121862 (2020).
  53. B. Linek, A. Łuszczak, M. Łuszczak, R. Pasechnik, W. Schäfer, and A. Szczurek, J. High Energy Phys. 10 (2023) 179.
  54. See Supplemental Material at http://link.aps.org/supplemental/10.1103/gbk8-z3dd for the derivation of the spin density matrix in the transverse case, which includes Ref. [55].
  55. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, MA, 1995).
  56. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
  57. P. Horodecki, Phys. Lett. A 232, 333 (1997).
  58. N. Gisin, Phys. Lett. A 154, 201 (1991).
  59. D. d’Enterria et al., J. Phys. G 52, 090501 (2025).
  60. Y. Hatta and J. Schoenleber, arXiv:2511.04537.

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