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  • Open Access

Pentaquarks made of light quarks and their admixture to baryons

Nicholas Miesch*, Edward Shuryak†, and Ismail Zahed‡

  • Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794–3800, USA

  • *Contact author: nicholas.miesch@stonybrook.edu
  • †Contact author: edward.shuryak@stonybrook.edu
  • ‡Contact author: ismail.zahed@stonybrook.edu

Phys. Rev. D 112, 074017 – Published 15 October, 2025

DOI: https://doi.org/10.1103/vdp9-mmbj

Abstract

This paper is a continuation of our studies of multiquark hadrons. The antisymmetrization of their wave functions required by Fermi statistics is nontrivial, as it mixes orbital, color, spin, and flavor structures. In our previous papers we developed a method to find them based on the representations of the permutation group, and derived the explicit wave functions for baryons excited to the first and second shells (L=1, 2), tetraquarks qqq¯q¯ and hexaquarks (6q). Now we apply it to light pentaquarks (qqqqq¯), in the S- and P-shells (L=0, 1). Using Jacobi coordinates, one can use the hyperdistance approximation in 12-dimensional space. We further address the issue of “unquenching” of baryons, by considering their mixing with pentaquarks, via two channels, through the addition of σ-like or π-like q¯q pairs. This mixing is central for understanding of the observed flavor asymmetry of the antiquark sea, the amount of orbital motion issue as well as other nucleon properties.

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References (53)

  1. M. Gell-Mann and M. Levy, Nuovo Cimento 16, 705 (1960).
  2. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 124, 246 (1961).
  3. A. Chodos, R. L. Jaffe, K. Johnson, C. B. Thorn, and V. F. Weisskopf, Phys. Rev. D 9, 3471 (1974).
  4. R. Friedberg and T. D. Lee, Phys. Rev. D 16, 1096 (1977).
  5. G. E. Brown and M. Rho, Phys. Lett. 82B, 177 (1979).
  6. R. Kokoski and N. Isgur, Phys. Rev. D 35, 907 (1987).
  7. P. Geiger and N. Isgur, Phys. Rev. D 41, 1595 (1990).
  8. A. Le Yaouanc, L. Oliver, O. Pene, and J. C. Raynal, Phys. Rev. D 8, 2223 (1973).
  9. E. Santopinto and R. Bijker, in Proceedings of the 11th Conference on Problems in Theoretical Nuclear Physics (2007), pp. 323–330.
  10. R. Bijker, E. Santopinto, and E. Santopinto, Phys. Rev. C 80, 065210 (2009).
  11. M. A. Nowak, M. Rho, and I. Zahed, Chiral Nuclear Dynamics (World Scientific, Singapore, 1996).
  12. G. A. Miller, arXiv:2208.12873.
  13. E. Shuryak, Phys. Rev. D 100, 114018 (2019).
  14. E. Shuryak and I. Zahed, Phys. Rev. D 107, 034027 (2023).
  15. N. Miesch, E. Shuryak, and I. Zahed, arXiv:2503.13273.
  16. C. S. An and B. Saghai, Phys. Rev. D 99, 094039 (2019).
  17. T. Nakano et al. (LEPS Collaboration), Phys. Rev. Lett. 91, 012002 (2003).
  18. M. Amaryan, Acta Phys. Pol. B 56, 3 (2025).
  19. D. Diakonov, V. Petrov, and M. V. Polyakov, Z. Phys. A 359, 305 (1997).
  20. M. Praszalowicz, Acta Phys. Pol. B 56, 3 (2025).
  21. E. Shuryak and I. Zahed, Phys. Lett. B 589, 21 (2004).
  22. A. V. Anisovich, R. Beck, E. Klempt, V. A. Nikonov, A. V. Sarantsev, and U. Thoma, Eur. Phys. J. A 48, 15 (2012).
  23. N. Miesch, E. Shuryak, and I. Zahed, Phys. Rev. D 111, 034006 (2025).
  24. N. Miesch and E. Shuryak, Phys. Rev. D 110, 094022 (2024).
  25. H. Kim, K. S. Kim, and M. Oka, Phys. Rev. D 102, 074023 (2020).
  26. P. Adlarson et al. (WASA-at-COSY Collaboration), Phys. Rev. Lett. 106, 242302 (2011).
  27. Note that while SparseArray format for large vectors and matrices may speed things up, in this form some general commands like Expand, Conjugate, ComplexExpand etc do not work (in version 14.1), thus it is safer to use Natural format for such manipulations.

  28. Note that in [16] the number of L=1 compatible states is 17, and they are not organized into Fermi-statistics-compliant combinations. We also disagree with the way their energies are derived from their Hamiltonian.

  29. V. Zelevinsky, Annu. Rev. Nucl. Part. Sci. 46, 237 (1996).
  30. V. V. Flambaum, A. A. Gribakina, G. F. Gribakin, and I. V. Ponomarev, arXiv:cond-mat/9710172.
  31. E. V. Shuryak and J. J. M. Verbaarschot, Nucl. Phys. A560, 306 (1993).
  32. J. J. M. Verbaarschot and I. Zahed, Phys. Rev. Lett. 70, 3852 (1993).
  33. J. Ferretti, G. Galatà, and E. Santopinto, Phys. Rev. C 88, 015207 (2013).
  34. M. A. Nowak, M. Rho, and I. Zahed, Phys. Rev. D 48, 4370 (1993).
  35. W. A. Bardeen and C. T. Hill, Phys. Rev. D 49, 409 (1994).
  36. M. A. Nowak, M. Rho, and I. Zahed, Acta Phys. Pol. B 35, 2377 (2004).
  37. B. Aubert et al. (BABAR Collaboration), Phys. Rev. Lett. 90, 242001 (2003).
  38. D. Besson et al. (CLEO Collaboration), Phys. Rev. D 68, 032002 (2003); 75, 119908(E) (2007).
  39. G. ’t Hooft, Phys. Rev. D 14, 3432 (1976); 18, 2199(E) (1978).
  40. E. V. Shuryak, Nucl. Phys. B203, 93 (1982).
  41. E. V. Shuryak, Rev. Mod. Phys. 65, 1 (1993).
  42. T. Schäfer and E. V. Shuryak, Rev. Mod. Phys. 70, 323 (1998).
  43. P. Geiger and N. Isgur, Phys. Rev. Lett. 67, 1066 (1991).
  44. G. T. Garvey, Phys. Rev. C 81, 055212 (2010).
  45. R. S. Towell et al. (NuSea Collaboration), Phys. Rev. D 64, 052002 (2001).
  46. A. Accardi, C. E. Keppel, S. Li, W. Melnitchouk, G. Niculescu, I. Niculescu, and J. F. Owens (CTEQ-Jefferson Lab (CJ) Collaboration), Phys. Lett. B 801, 135143 (2020).
  47. N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978).
  48. N. Isgur and G. Karl, Phys. Rev. D 19, 2653 (1979); 23, 817(E) (1981).
  49. C. S. An, D. O. Riska, and B. S. Zou, Phys. Rev. C 73, 035207 (2006).
  50. C. S. An, Q. B. Li, D. O. Riska, and B. S. Zou, Phys. Rev. C 74, 055205 (2006); 75, 069901(E) (2007).
  51. K. Xu, N. Ritjoho, S. Srisuphaphon, and Y. Yan, Int. J. Mod. Phys. Conf. Ser. 29, 1460251 (2014).
  52. S. Duan, C. S. An, and B. Saghai, Phys. Rev. D 93, 114006 (2016).
  53. Y. Yan and S. Srisuphaphon, Prog. Part. Nucl. Phys. 67, 496 (2012).

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