Hadronic molecular states from the \(K\bar{K}^{\ast}\) interaction

  • Pei-Liang Lü
  • Jun HeEmail author
Regular Article - Theoretical Physics


In this work, the \(K\bar{K}^{\ast}\) interaction is studied in a quasipotential Bethe-Salpeter equation approach combined with the one-boson-exchange model. With the help of the hidden-gauge Lagrangian, the exchanges of pseudoscalar mesons (\(\pi\) and \(\eta\)) and vector mesons (\(\rho\), \(\omega\) and \(\phi\)) are considered to describe the \(K\bar{K}^{\ast}\) interaction. Besides the direct vector-meson exchange which can be related to the Weinberg-Tomozawa term, pseudoscalar-meson exchanges also play important roles in the mechanism of the \(K\bar{K}^{\ast}\) interaction. The poles of scattering amplitude are searched to find the molecular states produced from the \(K\bar{K}^{\ast}\) interaction. In the case of quantum number \(I^{G}(J^{PC}) = 0^{+}(1^{++})\), a pole is found with a reasonable cutoff, which can be related to the \(f_{1}(1285)\) in experiment. Another bound state with \(0^{-}(1^{+-})\) is also produced from the \(K\bar{K}^{\ast}\) interaction, which can be related to the \(h_{1}(1380)\). In the isovector sector, the interaction is much weaker and a bound state with \(1^{+}(1^{+})\) relevant to the \(b_{1}(1235)\) is produced but at a larger cutoff. Our results suggest that in the hadronic molecular state picture the \(f_{1}(1285)\) and \(b_{1}(1235)\) are the strange partners of the X(3872) and \(Z_{c}(3900)\), respectively.


  1. 1.
    Z.F. Sun, J. He, X. Liu, Z.G. Luo, S.L. Zhu, Phys. Rev. D 84, 054002 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    Z.F. Sun, Z.G. Luo, J. He, X. Liu, S.L. Zhu, Chin. Phys. C 36, 194 (2012)CrossRefGoogle Scholar
  3. 3.
    Z.G. Wang, T. Huang, Eur. Phys. J. C 74, 2891 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    J. He, Phys. Rev. D 92, 034004 (2015)ADSCrossRefGoogle Scholar
  5. 5.
    Particle Data Group Collaboration (K.A. Olive et al.), Chin. Phys. C 38, 090001 (2014)CrossRefGoogle Scholar
  6. 6.
    L. Roca, E. Oset, J. Singh, Phys. Rev. D 72, 014002 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A 730, 392 (2004)ADSCrossRefGoogle Scholar
  8. 8.
    F. Aceti, J.M. Dias, E. Oset, Eur. Phys. J. A 51, 48 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    L.S. Geng, X.L. Ren, Y. Zhou, H.X. Chen, E. Oset, Phys. Rev. D 92, 014029 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    Y. Zhou, X.L. Ren, H.X. Chen, L.S. Geng, Phys. Rev. D 90, 014020 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    F. Aceti, M. Bayar, E. Oset, A. Martinez Torres, K.P. Khemchandani, J.M. Dias, F.S. Navarra, M. Nielsen, Phys. Rev. D 90, 016003 (2014)ADSCrossRefGoogle Scholar
  12. 12.
    M.C. Birse, Z. Phys. A 355, 231 (1996)ADSGoogle Scholar
  13. 13.
    H.X. Chen, W. Chen, X. Liu, S.L. Zhu, Phys. Rep. 639, 1 (2016)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    J. He, X. Liu, Eur. Phys. J. C 72, 1986 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    J. He, D.Y. Chen, X. Liu, Eur. Phys. J. C 72, 2121 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    J. He, P.L. Lü, Nucl. Phys. A 919, 1 (2013)ADSCrossRefGoogle Scholar
  17. 17.
    J. He, P.L. Lü, Chin. Phys. C 40, 043101 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    J. He, Phys. Rev. C 91, 018201 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    M. Bando, T. Kugo, S. Uehara, K. Yamawaki, T. Yanagida, Phys. Rev. Lett. 54, 1215 (1985)ADSCrossRefGoogle Scholar
  20. 20.
    M. Bando, T. Kugo, K. Yamawaki, Phys. Rep. 164, 217 (1988)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    H. Nagahiro, L. Roca, A. Hosaka, E. Oset, Phys. Rev. D 79, 014015 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    F. Aceti, M. Bayar, J.M. Dias, E. Oset, Eur. Phys. J. A 50, 103 (2014)ADSCrossRefGoogle Scholar
  23. 23.
    J. He, Phys. Rev. D 90, 076008 (2014)ADSCrossRefGoogle Scholar
  24. 24.
    R. Molina, E. Oset, Phys. Rev. D 80, 114013 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    F. Gross, A. Stadler, Phys. Rev. C 78, 014005 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    F. Gross, A. Stadler, Phys. Rev. C 82, 034004 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    J. He, Phys. Lett. B 753, 547 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985)ADSCrossRefGoogle Scholar
  29. 29.
    G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Phys. Lett. B 223, 425 (1989)ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Theoretical Physics Division, Institute of Modern PhysicsChinese Academy of SciencesLanzhouChina
  2. 2.Research Center for Hadron and CSR PhysicsInstitute of Modern Physics of CAS and Lanzhou UniversityLanzhouChina

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