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The European Physical Journal A

, Volume 38, Issue 3, pp 257–264 | Cite as

\( \eta\) and \( \eta{^\prime}\) mesons in the Dyson-Schwinger approach using a generalization of the Witten-Veneziano relation

  • D. HorvatićEmail author
  • D. Blaschke
  • Yu. Kalinovsky
  • D. Kekez
  • D. Klabučar
Regular Article - Theoretical Physics

Abstract

The description of the \( \eta\) and \( \eta^{{\prime}}_{}\) mesons in the Dyson-Schwinger approach has relied on the Witten-Veneziano relation. The present paper explores the consequences of using instead its generalization recently proposed by Shore. On the examples of three different model interactions, we find that irrespective of the concrete model dynamics, our Dyson-Schwinger approach is phenomenologically more successful in conjunction with the standard Witten-Veneziano relation than with the proposed generalization valid in all orders in the 1/N c expansion.

PACS

11.10.St Bound and unstable states; Bethe-Salpeter equations 12.38.-t Quantum chromodynamics 14.40.Aq \( \pi\) , K , and \( \eta\) mesons 12.38.Lg Other nonperturbative calculations 

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References

  1. 1.
    For example, see refs. Alkofer:2000wg,Roberts:2000hi,Roberts:2000aa,Holl:2006ni,Fischer:2006ub for recent reviews and references on various applications of the DS approach.Google Scholar
  2. 2.
    R. Alkofer, L. von Smekal, Phys. Rep. 353, 281 (2001).Google Scholar
  3. 3.
    C.D. Roberts, arXiv:nucl-th/0007054.Google Scholar
  4. 4.
    C.D. Roberts, S.M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000).Google Scholar
  5. 5.
    A. Höll, C.D. Roberts, S.V. Wright, arXiv:nucl-th/0601071.Google Scholar
  6. 6.
    C.S. Fischer, J. Phys. G 32, R253 (2006).Google Scholar
  7. 7.
    D. Klabučar, D. Kekez, Phys. Rev. D 58, 096003 (1998).Google Scholar
  8. 8.
    D. Kekez, D. Klabučar, M.D. Scadron, J. Phys. G 26, 1335 (2000).Google Scholar
  9. 9.
    P. Jain, H.J. Munczek, Phys. Rev. D 48, 5403 (1993).Google Scholar
  10. 10.
    D. Kekez, D. Klabučar, Phys. Rev. D 73, 036002 (2006).Google Scholar
  11. 11.
    D. Kekez, D. Klabučar, Phys. Rev. D 71, 014004 (2005).Google Scholar
  12. 12.
    D. Horvatić, D. Blaschke, D. Klabučar, A.E. Radzhabov, Phys. Part. Nucl. 39, 1033 (2008).Google Scholar
  13. 13.
    D. Horvatić, D. Klabučar, A.E. Radzhabov, Phys. Rev. D 76, 096009 (2007)Google Scholar
  14. 14.
    D. Blaschke, G. Burau, Y.L. Kalinovsky, P. Maris, P.C. Tandy, Int. J. Mod. Phys. A 16, 2267 (2001).Google Scholar
  15. 15.
    D. Kekez, B. Bistrović, D. Klabučar, Int. J. Mod. Phys. A 14, 161 (1999).Google Scholar
  16. 16.
    B. Bistrović, D. Klabučar, Phys. Lett. B 478, 127 (2000)Google Scholar
  17. 17.
    R. Alkofer, C.D. Roberts, Phys. Lett. B 369, 101 (1996).Google Scholar
  18. 18.
    D. Kekez, D. Klabučar, Phys. Rev. D 65, 057901 (2002).Google Scholar
  19. 19.
    O. Lakhina, P. Bicudo, arXiv:0708.0984.Google Scholar
  20. 20.
    M.S. Bhagwat, L. Chang, Y.X. Liu, C.D. Roberts, P.C. Tandy, Phys. Rev. C 76, 045203 (2007).Google Scholar
  21. 21.
    E. Witten, Nucl. Phys. B 156, 269 (1979).Google Scholar
  22. 22.
    G. Veneziano, Nucl. Phys. B 159, 213 (1979).Google Scholar
  23. 23.
    G.M. Shore, Nucl. Phys. B 744, 34 (2006).Google Scholar
  24. 24.
    G.M. Shore, Lect. Notes Phys. 737, 235 (2008).Google Scholar
  25. 25.
    D. Blaschke, D. Horvatić, D. Klabučar, A.E. Radzhabov, hep-ph/0703188, in Proceedings of the Mini-Workshop Progress in Quark Models, Bled, Slovenia, 2006, edited by B. Golli, M. Rosina, S. Širca (DMFA - založništvo, Ljubljana, 2006) p. 20.Google Scholar
  26. 26.
    B. Alles, M. D’Elia, A. Di Giacomo, Nucl. Phys. B 494, 281 (1997).Google Scholar
  27. 27.
    D. Blaschke, H.P. Pavel, V.N. Pervushin, G. Ropke, M.K. Volkov, Phys. Lett. B 397, 129 (1997).Google Scholar
  28. 28.
    Th. Feldmann, Int. J. Mod. Phys. A 15, 159 (2000).Google Scholar
  29. 29.
    Th. Feldmann, P. Kroll, B. Stech, Phys. Rev. D 58, 114006 (1998).Google Scholar
  30. 30.
    B. Lucini, M. Teper, U. Wenger, Nucl. Phys. B 715, 461 (2005).Google Scholar
  31. 31.
    L. Del Debbio, L. Giusti, C. Pica, Phys. Rev. Lett. 94, 032003 (2005).Google Scholar
  32. 32.
    B. Alles, M. D’Elia, A. Di Giacomo, Phys. Rev. D 71, 034503 (2005).Google Scholar
  33. 33.
    J. Gasser, H. Leutwyler, Nucl. Phys. B 250, 465 (1985).Google Scholar
  34. 34.
    H. Leutwyler, Nucl. Phys. Proc. Suppl. 64, 223 (1998).Google Scholar
  35. 35.
    R. Kaiser, H. Leutwyler, hep-ph/9806336, in Proceedings of the Workshop Nonperturbative Methods in Quantum Field Theory, Adelaide, Australia, 1998, edited by A.W. Schreiber, A.G. Williams, A.W. Thomas (World Scientific, Singapore, 1998).Google Scholar
  36. 36.
    J. Schechter, A. Subbaraman, H. Weigel, Phys. Rev. D 48, 339 (1993).Google Scholar
  37. 37.
    Th. Feldmann, P. Kroll, B. Stech, Phys. Lett. B 449, 339 (1999).Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • D. Horvatić
    • 1
    Email author
  • D. Blaschke
    • 2
    • 3
    • 4
  • Yu. Kalinovsky
    • 5
  • D. Kekez
    • 6
  • D. Klabučar
    • 1
  1. 1.Physics Department, Faculty of ScienceUniversity of ZagrebZagrebCroatia
  2. 2.Institute for Theoretical PhysicsUniversity of WroclawWroclawPoland
  3. 3.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussia
  4. 4.Institute of PhysicsUniversity of RostockRostockGermany
  5. 5.Laboratory for Information TechnologiesJoint Institute for Nuclear ResearchDubnaRussia
  6. 6.Rudjer Bošković InstituteZagrebCroatia

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