Central European Journal of Physics

, Volume 2, Issue 2, pp 367–381 | Cite as

Mean-field expansion and meson effects in chiral condensate of analytically regularized Nambu-Jona-Lasinio model

  • Rauf G. Jafarov
  • Vladimir E. Rochev
Article
  • 29 Downloads

Abstract

Scalar meson contributions in chiral quark condensate are calculated in the analytically regularized Nambu-Jona-Lasinio model using the framework of mean-field expansion in bilocal-source formalism. The sigma-meson contribution for physical values of the parameters is found to be small. Pion contribution is found to be significant and should be taken into account for the choice of the parameter values.

Keywords

Nambu-Jona-Lasinio model chiral condensate mean-field expansion analytical regularization meson contributions 

PACS (2000)

12.39.Fe 11.30.Rd 14.40.Aq 14.40.Cs 14.65.Bt 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Y. Nambu and G. Jona-Lasinio: “Dynamical model of elementary particles based on an analogy with superconductivity. I.”, Physical Review, Vol. 122, (1961), pp. 345–358.CrossRefADSGoogle Scholar
  2. [2]
    T. Eguchi and H. Sugawara: “Extended model of elementary particles based on an analogy with superconductivity”, Physical Review, Vol. D 10, (1974), pp. 4257–4262. K. Kikkawa: “Quantum corrections in superconductor models”, Progress of Theoretical Physics, Vol. 56, (1976), pp. 947–961.CrossRefADSGoogle Scholar
  3. 2a.
    H. Kleinert: “Hadronization of quark theories”, In: A. Zichichi (Ed.): Understanding the Fundamental Constituents of Matter, Plenum Press, New York, 1978, pp. 289–389.Google Scholar
  4. 2b.
    D. Ebert and M.K. Volkov: “Composite meson model with vector dominance based on U(2) invariant four quark interactions”, Zeitschrift für Physik, Vol. C 16, (1983), pp. 205–219.CrossRefGoogle Scholar
  5. [3]
    T. Hatsuda and T. Kunihoro: “Possible critical phenomena associated with the chiral symmetry breaking”, Physics Letters, Vol. B 145, (1984), pp. 7–10.CrossRefGoogle Scholar
  6. [3]a
    V. Bernard, U.-G. Meissner and I. Zahed: “Decoupling of the pion at finite temperature and density”, Physical Review, Vol. D 36, (1987), pp. 819–823.ADSCrossRefGoogle Scholar
  7. [3]b
    A.S. Vshivtsev, V.Ch. Zhukovsky and K.G. Klimenko: “New critical properties of the Nambu-Jona-Lasinio model with nonzero chemical potential”, Journal of Experimental and Theoretical Physics”, Vol. 84, (1997), pp. 1047–1053.CrossRefADSGoogle Scholar
  8. [3]c
    D. Ebert, K.G. Klimenko, M.A. Vdovichenko and A.S. Vshivtsev: “Magnetic oscillations in dense cold quark matter with four fermion interactions”, Physical Review, Vol. D 61, (2000), pp. 025005.ADSGoogle Scholar
  9. [3]d
    D. Ebert and K.G. Klimenko: “Quark droplets stability induced by external magnetic field”, (2003), hep-ph/0305149Google Scholar
  10. [4]
    S.P. Klevansky: “The Nambu-Jona-Lasinio model of quantum chromodynamics”, Reviews of Modern Physics, Vol. 64, (1992), pp. 649–708.MathSciNetCrossRefADSGoogle Scholar
  11. [5]
    T. Hatsuda and T. Kunihiro: “QCD Phenomenology based on a chiral effective Lagrangian”, Physics Reports, Vol. 247, (1994), pp. 221–367.CrossRefADSGoogle Scholar
  12. [6]
    P.P. Domitrovich, D. Bückers and H. Müther: “Nambu-Jona-Lasinio models beyond the mean field approximation”, Physical Review, Vol. C 48, (1993), pp. 413–422.ADSGoogle Scholar
  13. [7]
    E. Quack and S.P. Klevansky: “Effective 1/N c expansion in the Nambu-Jona-Lasinio model”, Physical Review, Vol. C 49, (1994), pp. 3283–3288.ADSGoogle Scholar
  14. [7]a
    D. Ebert, M. Nagy and M.K. Volkov: “To the problem of 1/N c approximation in the Nambu-Jona-Lasinio model”, Yadernaya Fizika, Vol. 59, (1996), pp. 149–152.Google Scholar
  15. [8]
    D. Blaschke et al.: “1/N c expansion of the quark condensate at finite temperature”, Physical Review, Vol. C 53, (1996), pp. 2394–2400.ADSGoogle Scholar
  16. [9]
    M. Huang, P. Zhuang and W. Chao: “The mesonic fluctuations and corrections in chiral symmetry breaking vacuum”, Physics Letters, Vol. B 514, (2001), pp. 63–71.MATHCrossRefGoogle Scholar
  17. [10]
    G. Ripka: “Quantum fluctuations of the quark condensate”, Nuclear Physics, Vol. A 683, (2001), 463–486.CrossRefGoogle Scholar
  18. [10]a
    R.S. Plant and M.C. Birse: “Mesonic fluctuations in a nonlocal NJL model”, Nuclear Physics, Vol. A 703, (2002), pp. 717–744.CrossRefGoogle Scholar
  19. [11]
    S. Krewald and K. Nakayama: “A new interpretation of dimensional regularization”, Annals of Physics, Vol. 216, (1992), pp. 201–225.MATHMathSciNetCrossRefADSGoogle Scholar
  20. [12]
    A.E. Radzhabov and M.K. Volkov: “Nonlocal chiral quark model with confinement”, (2003), hep-ph/0305272Google Scholar
  21. [13]
    V.E. Rochev: “A non-perturbative method for the calculation of Green functions”, Journal of Physics, Vol. A 30, (1997), pp. 3671–3679.MATHMathSciNetCrossRefGoogle Scholar
  22. [13]a
    V.E. Rochev and P.A. Saponov: “The four-fernion interaction in D=2,3,4: a nonperturbative treatment”, International Journal of Modern Physics, Vol. A 13, (1998), pp. 3649–3665.MATHCrossRefADSGoogle Scholar
  23. [13]b
    V.E. Rochev: “On nonperturbative calculations in quantum electrodynamics”, Journal of Physics”, Vol. A 33, (2000), 7379–7406.MATHMathSciNetCrossRefGoogle Scholar
  24. [14]
    V.E. Rochev: “An approach to approximate calculations of Green functions”, In: B.B. Levchenko and V.I. Savrin (Eds.): Proceedings of XIV International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP’99, Moscow 1999), MSU-Press, Moscow, 1999, pp. 572–578.Google Scholar
  25. [15]
    H. Kleinert and B. Van den Bossche: “No spontaneous breakdown of chiral symmetry in Nambu-Jona-Lasinio model?”, Physics Letters, Vol. B 474, (2000), pp. 336–346.CrossRefGoogle Scholar
  26. [16]
    T. Fujita, M. Hiramoto and H. Takahashi: “No Goldstone boson in the NJL and Thirring models”, (2003), hep-th/0306110Google Scholar

Copyright information

© Central European Science Journals 2004

Authors and Affiliations

  • Rauf G. Jafarov
    • 1
  • Vladimir E. Rochev
    • 2
  1. 1.Physical Department of Baku State UniversityBakuAzerbaijan
  2. 2.Institute for High Energy PhysicsProtvinoRussia

Personalised recommendations