Skip to main content
SpringerLink
Log in

Chiral perturbation theory in the Extended Nambu-Jona-Lasinio model

  • Papers
  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

The chiral perturbation theory is developed at the quark level within the Extended Nambu-Jona-Lasinio model which we used for the low-energy approximation of QCD in the leading order of the large N expansion. In terms of constituent-quark-loop diagrams we analyse all of the main low-energy effects caused by the first order corrections in the current quark mass expansions. For the correct description of theη →3π decays we confirm the important role of the final-state-interaction quoted by Gasser and Leutwyler.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Nambu Y., Jona-Lasinio G.: Phys. Rev.122 (1961) 345.

    Google Scholar 

  2. Eguchi T.: Phys. Rev. D14 (1976) 2755.

    Google Scholar 

  3. Kikkawa T. K.: Progr. Theor. Phys.56 (1976) 947.

    Google Scholar 

  4. Kleinert H.:in Proc. of Int. Summer School of Subnuclear Physics, Erice 1976 (ed. A. Zichichi), p.289.

  5. Ebert D., Volkov M. K.: Z. Phys. C16 (1983) 205.

    Google Scholar 

  6. Volkov M. K.: Ann. Phys.157 (1984) 282; Nucl. Part.17 (1986) 433.

    Google Scholar 

  7. Ebert D., Reinhardt H.: Nucl. Phys. B271 (1986) 188.

    Google Scholar 

  8. Ebert D., Ivanov A. N., Volkov M. K.: Fortschr. Phys.37 (1989) 486.

    Google Scholar 

  9. Dhar A., Shankar R., Wadia S. R.: Phys. Rev. D31 (1985) 3256

    Google Scholar 

  10. Ivanov A. N., Troitskaya N. I., Volkov M. K.: Phys. Lett. B175 (1986) 467; B184 (1986) 94:in Proc. VIII Int. Conf. on Problems of Quantum Field Theory, Alushta, October 1987, p. 190.

    Google Scholar 

  11. Volkov M. K., Ivanov A. N., Troitskaya N. I.: Yad. Fiz.47 (1989) 1152.

    Google Scholar 

  12. Ivanov A. N., Nagy M., Volkov M. K.: Phys. Lett. B200 (1988) 171.

    Google Scholar 

  13. Volkov M. K., Ivanov A. N., Nagy M., Troitskaya N. I.: Int. J. Mod. Phys. A4 (1989) 3193.

    Google Scholar 

  14. Ivanov A. N., Nagy M., Troitskaya N. I., Volkov M. K.: Phys. Lett. B235 (1990) 331.

    Google Scholar 

  15. Ivanov A. N.: The low energy theorems and connected topics in hadronic physics. Invited talk at the Int. Conf. “Hadron Structure-89”, Smolenice, CSFR, 25–29 Sept. 1989.

  16. Troitskaya N. I.: Some problems of the low-energy hadronic physics (Ph.D. Thesis). Leningrad Slate Univ., Leningrad, 1990.

    Google Scholar 

  17. Ivanov A. N., Nagy M., Troitskaya N. I.: Czech. J. Phys. B42 (1992) 21.

    Google Scholar 

  18. Gasser J., Leutwyler H.: Nucl. Phys. B94 (1975) 269.

    Google Scholar 

  19. Weinberg S.:in A Festschrift for I. I. Rabi (ed. L. Motz). Nat. Acad. Sci., New York. 1977, p. 185.

    Google Scholar 

  20. Leutwyler H.: Nucl. Phys. B337 (1990) 108.

    Google Scholar 

  21. Dashen R.: Phys. Rev.183 (1969) 1245.

    Google Scholar 

  22. Dashen R., Weinshtein M.: Phys. Rev.183 (1969) 1291.

    Google Scholar 

  23. Gasser J., Leutwyler H.: Nucl. Phys. B250 (1985) 465.

    Google Scholar 

  24. t'Hooft G.: Nucl. Phys. B72 (1974) 461; B75 (1974) 461.

    Google Scholar 

  25. Veneziano G.: Nucl. Phys. B117 (1976) 519.

    Google Scholar 

  26. Wilten E.: Nucl. Phys. B160 (1979) 57.

    Google Scholar 

  27. Yoshida K.: Nucl. Phys. B187 (1981) 103.

    Google Scholar 

  28. Bernard V., Jaffe R. L., Meissner U.-G.: Nucl. Phys. B308 (1988) 753.

    Google Scholar 

  29. Gasiorowicz S., Geffen D. A.: Rev. Mod. Phys.41 (1969) 531.

    Google Scholar 

  30. Weinberg S.: Phys. Rev. Lett.18 (1966) 188.

    Google Scholar 

  31. Lehmann H.: Acta Physica Austriaca, Suppl. XI (1975) 139.

    Google Scholar 

  32. Osborn H., Wallace D. J.: Nucl. Phys. B20 (1970) 23.

    Google Scholar 

  33. Cronin J. A.: Phys. Rev.161 (1967) 1483.

    Google Scholar 

  34. Roiesnel C., Truong T. N.: Nucl. Phys. B187 (1981) 293.

    Google Scholar 

  35. Gasser J., Leutwyler H.: Nucl. Phys. B250 (1985) 539.

    Google Scholar 

  36. Bardeen J., Cooper L. B., Schriffer J. R.: Phys. Rev.108 (1957) 1157.

    Google Scholar 

  37. Bogoliubov N. N., Tolmachev V. V., Shirkov D. V.: The new method in theory of superconductivity. Izdat. AN SSSR, Moscow, 1958 (in Russian).

    Google Scholar 

  38. Kokkedee J.J.J.: The quark model. W. A. Benjamin, Inc., New York-Amsterdam, 1969.

    Google Scholar 

  39. Gasser J., Leutwyler H.: Phys. Rep.87 (1982) 77.

    Google Scholar 

  40. Gell-Mann M., Oakes R. J., Renner B.: Phys. Rev.175 (1968) 2195.

    Google Scholar 

  41. Gross D. J., Treiman S. B., Wilczek F.: Phys. Rev. D19 (1979) 2188.

    Google Scholar 

  42. Veneziano G.: Nucl. Phys. B159 (1979) 213.

    Google Scholar 

  43. de Vecchia P.: Phys. Lett. B85 (1979) 357.

    Google Scholar 

  44. Witten E.: Nucl. Phys. B159 (1979) 269.

    Google Scholar 

  45. Reinders L. J., Rubinstein H. R.: Phys. Lett. B145 (1984) 108.

    Google Scholar 

  46. Wess J. B., Zumino B.: Phys. Lett. B37 (1971) 95.

    Google Scholar 

  47. Adler S. L.: Phys. Rev.177 (1969) 2426.

    Google Scholar 

  48. Bell J. S., Jackiw R.: Nouvo Cimento A60 (1969) 47.

    Google Scholar 

  49. Witten E.: Nucl. Phys. B223 (1983) 422; 433.

    Google Scholar 

  50. Ivanov A. N., Shechter V. M.: Yad. Fiz.31 (1980) 530;32 (1980) 796.

    Google Scholar 

  51. Ivanov A. N.: Yad. Fiz.33 (1981) 1679.

    Google Scholar 

  52. Ivanov A. N., Troitskaya N. I.: Yad. Fiz.36 (1982) 220.

    Google Scholar 

  53. Brown R. W., Shih C. C., Young B. L.: Phys. Rev.186 (1969) 1491.

    Google Scholar 

  54. Andrianov A. A., Novozhilov Yu. V.: Phys. Lett. B153 (1985) 422.

    Google Scholar 

  55. Andrianov A. A.: Phys. Lett. B157 (1985) 425.

    Google Scholar 

  56. Particle Data Group, Phys. Lett. B239 (1990) 1.

    Google Scholar 

  57. Fajfer S., Gérard J.-M.: Preprints MPI-PAE/PTh 80/87; 91/87, Max Planck Inst., Munich.

  58. Bay A. et al.: Phys. Lett. B174 (1986) 445.

    Google Scholar 

  59. Ivanov A. N., Nagy M., Troitskaya N. I., Volkov M. K.: Czech. J. Phys. B39 (1989) 1262.

    Google Scholar 

  60. Weinberg S.: Phys. Rev. Lett.18 (1967) 507.

    Google Scholar 

  61. Band H. R. et al. (MAC Collab.): Phys. Lett. B198 (1987) 297.

    Google Scholar 

  62. Schmidke W. B. et al. (Mark II): Phys. Rev. Lett.57 (1986) 527.

    Google Scholar 

  63. Ivanov A. N.: Int. J. Mod. Phys. A6 (1991) 4055.

    Google Scholar 

  64. Gell-Mann M.: Phys. Rev.125 (1962) 1067

    Google Scholar 

  65. Okubo S.: Progr. Theor. Phys.27 (1962) 949.

    Google Scholar 

  66. Aihra A., et al., Phys. Rev. D33 (1986) 844.

    Google Scholar 

  67. Kawamoto N., Smith J.: Nucl. Phys. B192 (1981) 100.

    Google Scholar 

  68. Bogoliubov N. N., Shirkov D. V.: Introduction to the quantum field theory. Nauka, Moscow, 1984.

    Google Scholar 

Download references

Author information

Author notes

  1. A. N. Ivanov & N. I. Troitskaya

    Present address: State Technical University, 194021, St. Petersburg, Russia

Authors and Affiliations

  1. Institute of Physics, Slovak Acad. Sci., Dúbravská cesta 9, CS-842, 28 Bratislava, Czechoslovakia

    A. N. Ivanov, M. Nagy & N. I. Troitskaya

Authors
  1. A. N. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Nagy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. I. Troitskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

We are very indebted to J. Gasser, G. Ecker and M. Sainio for helpfull discussions and A. Nogová for reading the manuscript. One of us, M.N., thanks A. Di Giacomo for his hospitality during the stay at the Department of Physics of the University of Pisa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivanov, A.N., Nagy, M. & Troitskaya, N.I. Chiral perturbation theory in the Extended Nambu-Jona-Lasinio model. Czech J Phys 42, 861–890 (1992). https://doi.org/10.1007/BF01605164

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01605164

Keywords

Search

Navigation