Zeitschrift für Physik A Hadrons and Nuclei

, Volume 352, Issue 2, pp 197–202 | Cite as

Pion, sigma and nucleon propagators in the linear σ-model

  • S. P. Flego
  • A. H. Blin
  • B. Hiller
  • M. C. Nemes
Heavy Ion Physics


We study the pion, sigma and nucleon propagators of the linear σ-model in the one-loop approximation. We show that in the renormalized model the meson propagators exhibit imaginary poles. Such nonphysical poles disappear when a cutoff is introduced. The maximum of this cutoff value is shown to be of the orderλc≈1.2 Gev. Once this value is fixed it is possible to find a set of parameters which allow for a selfconsistent interpretation of physical properties associated with the propagators. A 400 MeV wide resonance appears in the sigma propagator, the nucleon is a bound state and in its continuum two Roper resonances can be identified.




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  1. 1.
    Nambu, Y. and Jona-Lasinio, G., Phys. Rev.122 (1961) 345;124 (1961) 246.Google Scholar
  2. 2.
    Klevansky, S.P., Rev. Mod. Phys.64 (1992) 649, and references quoted therein.Google Scholar
  3. 3.
    Bernard, V., Blin, A.H., Hiller, B., Meissner, U.-G. and Ruivo, M.C., Phys. Lett.B305 (1993) 163.Google Scholar
  4. 4.
    Weinstein, J., Isgur, N., Phys. Rev.D41 (1990) 2236.Google Scholar
  5. 5.
    Lhose, D., Durso, J.W., Holinde, K., Speth, J., Nucl. Phys.A516 (1990) 513.Google Scholar
  6. 6.
    Cannata, F., Dedonder, J.P. and Lesniak, L., Z. Phys.A343 (1992) 451.Google Scholar
  7. 7.
    Jaffe, R.L., Phys. Rev.D15 (1977) 267 and 281.Google Scholar
  8. 8.
    van Beveren, E., Rupp, G., Rijken, T.A. and Dullemond, C., Phys. Rev.D27 (1983) 1527; van Beveren, E., Nucl. Phys.B21 (proc. Suppl.) (1991) 43.Google Scholar
  9. 9.
    Barnes, T., Phys. Lett.165B (1985) 434.Google Scholar
  10. 10.
    Morgan, D. and Pennington, M.R., Z. Phys.C37 (1988) 431.Google Scholar
  11. 11.
    Sharpe, S.R., Jaffe, R.L. and Pennington, M.R., Phys. Rev.D30 (1984) 1013.Google Scholar
  12. 12.
    Teshima, T. and Oneda, S., Phys. Rev.D33 (1986) 1974.Google Scholar
  13. 13.
    Morgan, D., Pennington, M.R., Phys. Lett.B258 (1991) 444.Google Scholar
  14. 14.
    Kusaka, K. and Weise, W., Z. Phys.A343 (1992) 229.Google Scholar
  15. 15.
    Gell-Mann, M. and Lévy, M., Nuovo Cimento16 (1960) 705.Google Scholar
  16. 16.
    Bessis, D. and Turchetti, G., Cargese Lectures in Physics5 (Gordon and Breach. New York, 1971) 119.Google Scholar
  17. 17.
    Perry, R.J., Phys. Lett.B199 (1987) 489.Google Scholar
  18. 18.
    Bajc, B., Blin, A.H., Hiller, B., Nemes, M.C. and Rosina, M., Z. Phys.A350 (1994) 229.Google Scholar
  19. 19.
    Bjorken, J.D. and Drell, S.D., Relativistic Quantum Mechanics (McGraw-Hill, Inc., New York, 1964).Google Scholar
  20. 20.
    Malheiro, M., Nemes, M.C., Nielsen, M. and da Providncia, J., Intern. Jour. Mod. Phys.A8 (1993) 787.Google Scholar
  21. 21.
    Blin, A.H., Hiller, B. and da Providencia, J., Phys. Lett.B241 (1990) 1.Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • S. P. Flego
    • 1
  • A. H. Blin
    • 2
  • B. Hiller
    • 2
  • M. C. Nemes
    • 3
  1. 1.Depto. de Fisica MatemâticaUniversidade de São Paulo, Instituto) de FisicaSão Paulo, SP
  2. 2.Centro de Física TeóricaUniversidade de CoimbraCoimbraPortugal
  3. 3.Depto. de Física, Inst. de Cs.ExactasUniversidade Federal de Minas GeraisB. Horizonte, MGBrasil

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