- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Chiral quark model in a Tamm-Dancoff inspired approximation

Dubravko Horvat*

Boris Podobnik† and Dubravko Tadić‡

  • Department of Physics, Faculty of Electrical Engineering, University of Zagreb, 10 000 Zagreb, Croatia

  • Department of Physics, University of Zagreb, Bijenička c. 32, 10 000 Zagreb, Croatia

  • *Email address: dubravko.horvat@fer.hr
  • †Email address: bp@phy.hr
  • ‡Email address: tadic@phy.hr
PDF

Phys. Rev. D 58, 034003 – Published 24 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.034003

Abstract

A procedure inspired by the Tamm-Dancoff method is applied to the chiral quark model. It is illustrated here by the chiral σ model embedded in the chiral bag environment. This simple model is used as an example and as the test for the Tamm-Dancoff inspired approximation (TDIA). Here the TDIA is employed in two ways: (i) a set of field operator equations of motion is solved between quark states and (ii) the Hamilton field operator is averaged between suitable hadron states, and the equations of motion are derived for these mean fields. The second approach is analogous to the usual one which employs hedgehog quarks, which is also reproduced here. It turns out that the energy minimum (i.e., hadron masses) can be found with the TDIA also. Model predictions for the axial-vector coupling constant and for the nucleon magnetic moment obtained in the TDIA are comparable to those obtained using the usual hedgehog-based approximation. The TDIA can be used in more complex models too.

View figure in article

References (26)

  1. I. Tamm, J. Phys. (Moscow) 9, 449 (1945).
  2. S. M. Dancoff, Phys. Rev. 78, 382 (1950).
  3. H. A. Bethe and F. de Hoffmann, Mesons and Fields (Row, Peterson, Evanston, IL, 1955), Vol. II.
  4. R. J. Perry, A. Harindranath, and K. G. Wilson, Phys. Rev. Lett. 65, 2959 (1990).
  5. E. P. Wigner, Phys. Rev. 94, 77 (1954).
  6. M. C. Birse and M. K. Banerjee, Phys. Lett. 136B, 284 (1984); Phys. Rev. D 31, 118 (1985); ibid.M. C. Birse, 33, 1934 (1986).
  7. A. W. Thomas, in Advances in Nuclear Physics, edited by J. W. Negele and E. Vogt (Plenum, New York, 1984), Vol. 13, p. 1; G. E. Brown and M. Rho, Phys. Lett. 82B, 177 (1979); ibid.G. E. Brown, M. Rho, and V. Vento, 84B, 383 (1979); H. Hogaasen and F. Myhrer, Z. Phys. C 21, 73 (1983); Xue-Qian Li and Zhen Qi, Commun. Theor. Phys. 18, 213 (1992); G. E. Brown and M. Rho, Comments Nucl. Part. Phys. 18, 1 (1988); F. Myhrer, in Quarks and Nuclei, Vol. 1 of International Review of Nuclear Physics, edited by W. Weise (World Scientific, Singapore, 1984); A. Hosaka and H. Toki, Phys. Rep. 277, 65 (1996).
  8. P. M. Wort, Phys. Rev. D 47, 608 (1993).
  9. S. Glazek et al., Phys. Rev. D 47, 1599 (1993).
  10. K. Harada et al., Phys. Rev. D 54, 7656 (1996).
  11. K. Harada et al., Phys. Rev. D 52, 2429 (1995).
  12. G. Källen, Quantum Electrodynamics (Springer-Verlag, New York, 1972).
  13. A. Chodos and B. C. Thorn, Phys. Rev. D 12, 2733 (1975).
  14. T. H. R. Skyrme, Proc. R. Soc. London A260, 127 (1961); ibid.A262, 237 (1961); Nucl. Phys. 31, 550 (1962); G. S. Adkins, C. R. Nappi, and E. Witten, B228, 552 (1983); ibid.B233, 109 (1984); I. Zahed and G. E. Brown, Phys. Rep. 142, 1 (1986).
  15. J. G. Taylor, Ann. Phys. (N.Y.) 115, 153 (1978); M. Bolsterli, Phys. Rev. D 24, 400 (1981).
  16. M. Fiolhais, J. N. Urbano, and K. Goeke, Phys. Lett. 150B, 253 (1985); ibid.K. Goeke, J. N. Urbano, M. Fiolhais, and M. Harvey, 164B, 249 (1985); E. Ruiz Arriola, P. Alberto, J. N. Urbano, and K. Goeke, Z. Phys. A 333, 203 (1989); T. Neuber, M. Fiolhais, K. Goeke, and J. N. Urbano, Nucl. Phys. A560, 909 (1993).
  17. A. P. Balachandran, Lectures delivered at the Theoretical Advanced Study Institute in Elementary Particle Physics, Yale University, 1985 (unpublished); G. Holzwarth and B. Schwesinger, Rep. Prog. Phys. 49, 825 (1986); see also Refs. [14][15][16].
  18. H. J. Pirner, Prog. Part. Nucl. Phys. 29, 33 (1992); ibid.M. K. Banerjee, 31, 77 (1993).
  19. D. Horvat and D. Tadić, Z. Phys. C 31, 311 (1986); ibid.35, 231 (1987); ibid.D. Horvat, Z. Narančić, and D. Tadić, 38, 431 (1988); D. Horvat, B. Podobnik, and D. Tadić, Fiz. B 2, 49 (1993).
  20. M. C. Birse, Prog. Part. Nucl. Phys. 25, 1 (1990).
  21. J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1964).
  22. R. F. Alvarez-Estrada, F. Fernandez, J. L. Sanchez-Gomez, and V. Vento, Models of Hadron Structure Based on Quantum Chromodynamics, Vol. 259 of Lecture Notes in Physics (Springer, Berlin, 1986).
  23. K. Goeke, F. Grümmer, M. Fiolhais, and J. N. Urbano, in Nuclei, Neutrons and Energy, Proceedings of the VIII International School on Nuclear Physics, Neutron Physics and Nuclear Energy, Varna, 1987, edited by W. Andrejtscheff, Chr. V. Christov, and D Elenkov (World Scientific, Singapore, 1988); K. Goeke, M. Harvey, F. Grümmer, and J. N. Urbano, Phys. Rev. D 37, 754 (1988).
  24. U. Ascher, J. Christiansen, and R. D. Russel, Math. Comput. 33, 659 (1979); ACM Trans. Math. Softw. 7, 209 (1981); SIAM (Soc. Ind. Appl. Math.) Rev. 23, 238 (1981).
  25. L. R. Dodd and M. A. Lohe, Phys. Rev. D 32, 1816 (1985).
  26. S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Row, Peterson, Evanston, IL, 1961).

Outline

Information

Phys. Rev. D 58, 034003– Published 24 June, 1998
  • Received 16 January 1998

© 1998 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation