Vector and scalar mesons in the Skyrmion model

M. Mashaal; T. N. Pham; Tran N. Truong

doi:10.1103/PhysRevD.34.3484

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Vector and scalar mesons in the Skyrmion model

M. Mashaal, T. N. Pham, and Tran N. Truong

Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau, France

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Phys. Rev. D 34, 3484 – Published 1 December, 1986

DOI: https://doi.org/10.1103/PhysRevD.34.3484

Abstract

It is shown how the Skyrme and the non-Skyrme terms arise naturally from an effective chiral Lagrangian with the vector and scalar mesons. Some errors in the literature concerning the use of the Skyrme and the non-Skyrme terms are pointed out.

References (23)

T. H. R. Skyrme, Proc. R. Soc. London A260, 127 (1961).
A. P. Balachandran, V. P. Nair, S. G. Rajeev and A. Stern, Phys. Rev. Lett. 49, 1124 (1982).
N. K. Pak and A. C. Tze, Ann. Phys. (N.Y.) 117, 164 (1979).
E. Witten, Nucl. Phys. B223, 422 (1983); ibid. B223, 433 (1983).
J. F. Donoghue, E. Golowich and B. R. Holstein, Phys. Rev. Lett. 53, 747 (1984).
T. N. Pham and Tran N. Truong, Phys. Rev. D 31, 3027 (1985); Phys. Lett. B (to be published).
M. Mashaal, T. N. Pham and Tran N. Truong, Phys. Rev. Lett. 56, 436 (1986).
G. Adkins, C. Nappi and E. Witten, Nucl. Phys. B228, 552 (1983).
G. Adkins, Phys. Rev. D 33, 193 (1986); M. Lacombe, B. Loiseau, R. Vinh Mau and W. N. Cottingham, Phys. Lett. 169B, 121 (1986).
I. J. R. Aitchison, C. M. Fraser and P. J. Miron, Phys. Rev. D 33, 1994 (1986).
M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, Phys. Rev. Lett. 54, 1215 (1985).
P. Q. Hung, Phys. Lett. 168B, 253 (1986); M. Abud, G. Mariella, F. Nicodemi, R. Pettorino and K. Yoshida, ibid. 159B, 155 (1985).
S. Coleman, J. Wess and B. Zumino, Phys. Rev. 177, 2239 (1969); C. G. Callan, S. Coleman, J. Wess and B. Zumino, ibid. 177, 2247 (1969).
J. Cronin, Phys. Rev. 161, 1483 (1967).
S. Weinberg, Phys. Rev. 166, 1568 (1968).
K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett. 16, 255 (1966); Riazzuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966).
M. L. Goldberger, H. Miyazawa and R. Oehme, Phys. Rev. 99, 986 (1955).
S. L. Adler, Phys. Rev. Lett. 14, 1051 (1965); W. I. Weisberger, ibid. 14, 1047 (1965).
J. Wess and B. Zumino, Phys. Rev. 163, 1727 (1967).
G. Adkins and C. Nappi, Phys. Lett. 137B, 251 (1984).
A small contribution to the non-Skyrme term from higher scalar meson resonances is also neglected here. See T. N. Pham, Phys. Rev. D 33, 1499 (1986).
Note the factor 1/2 in $H_{omega}$ which was missing in Eq. (5d) of Ref. 7.
G. H. Derrick, J. Math. Phys. 5, 1252 (1964).

[c1] T. H. R. Skyrme, Proc. R. Soc. London A260, 127 (1961).

[c2] A. P. Balachandran, V. P. Nair, S. G. Rajeev and A. Stern, Phys. Rev. Lett. 49, 1124 (1982).

[c3] N. K. Pak and A. C. Tze, Ann. Phys. (N.Y.) 117, 164 (1979).

[c4] E. Witten, Nucl. Phys. B223, 422 (1983); ibid. B223, 433 (1983).

[c5] J. F. Donoghue, E. Golowich and B. R. Holstein, Phys. Rev. Lett. 53, 747 (1984).

[c6] T. N. Pham and Tran N. Truong, Phys. Rev. D 31, 3027 (1985); Phys. Lett. B (to be published).

[c7] M. Mashaal, T. N. Pham and Tran N. Truong, Phys. Rev. Lett. 56, 436 (1986).

[c8] G. Adkins, C. Nappi and E. Witten, Nucl. Phys. B228, 552 (1983).

[c9] G. Adkins, Phys. Rev. D 33, 193 (1986); M. Lacombe, B. Loiseau, R. Vinh Mau and W. N. Cottingham, Phys. Lett. 169B, 121 (1986).

[c10] I. J. R. Aitchison, C. M. Fraser and P. J. Miron, Phys. Rev. D 33, 1994 (1986).

[c11] M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, Phys. Rev. Lett. 54, 1215 (1985).

[c12] P. Q. Hung, Phys. Lett. 168B, 253 (1986); M. Abud, G. Mariella, F. Nicodemi, R. Pettorino and K. Yoshida, ibid. 159B, 155 (1985).

[c13] S. Coleman, J. Wess and B. Zumino, Phys. Rev. 177, 2239 (1969); C. G. Callan, S. Coleman, J. Wess and B. Zumino, ibid. 177, 2247 (1969).

[c14] J. Cronin, Phys. Rev. 161, 1483 (1967).

[c15] S. Weinberg, Phys. Rev. 166, 1568 (1968).

[c16] K. Kawarabayashi and M. Suzuki, Phys. Rev. Lett. 16, 255 (1966); Riazzuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966).

[c17] M. L. Goldberger, H. Miyazawa and R. Oehme, Phys. Rev. 99, 986 (1955).

[c18] S. L. Adler, Phys. Rev. Lett. 14, 1051 (1965); W. I. Weisberger, ibid. 14, 1047 (1965).

[c19] J. Wess and B. Zumino, Phys. Rev. 163, 1727 (1967).

[c20] G. Adkins and C. Nappi, Phys. Lett. 137B, 251 (1984).

[c21] A small contribution to the non-Skyrme term from higher scalar meson resonances is also neglected here. See T. N. Pham, Phys. Rev. D 33, 1499 (1986).

[c22] Note the factor 1/2 in $H_{omega}$ which was missing in Eq. (5d) of Ref. 7.

[c23] G. H. Derrick, J. Math. Phys. 5, 1252 (1964).

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Vector and scalar mesons in the Skyrmion model

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References (23)

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