Phenomenological Lagrangian Model of Chiral <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo><mn></mn><mo>×</mo><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo><mn></mn></math></span> for Mesons and Baryons with Symmetry Breaking

Yuk-Ming P. Lam; Yee Yen Lee

doi:10.1103/PhysRevD.2.2976

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Phenomenological Lagrangian Model of Chiral $SU (3) \times SU (3)$ for Mesons and Baryons with Symmetry Breaking

Yuk-Ming P. Lam^* and Yee Yen Lee^†

The Enrico Fermi Institute and the Department of Physics, The University of Chicago, Chicago, Illinois 60637

^*Present address: Department of Physics, University of Pittsburgh, Pittsburgh, Pa. 15213.
^†Present address: Institute of Physics, National Tsing Hua University, Hsin Chu, Taiwan, Republic of China.

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Phys. Rev. D 2, 2976 – Published 15 December, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.2976

Abstract

Using the techniques of nonlinear realization of $SU (3) \times SU (3)$ , we write a Lagrangian for the pseudoscalar nonet and $½^{+}$ -baryon octet with a symmetry-breaking term transforming like a vector in a (3,3*) ⊕ (3*,3) representation of $SU (3) \times SU (3)$ . This Lagrangian yields a mass formula (different from the Gell-Mann-Okubo mass formula) for the pseudoscalar octet, and, if we neglect $η - η^{'}$ mixing, then this formula fits the experimental masses to an accuracy of about 1 MeV. From this Lagrangian, explicit expressions for the axial-vector currents in terms of particle fields are obtained. The tree-diagram prescription then yields a modified Goldberger-Treiman relation consistent with experimental measurements.

References (10)

Y. Nambu, Phys. Rev. Letters 4, 380 (1960) Y. Nambu and D. Lurié, Phys. Rev. 125, 1429 (1962)
M. Gell-Mann, Physics 1, 63 (1964)
S. Weinberg, in Proceedings of the Fourteenth International Conference on High-Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, 1968)
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)
M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2193 (1968)
Y. M. P. Lam and Y. Y. Lee, Phys. Rev. Letters 23, 734 (1969)
F. von Hippel and J. K. Kim, Phys. Rev. Letters 22, 740 (1969)
H. Filthuth, Proceedings of the Topical Conference on Weak Interactions, CERN, 1969 (unpublished)
Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)
H. Pagels, Phys. Rev. 179, 1337 (1969)

[c1] Y. Nambu, Phys. Rev. Letters 4, 380 (1960) Y. Nambu and D. Lurié, Phys. Rev. 125, 1429 (1962)

[c2] M. Gell-Mann, Physics 1, 63 (1964)

[c3] S. Weinberg, in Proceedings of the Fourteenth International Conference on High-Energy Physics, Vienna, 1968, edited by J. Prentki and J. Steinberger (CERN, Geneva, 1968)

[c4] 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)

[c5] M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2193 (1968)

[c6] Y. M. P. Lam and Y. Y. Lee, Phys. Rev. Letters 23, 734 (1969)

[c7] F. von Hippel and J. K. Kim, Phys. Rev. Letters 22, 740 (1969)

[c8] H. Filthuth, Proceedings of the Topical Conference on Weak Interactions, CERN, 1969 (unpublished)

[c9] Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)

[c10] H. Pagels, Phys. Rev. 179, 1337 (1969)

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Phenomenological Lagrangian Model of Chiral $SU (3) \times SU (3)$ for Mesons and Baryons with Symmetry Breaking

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Phenomenological Lagrangian Model of Chiral SU(3)×SU(3) for Mesons and Baryons with Symmetry Breaking

Abstract

References (10)

Phenomenological Lagrangian Model of Chiral $SU (3) \times SU (3)$ for Mesons and Baryons with Symmetry Breaking