Vector-Meson Mixing and Broken Nonet Symmetry

B. G. Kenny

doi:10.1103/PhysRevD.7.2776

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Vector-Meson Mixing and Broken Nonet Symmetry

B. G. Kenny^*

The Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637
Department of Physics, University of Virginia, Charlottesville, Virginia 22901

^*Permanent Address: Theoretical Physics, Research School of Physical Sciences, The Australian National University, Canberra, Australia.

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Phys. Rev. D 7, 2776 – Published 1 May, 1973

DOI: https://doi.org/10.1103/PhysRevD.7.2776

Abstract

Vector-meson mixing is investigated using a simple ansatz for the vector-meson nonet propagator. The first and the modified second spectral-function sum rules of Weinberg are tested using this ansatz. As a consequence it is found that the first sum rules possess a higher symmetry than is usually assumed. The modifications to the second sum rules are found to be incorrect in certain cases. In addition the $ω - φ$ mixing angle is estimated and found to be close to the ideal value. The quantity $\frac{f_{κ}}{f_{π}}$ is calculated and used to test the validity of a conjectured modified second sum rule. Finally two independent methods are used to estimate $Δ (0) = \frac{1}{2} f_{κ}^{2} m_{κ}^{2}$ . Agreement is found between the methods, but the result is found to be larger by a factor of 2 than the usually accepted "standard value."

References (19)

B. G. Kenny, Phys. Rev. D 6, 2617 (1972)
S. Weinberg, Phys. Rev. Letters 18, 507 (1967) S. Glashow, H. Schnitzer, and S. Weinberg, ibid. 19, 139 (1967)
S. Okubo, in Proceedings of the 1967 International Conference on Particles and Fields, edited by C. Hagen, G. Guralnik, and V. Mathur (Interscience, New York, 1967) S. Okubo, Lectures given at the University of Islamabad, 1967 (unpublished)
R. J. Oakes and J. J. Sakurai, Phys. Rev. Letters 19, 1266 (1967)
N. M. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157, 1376 (1967)
J. D. Bjorken, Phys. Rev. 148, 1467 (1966)
M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) S. L. Glashow and S. Weinberg, Phys. Rev. Letters 20, 224 (1968)
A. N. Kamai, Nucl. Phys. B12, 123 (1969) C. S. Lai and S. Y. Lo, Proc. Phys. Soc. (London) A4, 859 (1971)
P. Carruthers, Phys. Reports 1C, 1 (1971)
S. Coleman and H. Schnitzer, Phys. Rev. 134, B863 (1964)
S. Gasiorowicz and D. Geffen, Rev. Mod. Phys. 41, 531 (1969)
D. Benaksas, G. Cosme, J. Jean-Marie, S. Jullian, F. Laplanche, J. LeFrancois, A. D. Liberman, G. Parrour, J. P. Repellin, and G. Sauvage, Phys. Letters 39B, 289 (1972)
K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 144, 1071 (1966)
S. Glashow and S. Weinberg, Phys. Rev. Letters 20, 224 (1968)
L. M. Chounet, J. M. Gaillard, and M. K. Gaillard, Phys. Reports 4C, 199 (1972)
L.-F. Li and H. Pagels, Phys. Rev. D 4, 255 (1971)
K. Tanaka and R. Torgerson, Phys. Rev. D 5, 1164 (1972)
V. S. Mathur and S. Okubo, Phys. Rev. D 1, 3468 (1970)
[17]

[c1] B. G. Kenny, Phys. Rev. D 6, 2617 (1972)

[c2] S. Weinberg, Phys. Rev. Letters 18, 507 (1967) S. Glashow, H. Schnitzer, and S. Weinberg, ibid. 19, 139 (1967)

[c3] S. Okubo, in Proceedings of the 1967 International Conference on Particles and Fields, edited by C. Hagen, G. Guralnik, and V. Mathur (Interscience, New York, 1967) S. Okubo, Lectures given at the University of Islamabad, 1967 (unpublished)

[c4] R. J. Oakes and J. J. Sakurai, Phys. Rev. Letters 19, 1266 (1967)

[c5] N. M. Kroll, T. D. Lee, and B. Zumino, Phys. Rev. 157, 1376 (1967)

[c6] J. D. Bjorken, Phys. Rev. 148, 1467 (1966)

[c7] M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) S. L. Glashow and S. Weinberg, Phys. Rev. Letters 20, 224 (1968)

[c8] A. N. Kamai, Nucl. Phys. B12, 123 (1969) C. S. Lai and S. Y. Lo, Proc. Phys. Soc. (London) A4, 859 (1971)

[c9] P. Carruthers, Phys. Reports 1C, 1 (1971)

[c10] S. Coleman and H. Schnitzer, Phys. Rev. 134, B863 (1964)

[c11] S. Gasiorowicz and D. Geffen, Rev. Mod. Phys. 41, 531 (1969)

[c12] D. Benaksas, G. Cosme, J. Jean-Marie, S. Jullian, F. Laplanche, J. LeFrancois, A. D. Liberman, G. Parrour, J. P. Repellin, and G. Sauvage, Phys. Letters 39B, 289 (1972)

[c13] K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 144, 1071 (1966)

[c14] S. Glashow and S. Weinberg, Phys. Rev. Letters 20, 224 (1968)

[c15] L. M. Chounet, J. M. Gaillard, and M. K. Gaillard, Phys. Reports 4C, 199 (1972)

[c16] L.-F. Li and H. Pagels, Phys. Rev. D 4, 255 (1971)

[c17] K. Tanaka and R. Torgerson, Phys. Rev. D 5, 1164 (1972)

[c18] V. S. Mathur and S. Okubo, Phys. Rev. D 1, 3468 (1970)

[c19] [17]

Physical Review D

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Vector-Meson Mixing and Broken Nonet Symmetry

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