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Splitting, Mixing, and Small Perturbations in Multiplets of Vector Mesons
Phys. Rev. 174, 2113 – Published 25 October, 1968
DOI: https://doi.org/10.1103/PhysRev.174.2113
Abstract
Various aspects of multiplet mixing are studied within the context of a model with fixed kinematics of broken symmetry for the vector mesons. The validity of first-order mass formulas is investigated in terms of a perturbation expansion based on intermultiplet coupling. It is shown that such an expansion is linear within a few percent over extrapolations needed to reach the physical masses. Because of the intermultiplet coupling, the imposition of self-consistency determines the magnitudes of the mass shifts rather than simply the mass ratios. Self-consistency also yields the mixing angle. Of the two solutions permitted by self-consistency, viz., a symmetric and an asymmetric solution, the symmetric solution is characterized by rapid variation of the intermultiplet coupling. Small perturbations can prevent self-consistency because of this rapid variation, and exclude the symmetric solution, forcing the dynamical system into the disjoint, asymmetrical configuration. It is suggested that these results do not depend on the model in an essential manner and are of a more general character.
References (9)
- M. Gell-Mann and Y. Ne'eman, The Eightfold Way (W. A. Benjamin, Inc., New York, 1964)
- L. F. Cook and J. E. Paton, Phys. Rev. 137, B1267 (1965)
- F. Zachariasen and C. Zemach, Phys. Rev. 128, 849 (1962) J. Fulco, G. Shaw, and D. Wong, ibid. 137, B1242 (1965)
- A. J. Rivers, Phys. Rev. 152, 1263 (1966)
- S. L. Glashow, Phys. Rev. 130, 2132 (1963)
- E. C. G. Sudarshan and N. Mukunda, Phys. Rev. 158, 1424 (1967) A. Pais, ibid. 173, 1587 (1968)
- R. Dashen and S. Frautschi, Phys. Rev. 137, B1318 (1965)
- A. R. Swift, Phys. Rev. 156, 1729 (1967)
- J. J. Brehm and L. F. Cook, Phys. Rev. 170, 1387 (1968)