Some Difficulties with the Use of the Kemmer-Duffin Formalism for Pseudoscalar Mesons

Nilendra G. Deshpande; Peter C. McNamee

doi:10.1103/PhysRevD.5.1012

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Some Difficulties with the Use of the Kemmer-Duffin Formalism for Pseudoscalar Mesons

Nilendra G. Deshpande and Peter C. McNamee^*

Northwestern University, Department of Physics, Evanston, Illinois 60201

^*Present address: Instituut voor Theoretische Fysica, Universiteit Leuven, Louvain, Belgium.

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Phys. Rev. D 5, 1012 – Published 15 February, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.1012

Abstract

While the Kemmer-Duffin formalism for pseudoscalar mesons eliminates some difficulties in the analysis of $K_{l 3}$ form factors, it gives rise to difficulties in other areas. It is shown that this formalism leads to: (i) a linear Gell-Mann—Okubo mass formula for mesons; (ii) an incompatibility between SU(3)-symmetric meson-nucleon couplings and experiment; (iii) (3*,3) breaking of chiral symmetry ( $H^{'} = u^{0} + c u^{8}$ ) leads to $c = - 0.9$ and $\frac{f_{K}}{f_{π}} = {(\frac{m_{π}}{m_{K}})}^{\frac{1}{2}}$ .

References (12)

E. Fischbach et al., Phys. Rev. Letters 26, 1200 (1971)
R. J. Duffin, Phys. Rev. 54, 1114 (1938) N. Kemmer, Proc. Roy. Soc. (London) A173, 91 (1939) F. J. Belinfante, Physica 6, 849 (1939)
E. Fischbach et al., Phys. Rev. Letters 27, 1403 (1971)
[1] N. Deshpande and P. McNamee, Phys. Rev. D (to be published)
Omitted endnote
Omitted endnote
R. D. Field and J. D. Jackson, Phys. Rev. D 4, 693 (1971) J. K. Kim, Phys. Rev. Letters 19, 1079 (1967) C. H. Chan and F. T. Meiere, ibid. 20, 588 (1968) Phys. Letters 28B, 125 (1968) N. Zovko, ibid. 23, 143 (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)
Omitted endnote
Omitted endnote
[3]

[c1] E. Fischbach et al., Phys. Rev. Letters 26, 1200 (1971)

[c2] R. J. Duffin, Phys. Rev. 54, 1114 (1938) N. Kemmer, Proc. Roy. Soc. (London) A173, 91 (1939) F. J. Belinfante, Physica 6, 849 (1939)

[c3] E. Fischbach et al., Phys. Rev. Letters 27, 1403 (1971)

[c4] [1] N. Deshpande and P. McNamee, Phys. Rev. D (to be published)

[c5] Omitted endnote

[c6] Omitted endnote

[c7] R. D. Field and J. D. Jackson, Phys. Rev. D 4, 693 (1971) J. K. Kim, Phys. Rev. Letters 19, 1079 (1967) C. H. Chan and F. T. Meiere, ibid. 20, 588 (1968) Phys. Letters 28B, 125 (1968) N. Zovko, ibid. 23, 143 (1966)

[c8] M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968)

[c9] S. L. Glashow and S. Weinberg, Phys. Rev. Letters 20, 224 (1968)

[c10] Omitted endnote

[c11] Omitted endnote

[c12] [3]

Physical Review D

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Some Difficulties with the Use of the Kemmer-Duffin Formalism for Pseudoscalar Mesons

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