Nonleptonic Decays of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>Ω</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math></span> in the Current-Current Model

L. R. Ram Mohan

doi:10.1103/PhysRevD.1.266

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Nonleptonic Decays of the $Ω^{-}$ in the Current-Current Model

L. R. Ram Mohan

Department of Physics, Purdue University, Lafayette, Indiana 47907 and Department of Physics, University of Sussex, Brighton, England

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Phys. Rev. D 1, 266 – Published 1 January, 1970

DOI: https://doi.org/10.1103/PhysRevD.1.266

Abstract

The decuplet parity-conserving weak spurion has been evaluated in the Sugawara-Suzuki model by assuming that the relevant matrix elements, in a currentXcurrent model, are saturated by baryon octet and decuplet single-particle intermediate states. $SU (6)$ symmetry has been used to determine the decuplet form factors at zero momentum transfer. In this approach, octet dominance for the decuplet spurion emerges in a natural manner. The $P$ -wave $Ω^{-}$ decay amplitudes are obtained with the baryon octet and decuplet spurion strengths as input. By assuming that the $D$ -wave amplitudes for $Ω^{-} \to Λ K, Ξ π$ decays are given by the $K^{*}$ -pole model, we predict a zero asymmetry parameter for $Ω^{-} \to Λ K$ and a maximal one ( $α \approx 1$ ) for $Ω^{-} \to Ξ π$ decays. The total decay rate of the $Ω^{-}$ is estimated to be $Γ (Ω^{-}) ≅ 8 \times 10^{9}$ $\sec^{- 1}$ , which is in good agreement with experiment.

References (28)

H. Sugawara, Phys. Rev. Letters 15, 870 (1965) M. Suzuki, ibid. 15, 968 (1965)
Y. T. Chiu and J. Schechter, Phys. Rev. Letters 16, 1022 (1966) Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 150, 1201 (1966)
S. Biswas, Aditya Kumar, and R. Saxena, Phys. Rev. Letters 17, 268 (1966) Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967)
Y. Hara, Y. Nambu, and J. Schechter, Phys. Rev. Letters 16, 380 (1966) L. S. Brown and C. M. Sommerfield, ibid. 16, 751 (1966) S. Badier and C. Bouchait, Phys. Letters 20, 529 (1966)
R. P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958) S. Gerstein and Ya. Zeldovich, Zh. Eksperim. i Teor. Fiz. 2, 576 (1956) [English transl.: Soviet Phys.—JETP 29, 698 (1955)]
Y. Nambu, Phys. Rev. Letters 4, 380 (1960)
W. A. Simmons, Phys. Rev. 164, 1956 (1967)
L. Chan, K. Chen, J. Dunning, Jr., N. Ramsey, J. Walker, and R. Wilson, Phys. Rev. 141, 1298 (1966)
M. Gourdin and Ph. Salin, Nuovo Cimento 27, 193 (1963)
C. H. Albright and L. S. Liu, Phys. Rev. 140, B748 (1965) ibid.140, B1611 (1965)
A. Pais, Rev. Mod. Phys. 38, 215 (1966)
A. Pais ([11])
M. A. B. Bég, B. W. Lee, and A. Pais, Phys. Rev. Letters 13, 514 (1964)
S. Pakvasa and S. P. Rosen, Phys. Rev. 147, 1166 (1966) M. A. B. Bég and A. Pais, Phys. Rev. Letters 14, 51 (1965) I. J. Muzinich, Phys. Letters 14, 252 (1965)
S. Okubo, Progr. Theoret. Phys. (Kyoto) 27, 949 (1962)
H. Filthuth, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished)
E. Fischbach, Phys. Rev. 170, 1398 (1968)
N. Cabibbo, Phys. Rev. Letters 10, 531 (1965)
M. Suzuki, Progr. Theoret. Phys. (Kyoto) 32, 138 (1964) S. Pakvasa and S. P. Rosen ([14]) Y. Hara, Phys. Rev. 150, 1175 (1966) A. P. Balachandran, M. G. Gundzik, and S. Pakvasa, ibid. 153, 1553 (1967) K. Ohya, M. Imoto, and S. Kawasaki, Progr. Theoret. Phys. (Kyoto) 39, 1268 (1968)
X. Y. Pham and R. Zaoui, Phys. Rev. 167, 1319 (1968)
S. L. Glashow and R. Socolow, Phys. Letters 10, 143 (1964)
F. C. P. Chan, Phys. Rev. 171, 1543 (1968)
L. R. Ram Mohan, Phys. Rev. 179, 1561 (1969)
Arvind Kumar and J. C. Pati, Phys. Rev. Letters 18, 1230 (1967) M. Hirano, K. Fujii, and O. Terazawa, Progr. Theoret. Phys. (Kyoto) 40, 114 (1968) B. W. Lee, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished)
A. H. Rosenfeld et al., Rev. Mod. Phys. 41, 109 (1969)
J. Schwinger, Phys. Rev. Letters 12, 630 (1964) ibid.13, 355 (1964) B. W. Lee and A. R. Swift, Phys. Rev. 136, B228 (1964)
D. S. Carlstone, S. P. Rosen, and S. Pakvasa, Phys. Rev. 174, 1877 (1968)
B. W. Lee, Phys. Rev. 140, B152 (1965)

[c1] H. Sugawara, Phys. Rev. Letters 15, 870 (1965) M. Suzuki, ibid. 15, 968 (1965)

[c2] Y. T. Chiu and J. Schechter, Phys. Rev. Letters 16, 1022 (1966) Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 150, 1201 (1966)

[c3] S. Biswas, Aditya Kumar, and R. Saxena, Phys. Rev. Letters 17, 268 (1966) Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967)

[c4] Y. Hara, Y. Nambu, and J. Schechter, Phys. Rev. Letters 16, 380 (1966) L. S. Brown and C. M. Sommerfield, ibid. 16, 751 (1966) S. Badier and C. Bouchait, Phys. Letters 20, 529 (1966)

[c5] R. P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958) S. Gerstein and Ya. Zeldovich, Zh. Eksperim. i Teor. Fiz. 2, 576 (1956) [English transl.: Soviet Phys.—JETP 29, 698 (1955)]

[c6] Y. Nambu, Phys. Rev. Letters 4, 380 (1960)

[c7] W. A. Simmons, Phys. Rev. 164, 1956 (1967)

[c8] L. Chan, K. Chen, J. Dunning, Jr., N. Ramsey, J. Walker, and R. Wilson, Phys. Rev. 141, 1298 (1966)

[c9] M. Gourdin and Ph. Salin, Nuovo Cimento 27, 193 (1963)

[c10] C. H. Albright and L. S. Liu, Phys. Rev. 140, B748 (1965) ibid.140, B1611 (1965)

[c11] A. Pais, Rev. Mod. Phys. 38, 215 (1966)

[c12] A. Pais ([11])

[c13] M. A. B. Bég, B. W. Lee, and A. Pais, Phys. Rev. Letters 13, 514 (1964)

[c14] S. Pakvasa and S. P. Rosen, Phys. Rev. 147, 1166 (1966) M. A. B. Bég and A. Pais, Phys. Rev. Letters 14, 51 (1965) I. J. Muzinich, Phys. Letters 14, 252 (1965)

[c15] S. Okubo, Progr. Theoret. Phys. (Kyoto) 27, 949 (1962)

[c16] H. Filthuth, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished)

[c17] E. Fischbach, Phys. Rev. 170, 1398 (1968)

[c18] N. Cabibbo, Phys. Rev. Letters 10, 531 (1965)

[c19] M. Suzuki, Progr. Theoret. Phys. (Kyoto) 32, 138 (1964) S. Pakvasa and S. P. Rosen ([14]) Y. Hara, Phys. Rev. 150, 1175 (1966) A. P. Balachandran, M. G. Gundzik, and S. Pakvasa, ibid. 153, 1553 (1967) K. Ohya, M. Imoto, and S. Kawasaki, Progr. Theoret. Phys. (Kyoto) 39, 1268 (1968)

[c20] X. Y. Pham and R. Zaoui, Phys. Rev. 167, 1319 (1968)

[c21] S. L. Glashow and R. Socolow, Phys. Letters 10, 143 (1964)

[c22] F. C. P. Chan, Phys. Rev. 171, 1543 (1968)

[c23] L. R. Ram Mohan, Phys. Rev. 179, 1561 (1969)

[c24] Arvind Kumar and J. C. Pati, Phys. Rev. Letters 18, 1230 (1967) M. Hirano, K. Fujii, and O. Terazawa, Progr. Theoret. Phys. (Kyoto) 40, 114 (1968) B. W. Lee, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished)

[c25] A. H. Rosenfeld et al., Rev. Mod. Phys. 41, 109 (1969)

[c26] J. Schwinger, Phys. Rev. Letters 12, 630 (1964) ibid.13, 355 (1964) B. W. Lee and A. R. Swift, Phys. Rev. 136, B228 (1964)

[c27] D. S. Carlstone, S. P. Rosen, and S. Pakvasa, Phys. Rev. 174, 1877 (1968)

[c28] B. W. Lee, Phys. Rev. 140, B152 (1965)

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Nonleptonic Decays of the $Ω^{-}$ in the Current-Current Model

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Nonleptonic Decays of the Ω− in the Current-Current Model

Abstract

References (28)

Nonleptonic Decays of the $Ω^{-}$ in the Current-Current Model