Sum Rules for <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>CP</mi></math></span>-Nonconserving <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>BB</mi><mi>π</mi></math></span> Amplitudes in Glashow's Model

L. R. Ram Mohan

doi:10.1103/PhysRevD.4.825

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Sum Rules for $CP$ -Nonconserving $BB π$ Amplitudes in Glashow's Model

L. R. Ram Mohan

Department of Physics, Purdue University, Lafayette, Indiana 47907

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Phys. Rev. D 4, 825 – Published 1 August, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.825

Abstract

Current algebra has been used to derive sum rules for the $CP$ -nonconserving $Δ S = 1$ and $Δ S = 0$ nonleptonic transitions $B \to B^{'} π$ in Glashow's model. Within the saturation scheme of Chiu, Schechter, and Ueda for the matrix elements of the weak current × current Hamiltonian between single baryon states, it is shown that the $CP$ -nonconserving amplitudes do have octet dominance. The one-pion exchange contribution to the weak $P$ - and $T$ -violating nucleon-nucleon potential has been calculated by relating the weak $NN π$ vertex to hyperon decay amplitudes.

References (18)

J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Letters 13, 138 (1964)
S. L. Glashow, Phys. Rev. Letters 14, 35 (1965)
R. J. Oakes, Phys. Rev. Letters 20, 1539 (1968) ibid.21, 589(E) (1968) T. Das, ibid. 21, 409 (1968) F. Zachariasen and G. Zwieg, Phys. Rev. 182, 1446 (1969)
C. H. Albright, Phys. Rev. 187, 1881 (1969)
H. Sugawara, Phys. Rev. Letters 15, 870 (1965) M. Suzuki, ibid. 15, 986 (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. P. Saxena, Phys. Rev. Letters 17, 268 (1966) Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967) W. A. Simmons, Phys. Rev. 164, 1956 (1967)
C. W. Kim and H. Primakoff, Phys. Rev. 180, 1502 (1969)
J. C. Pati, Phys. Rev. Letters 20, 812 (1968)
V. W. Cohen, R. Nathans, H. B. Silsbee, E. Lipworth, and N. F. Ramsey, Phys. Rev. 177, 1942 (1969)
L. R. Ram Mohan, Phys. Rev. D 1, 266 (1970)
[10] [6] Y. T. Chiu, J. Schechter, and Y. Ueda, Nuovo Cimento 47A, 214 (1967) [6]
E. Fischbach, Phys. Rev. 170, 1398 (1968)
H. Filthuth, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished)
R. J. Blin-Stoyle, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished) E. M. Henley, Ann. Rev. Nucl. Sci. 19, 367 (1969)
B. H. J. McKellar, Phys. Letters 26B, 107 (1967)
G. Barton, Nuovo Cimento 19, 512 (1961)
B. R. Holstein, Phys. Rev. 171, 1668 (1968)
Z. Szymanski, Nucl. Phys. A113, 385 (1968)

[c1] J. H. Christenson, J. W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Letters 13, 138 (1964)

[c2] S. L. Glashow, Phys. Rev. Letters 14, 35 (1965)

[c3] R. J. Oakes, Phys. Rev. Letters 20, 1539 (1968) ibid.21, 589(E) (1968) T. Das, ibid. 21, 409 (1968) F. Zachariasen and G. Zwieg, Phys. Rev. 182, 1446 (1969)

[c4] C. H. Albright, Phys. Rev. 187, 1881 (1969)

[c5] H. Sugawara, Phys. Rev. Letters 15, 870 (1965) M. Suzuki, ibid. 15, 986 (1965)

[c6] 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. P. Saxena, Phys. Rev. Letters 17, 268 (1966) Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967) W. A. Simmons, Phys. Rev. 164, 1956 (1967)

[c7] C. W. Kim and H. Primakoff, Phys. Rev. 180, 1502 (1969)

[c8] J. C. Pati, Phys. Rev. Letters 20, 812 (1968)

[c9] V. W. Cohen, R. Nathans, H. B. Silsbee, E. Lipworth, and N. F. Ramsey, Phys. Rev. 177, 1942 (1969)

[c10] L. R. Ram Mohan, Phys. Rev. D 1, 266 (1970)

[c11] [10] [6] Y. T. Chiu, J. Schechter, and Y. Ueda, Nuovo Cimento 47A, 214 (1967) [6]

[c12] E. Fischbach, Phys. Rev. 170, 1398 (1968)

[c13] H. Filthuth, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished)

[c14] R. J. Blin-Stoyle, in Proceedings of the Topical Conference on Weak Interactions, CERN, Geneva, 1969 (unpublished) E. M. Henley, Ann. Rev. Nucl. Sci. 19, 367 (1969)

[c15] B. H. J. McKellar, Phys. Letters 26B, 107 (1967)

[c16] G. Barton, Nuovo Cimento 19, 512 (1961)

[c17] B. R. Holstein, Phys. Rev. 171, 1668 (1968)

[c18] Z. Szymanski, Nucl. Phys. A113, 385 (1968)

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Sum Rules for $CP$ -Nonconserving $BB π$ Amplitudes in Glashow's Model

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Sum Rules for CP-Nonconserving BBπ Amplitudes in Glashow's Model

Abstract

References (18)

Sum Rules for $CP$ -Nonconserving $BB π$ Amplitudes in Glashow's Model