Once-Subtracted Dispersion Relations, Current Algebra, and Nonleptonic Weak Decays of Hyperons

K. J. Sebastian

doi:10.1103/PhysRevD.4.771

Access by Xinjiang University

Once-Subtracted Dispersion Relations, Current Algebra, and Nonleptonic Weak Decays of Hyperons

K. J. Sebastian

Lowell Technological Institute, Lowell, Massachusetts, 01854

PDF

Phys. Rev. D 4, 771 – Published 1 August, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.771

Abstract

Nonleptonic weak decays of hyperons and the $K_{1} \to 2 π$ decay are carefully analyzed using current algebra, partial conservation of axial-vector current, and once-subtracted dispersion relations, a method suggested by Okubo, Mathur, and Marshak. We have calculated the dispersion integral by assuming it to be saturated by the low-mass intermediate states of the nucleon octet, of the ${\frac{3}{2}}^{+}$ decuplet of $Δ (1236)$ , and of the $½^{-}$ ${SU}_{3}$ singlet $Y_{0}^{*} (1405)$ , in the case of hyperon decays, and by the intermediate states of vector mesons and a possible $0^{+}$ scalar-meson nonet, in the case of $K_{1} \to 2 π$ decay. The matrix element of the parity-violating weak Hamiltonian density between two baryons (which is required to evaluate the hyperon decay amplitudes) is related to the $K_{1} \to 2 π$ decay amplitude by the $K_{1}$ tadpole mechanism. With pseudovector ${SU}_{3}$ -symmetric coupling among the nucleon and pseudoscalar-meson octets, we are able to obtain a good fitting of all the hyperon decay amplitudes in terms of four parameters. We also find that the corrections to the soft-pion values are very important not only for $P$ -wave hyperon decay amplitudes, but also for $S$ -wave amplitudes. They are also extremely important for $K_{1} \to 2 π$ decays. Furthermore, we find that, contrary to the findings of Hara and Nambu, there is no evidence for the concept of a "universal parityconserving spurion" in hyperon and $K_{1} \to 2 π$ weak decays.

References (42)

H. Sugawara, Phys. Rev. Letters 15, 870 (1965) ibid.15, 997 (1965)
M. Suzuki, Phys. Rev. Letters 15, 986 (1965)
Y. Hara, Y. Nambu, and J. Schechter, Phys. Rev. Letters 16, 380 (1966)
S. Badier and C. Bouchiat, Phys. Rev. Letters 20, 529 (1966)
L. S. Brown and C. M. Sommerfield, Phys. Rev. Letters 16, 751 (1966)
A. Kumar and J. C. Pati, Phys. Rev. Letters 18, 1230 (1967)
Y. T. Chiu and J. Schechter, Phys. Rev. Letters 16, 1022 (1966)
S. Biswas, A. Kumar, and R. Saxena, Phys. Rev. Letters 17, 268 (1966)
Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967)
([6])
M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964)
[J. C. Pati and C. H. Woo, Phys. Rev. D 3, 2920 (1971).] [7–9]
M. Gell-Mann, Phys. Rev. Letters 12, 155 (1964)
J. C. Pati and S. Oneda, Phys. Rev. 140, B1351 (1965) D. Loebbaka, S. Oneda, and J. C. Pati, ibid. 144, 1280 (1966) D. Loebbaka and J. C. Pati, ibid. 147, 1046 (1966) [6]
[6,14] [6,14]
S. Matsuda and S. Oneda, Phys. Rev. 185, 1887 (1969) G. Fourez, ibid. 178, 2454 (1969)
J. Shimada and S. Bludman, Phys. Rev. D 1, 2687 (1970)
S. Okubo, Ann. Phys. (N. Y.) 47, 351 (1968)
S. Matsuda, S. Oneda, and P. S. Desai, Phys. Rev. 178, 2129 (1969) [16], Sec. VI
Y. Hara and Y. Nambu, Phys. Rev. Letters 16, 875 (1966)
S. Gasiorowicz, Elementary Particle Physics (Wiley, New York, 1966), pp. 280-281
P. Carruthers, Introduction to Unitary Symmetry (Wiley-Interscience, New York, 1966)
Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)
K. J. Braun, D. Cline, and V. Scherer, Phys. Rev. Letters 21, 1275 (1968)
B. Dutta-Roy and I. R. Lapidus, Phys. Rev. 169, 1357 (1968)
B. Dutta-Roy and A. Martin, Phys. Rev. 176, 1979 (1969)
T. G. Trippe et al., Phys. Letters 28B, 203 (1968)
J. C. Pati and K. J. Sebastian, Phys. Rev. 174, 2033 (1968)
S. P. de Alwis and D. A. Nutbrown, Nuovo Cimento 58A, 876 (1968)
Omitted endnote
([26])
S. Okubo, R. E. Marshak, and V. S. Mathur, Phys. Rev. Letters 19, 407 (1967)
[32]
Omitted endnote
M. L. Goldberger and S. B. Treiman, Phys. Rev. 110, 1178 (1958)
N. Cabibbo, Rapporteur's talk, in Proceedings of the Thirteenth International Conference on High Energy Physics, Berkeley, 1966 (University of California Press, Berkeley, 1967) H. Filthuth, in Topical Conference on Weak Interactions, CERN Geneva, 1969 (CERN, Geneva, Switzerland, 1969)
S. Matsuda and S. Oneda, Phys. Rev. 158, 1594 (1964)
G. Fourez, Nucl. Phys. B18, 189 (1970)
D. A. Nutbrown, Nuovo Cimento 56A, 479 (1968)
S. Coleman and S. L. Glashow, Phys. Rev. 134, B671 (1964)
S. L. Adler and R. F. Dashen, Current Algebras and Applications to Particle Physics (W. A. Benjamin, New York, 1968), p. 133 [40]
Omitted endnote

[c1] H. Sugawara, Phys. Rev. Letters 15, 870 (1965) ibid.15, 997 (1965)

[c2] M. Suzuki, Phys. Rev. Letters 15, 986 (1965)

[c3] Y. Hara, Y. Nambu, and J. Schechter, Phys. Rev. Letters 16, 380 (1966)

[c4] S. Badier and C. Bouchiat, Phys. Rev. Letters 20, 529 (1966)

[c5] L. S. Brown and C. M. Sommerfield, Phys. Rev. Letters 16, 751 (1966)

[c6] A. Kumar and J. C. Pati, Phys. Rev. Letters 18, 1230 (1967)

[c7] Y. T. Chiu and J. Schechter, Phys. Rev. Letters 16, 1022 (1966)

[c8] S. Biswas, A. Kumar, and R. Saxena, Phys. Rev. Letters 17, 268 (1966)

[c9] Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967)

[c10] ([6])

[c11] M. Gell-Mann and Y. Ne'eman, The Eightfold Way (Benjamin, New York, 1964)

[c12] [J. C. Pati and C. H. Woo, Phys. Rev. D 3, 2920 (1971).] [7–9]

[c13] M. Gell-Mann, Phys. Rev. Letters 12, 155 (1964)

[c14] J. C. Pati and S. Oneda, Phys. Rev. 140, B1351 (1965) D. Loebbaka, S. Oneda, and J. C. Pati, ibid. 144, 1280 (1966) D. Loebbaka and J. C. Pati, ibid. 147, 1046 (1966) [6]

[c15] [6,14] [6,14]

[c16] S. Matsuda and S. Oneda, Phys. Rev. 185, 1887 (1969) G. Fourez, ibid. 178, 2454 (1969)

[c17] J. Shimada and S. Bludman, Phys. Rev. D 1, 2687 (1970)

[c18] S. Okubo, Ann. Phys. (N. Y.) 47, 351 (1968)

[c19] S. Matsuda, S. Oneda, and P. S. Desai, Phys. Rev. 178, 2129 (1969) [16], Sec. VI

[c20] Y. Hara and Y. Nambu, Phys. Rev. Letters 16, 875 (1966)

[c21] S. Gasiorowicz, Elementary Particle Physics (Wiley, New York, 1966), pp. 280-281

[c22] P. Carruthers, Introduction to Unitary Symmetry (Wiley-Interscience, New York, 1966)

[c23] Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)

[c24] K. J. Braun, D. Cline, and V. Scherer, Phys. Rev. Letters 21, 1275 (1968)

[c25] B. Dutta-Roy and I. R. Lapidus, Phys. Rev. 169, 1357 (1968)

[c26] B. Dutta-Roy and A. Martin, Phys. Rev. 176, 1979 (1969)

[c27] T. G. Trippe et al., Phys. Letters 28B, 203 (1968)

[c28] J. C. Pati and K. J. Sebastian, Phys. Rev. 174, 2033 (1968)

[c29] S. P. de Alwis and D. A. Nutbrown, Nuovo Cimento 58A, 876 (1968)

[c30] Omitted endnote

[c31] ([26])

[c32] S. Okubo, R. E. Marshak, and V. S. Mathur, Phys. Rev. Letters 19, 407 (1967)

[c33] [32]

[c34] Omitted endnote

[c35] M. L. Goldberger and S. B. Treiman, Phys. Rev. 110, 1178 (1958)

[c36] N. Cabibbo, Rapporteur's talk, in Proceedings of the Thirteenth International Conference on High Energy Physics, Berkeley, 1966 (University of California Press, Berkeley, 1967) H. Filthuth, in Topical Conference on Weak Interactions, CERN Geneva, 1969 (CERN, Geneva, Switzerland, 1969)

[c37] S. Matsuda and S. Oneda, Phys. Rev. 158, 1594 (1964)

[c38] G. Fourez, Nucl. Phys. B18, 189 (1970)

[c39] D. A. Nutbrown, Nuovo Cimento 56A, 479 (1968)

[c40] S. Coleman and S. L. Glashow, Phys. Rev. 134, B671 (1964)

[c41] S. L. Adler and R. F. Dashen, Current Algebras and Applications to Particle Physics (W. A. Benjamin, New York, 1968), p. 133 [40]

[c42] Omitted endnote

Physical Review D

Export citation

Export citation

Once-Subtracted Dispersion Relations, Current Algebra, and Nonleptonic Weak Decays of Hyperons

Abstract

References (42)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation