Behavior of Space Components of Currents Under <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo><mn></mn><mo>⊗</mo><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo><mn></mn></math></span> Transformations

J. Katz; L. R. Ram Mohan

doi:10.1103/PhysRevD.4.415

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Behavior of Space Components of Currents Under $SU (3) \otimes SU (3)$ Transformations

J. Katz and L. R. Ram Mohan

Department of Physics, Purdue University, Lafayette, Indiana 47907

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Phys. Rev. D 4, 415 – Published 15 July, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.415

Abstract

We suggest that the equal-time commutators between the axial charges and the space components of the currents should be modified. We then present a model which provides a natural explanation for the value $ξ = - 1$ for the ratio of form factors in $K_{l 3}$ decays and, in addition, leads to the usual good results of current algebra.

References (26)

S. L. Adler and R. F. Dashen, Current Algebra and Applications to Particle Physics (Benjamin, New York, 1968)
J. Katz and M. Sugawara (unpublished)
J. Katz (unpublished)
J. S. Bell and R. Jackiw, Nuovo Cimento 60, 47 (1969) S. Adler, Phys. Rev. 177, 2426 (1969) K. Wilson, ibid. 179, 1499 (1969)
T. K. Kuo and M. Sugawara, Phys. Rev. 163, 1716 (1967) D. J. Gross and R. Jackiw, 166, 1287 (1968) Nucl. Phys. B14, 269 (1969)
H. Genz and J. Katz, Phys. Rev. D 2, 2225 (1970)
J. Katz (unpublished)
M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968)
J. J. J. Kokkedee, The Quark Model (Benjamin, New York, 1969)
B. W. Lee, Phys. Rev. Letters 14, 676 (1965)
S. Weinberg, Phys. Rev. Letters 17, 336 (1966)
R. E. Marshak, Riazuddin, and C. P. Ryan, Theory of Weak Interactions in Particle Physics (Wiley-Interscience, New York, 1969), Chap. 5, p. 496
R. P. Ely et al., Phys. Rev. 180, 1319 (1969)
C. G. Callan and S. B. Treiman, Phys. Rev. Letters 16, 153 (1966) V. S. Mathur, S. Okubo, and L. K. Pandit, ibid. 16, 371 (1966)
H. Sugawara, Phys. Rev. Letters 15, 870 (1965) M. Suzuki, ibid. 15, 968 (1965)
S. P. Rosen, Phys. Rev. 137, B431 (1965)
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. Bouchiat, Phys. Letters 20, 529 (1966)
B. W. Lee, Phys. Rev. Letters 12, 83 (1964) H. Sugawara, Progr. Theoret. Phys. (Kyoto) 31, 213 (1964)
Y. T. Chiu and J. Schechter, Phys. Rev. Letters 16, 1022 (1966) Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 150, 2101 (1966) S. Biswas, Aditya Kumar, and R. P. Saxena, Phys. Rev. Letters 17, 268 (1966) Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967) L. R. Ram Mohan, Phys. Rev. D 1, 266 (1970)
W. A. Simmons, Phys. Rev. 164, 1956 (1967) D. S. Carlstone, S. P. Rosen and S. Pakvasa, 174, 1877 (1968) L. R. Ram Mohan, Phys. Rev. D 2, 2101 (1970)
Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 157, 1317 (1967)
Y. Hara and Y. Nambu, Phys. Rev. Letters 16, 875 (1966) D. K. Elias and J. C. Taylor, Nuovo Cimento 44A, 518 (1966) S. K. Bose and S. N. Biswas, Phys. Rev. Letters 16, 330 (1966) H. D. I. Abarbanel, Phys. Rev. 153, 1547 (1967)
S. Weinberg, Phys. Rev. Letters 4, 87 (1960) ibid.4, 585 (1960) G. Barton, C. Kacser, and S. P. Rosen, Phys. Rev. 130, 783 (1963)
B. H. Kellet, Nucl. Phys. B26, 237 (1971)
N. Kroll and M. A. Ruderman, Phys. Rev. 93, 233 (1954)
S. Okubo, Nuovo Cimento 41A, 586 (1966)

[c1] S. L. Adler and R. F. Dashen, Current Algebra and Applications to Particle Physics (Benjamin, New York, 1968)

[c2] J. Katz and M. Sugawara (unpublished)

[c3] J. Katz (unpublished)

[c4] J. S. Bell and R. Jackiw, Nuovo Cimento 60, 47 (1969) S. Adler, Phys. Rev. 177, 2426 (1969) K. Wilson, ibid. 179, 1499 (1969)

[c5] T. K. Kuo and M. Sugawara, Phys. Rev. 163, 1716 (1967) D. J. Gross and R. Jackiw, 166, 1287 (1968) Nucl. Phys. B14, 269 (1969)

[c6] H. Genz and J. Katz, Phys. Rev. D 2, 2225 (1970)

[c7] J. Katz (unpublished)

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

[c9] J. J. J. Kokkedee, The Quark Model (Benjamin, New York, 1969)

[c10] B. W. Lee, Phys. Rev. Letters 14, 676 (1965)

[c11] S. Weinberg, Phys. Rev. Letters 17, 336 (1966)

[c12] R. E. Marshak, Riazuddin, and C. P. Ryan, Theory of Weak Interactions in Particle Physics (Wiley-Interscience, New York, 1969), Chap. 5, p. 496

[c13] R. P. Ely et al., Phys. Rev. 180, 1319 (1969)

[c14] C. G. Callan and S. B. Treiman, Phys. Rev. Letters 16, 153 (1966) V. S. Mathur, S. Okubo, and L. K. Pandit, ibid. 16, 371 (1966)

[c15] H. Sugawara, Phys. Rev. Letters 15, 870 (1965) M. Suzuki, ibid. 15, 968 (1965)

[c16] S. P. Rosen, Phys. Rev. 137, B431 (1965)

[c17] 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. Bouchiat, Phys. Letters 20, 529 (1966)

[c18] B. W. Lee, Phys. Rev. Letters 12, 83 (1964) H. Sugawara, Progr. Theoret. Phys. (Kyoto) 31, 213 (1964)

[c19] Y. T. Chiu and J. Schechter, Phys. Rev. Letters 16, 1022 (1966) Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 150, 2101 (1966) S. Biswas, Aditya Kumar, and R. P. Saxena, Phys. Rev. Letters 17, 268 (1966) Y. Hara, Progr. Theoret. Phys. (Kyoto) 37, 710 (1967) L. R. Ram Mohan, Phys. Rev. D 1, 266 (1970)

[c20] W. A. Simmons, Phys. Rev. 164, 1956 (1967) D. S. Carlstone, S. P. Rosen and S. Pakvasa, 174, 1877 (1968) L. R. Ram Mohan, Phys. Rev. D 2, 2101 (1970)

[c21] Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 157, 1317 (1967)

[c22] Y. Hara and Y. Nambu, Phys. Rev. Letters 16, 875 (1966) D. K. Elias and J. C. Taylor, Nuovo Cimento 44A, 518 (1966) S. K. Bose and S. N. Biswas, Phys. Rev. Letters 16, 330 (1966) H. D. I. Abarbanel, Phys. Rev. 153, 1547 (1967)

[c23] S. Weinberg, Phys. Rev. Letters 4, 87 (1960) ibid.4, 585 (1960) G. Barton, C. Kacser, and S. P. Rosen, Phys. Rev. 130, 783 (1963)

[c24] B. H. Kellet, Nucl. Phys. B26, 237 (1971)

[c25] N. Kroll and M. A. Ruderman, Phys. Rev. 93, 233 (1954)

[c26] S. Okubo, Nuovo Cimento 41A, 586 (1966)

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Behavior of Space Components of Currents Under $SU (3) \otimes SU (3)$ Transformations

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Behavior of Space Components of Currents Under SU(3)⊗SU(3) Transformations

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References (26)

Behavior of Space Components of Currents Under $SU (3) \otimes SU (3)$ Transformations