Veneziano Amplitudes for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>KK</mi></math> Scattering and Chiral Symmetry Breaking

Douglas W. McKay; William F. Palmer; Walter W. Wada

doi:10.1103/PhysRevD.2.742

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Veneziano Amplitudes for $π π$ , $π K$ , and $KK$ Scattering and Chiral Symmetry Breaking

Douglas W. McKay, William F. Palmer, and Walter W. Wada

The Ohio State University, Columbus, Ohio 43210

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Phys. Rev. D 2, 742 – Published 15 August, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.742

Abstract

$π π$ , $π K$ , and $KK$ single- and multiple-term Veneziano amplitudes are studied as a coupled system. Adler and Adler-Weisberger conditions are imposed, and it is found that the single-term system cannot satisfy all of the PCAC (partial conservation of axial-vector current) and charge-algebra constraints. The multiple-term system, constructed to satisfy these constraints, results in much improved width predictions. These improved amplitudes are used to study chiral symmetry breaking by investigating the $Σ$ terms. It is found that a single $(3, 3^{*}) \oplus (3^{*}, 3)$ representation is not sufficient to explain the symmetry breaking, whereas a mixture of $(3, 3^{*}) \oplus (3^{*}, 3)$ and $(1, 8) \oplus (8, 1)$ is sufficient (but not necessary). The admixture of $(1, 8) \oplus (8, 1)$ is considerable.

References (28)

G. Veneziano, Nuovo Cimento 57A, 190 (1968)
M. Jacob, in Proceedings of the Lund Conference, 1969 (unpublished) C. Lovelace, in Proceedings of the Irvine Conference on Regge Poles, 1969 (unpublished)
C. Lovelace, Phys. Letters 28B, 265 (1968)
Dennis Corrigan, Phys. Rev. 188, 2465 (1969) Kashyap Vasavada, Phys. Rev. D 1, 88 (1970) Kyungsik Kang, Brown University report (unpublished) N. G. Antoniou, A. Bartl, and F. Widder, Tubingen University report (unpublished)
K. Kawarabayashi, S. Kitakado, and H. Yabuki, Phys. Letters 28B, 432 (1969)
O. W. Greenberg, in Proceedings of the Lund Conference, 1969 (unpublished)
H. Harari, Phys. Rev. Letters 22, 562 (1969) J. L. Rosner, ibid. 22, 689 (1969)
J. A. Cronin and K. Kang, Phys. Rev. Letters 23, 1004 (1969) Hugh Osborn, Nucl. Phys. B17, 141 (1970) Riazuddin and Fayyazuddin, Phys. Rev. D 1, 282 (1970)
S. L. Adler, Phys. Rev. 139, B1638 (1965)
S. L. Adler, Phys. Rev. Letters 14, 1051 (1965) W. I. Weisberger, ibid. 14, 1047 (1965) S. L. Adler, Phys. Rev. 140, B763 (1965) W. I. Weisberger, ibid. 143, 1302 (1966)
([8])
M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968)
D. W. McKay and W. W. Wada, Phys. Rev. Letters 23, 619 (1969)
Omitted endnote
Y. Oyanagi and N. Tokuda, Progr. Theoret. Phys. (Kyoto) 42, 430 (1969) [8]
N. Brene, M. Roos. and A. Sirlin, Nucl. Phys. B6, 255 (1968)
[4]
Omitted endnote
Omitted endnote
K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)
Omitted endnote
S. L. Adler, Phys. Rev. 140, B736 (1965) ibid.143, 1144 (1966) W. I. Weisberger, ibid. 143, 1302 (1966) K. Kawarabayashi and W. W. Wada, ibid. 146, 1209 (1966)
P. R. Auvil and N. G. Deshpande, Phys. Rev. 183, 1463 (1969)
B. Renner and A. Sudberry, Nucl. Phys. B13, 27 (1960) N. H. Fuchs and T. K. Kuo, Nuovo Cimento 64A, 382 (1969) Y. Y. Lee, ibid. 64A, 474 (1969)
[8]
([8]) F. Csikor [Phys. Letters 31B, 141 (1970)] ([8]) H. Suura [Phys. Rev. Letters 23, 551 (1969)] [10]
Steven Weinberg, Phys. Rev. Letters 17, 616 (1966)
[8] F. Hussain and M. S. K. Razmi, University of Islamabad report (unpublished)

[c1] G. Veneziano, Nuovo Cimento 57A, 190 (1968)

[c2] M. Jacob, in Proceedings of the Lund Conference, 1969 (unpublished) C. Lovelace, in Proceedings of the Irvine Conference on Regge Poles, 1969 (unpublished)

[c3] C. Lovelace, Phys. Letters 28B, 265 (1968)

[c4] Dennis Corrigan, Phys. Rev. 188, 2465 (1969) Kashyap Vasavada, Phys. Rev. D 1, 88 (1970) Kyungsik Kang, Brown University report (unpublished) N. G. Antoniou, A. Bartl, and F. Widder, Tubingen University report (unpublished)

[c5] K. Kawarabayashi, S. Kitakado, and H. Yabuki, Phys. Letters 28B, 432 (1969)

[c6] O. W. Greenberg, in Proceedings of the Lund Conference, 1969 (unpublished)

[c7] H. Harari, Phys. Rev. Letters 22, 562 (1969) J. L. Rosner, ibid. 22, 689 (1969)

[c8] J. A. Cronin and K. Kang, Phys. Rev. Letters 23, 1004 (1969) Hugh Osborn, Nucl. Phys. B17, 141 (1970) Riazuddin and Fayyazuddin, Phys. Rev. D 1, 282 (1970)

[c9] S. L. Adler, Phys. Rev. 139, B1638 (1965)

[c10] S. L. Adler, Phys. Rev. Letters 14, 1051 (1965) W. I. Weisberger, ibid. 14, 1047 (1965) S. L. Adler, Phys. Rev. 140, B763 (1965) W. I. Weisberger, ibid. 143, 1302 (1966)

[c11] ([8])

[c12] M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968)

[c13] D. W. McKay and W. W. Wada, Phys. Rev. Letters 23, 619 (1969)

[c14] Omitted endnote

[c15] Y. Oyanagi and N. Tokuda, Progr. Theoret. Phys. (Kyoto) 42, 430 (1969) [8]

[c16] N. Brene, M. Roos. and A. Sirlin, Nucl. Phys. B6, 255 (1968)

[c17] [4]

[c18] Omitted endnote

[c19] Omitted endnote

[c20] K. Kawarabayashi and M. Suzuki, Phys. Rev. Letters 16, 255 (1966) Riazuddin and Fayyazuddin, Phys. Rev. 147, 1071 (1966)

[c21] Omitted endnote

[c22] S. L. Adler, Phys. Rev. 140, B736 (1965) ibid.143, 1144 (1966) W. I. Weisberger, ibid. 143, 1302 (1966) K. Kawarabayashi and W. W. Wada, ibid. 146, 1209 (1966)

[c23] P. R. Auvil and N. G. Deshpande, Phys. Rev. 183, 1463 (1969)

[c24] B. Renner and A. Sudberry, Nucl. Phys. B13, 27 (1960) N. H. Fuchs and T. K. Kuo, Nuovo Cimento 64A, 382 (1969) Y. Y. Lee, ibid. 64A, 474 (1969)

[c25] [8]

[c26] ([8]) F. Csikor [Phys. Letters 31B, 141 (1970)] ([8]) H. Suura [Phys. Rev. Letters 23, 551 (1969)] [10]

[c27] Steven Weinberg, Phys. Rev. Letters 17, 616 (1966)

[c28] [8] F. Hussain and M. S. K. Razmi, University of Islamabad report (unpublished)

Physical Review D

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Veneziano Amplitudes for $π π$ , $π K$ , and $KK$ Scattering and Chiral Symmetry Breaking

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Veneziano Amplitudes for ππ, πK, and KK Scattering and Chiral Symmetry Breaking

Abstract

References (28)

Veneziano Amplitudes for $π π$ , $π K$ , and $KK$ Scattering and Chiral Symmetry Breaking