Nature of <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> Symmetry Breaking—Results from a Systematic Test of the Soft-Meson Theorems

Frank von Hippel; Jae Kwan Kim

doi:10.1103/PhysRevD.1.151

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Nature of $SU (3) \times SU (3)$ Symmetry Breaking—Results from a Systematic Test of the Soft-Meson Theorems

Frank von Hippel^*

Jae Kwan Kim

Department of Physics, Institute of Theoretical Physics, Stanford University, Stanford, California 94305

Department of Physics, Harvard University, Cambridge, Massachusetts 02138

^*Alfred P. Sloan Foundation Fellow. Address 1969-70: Theory Group, Lawrence Radiation Laboratory, University of California, Berkeley, Calif.

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Phys. Rev. D 1, 151 – Published 1 January, 1970Erratum Phys. Rev. D 3, 2923 (1971)

DOI: https://doi.org/10.1103/PhysRevD.1.151

Abstract

We make a systematic test of soft-meson-theorem predictions for both elastic and inelastic pseudoscalar-meson-baryon threshold scattering amplitudes. The predictions are obtained by using an extrapolation procedure developed by Fubini and Furlan and by ourselves. Our results give considerable support to a theory of $SU (3) \times SU (3)$ symmetry breaking proposed recently by Gell-Mann, Oakes, and Renner, and imply that, in the absence of symmetry breaking, the mass of the $J^{p} = {\frac{1}{2}}^{+}$ baryon octet would be approximately that of the physical nucleon.

Erratum

Nature of $SU (3) \times SU (3)$ Symmetry Breaking — Results from a Systematic Test of the Soft-Meson Theorems

Frank von Hippel and Jae Kwan Kim

Phys. Rev. D 3, 2923 (1971)

References (27)

F. von Hippel and J. K. Kim, Phys. Rev. Letters 22, 740 (1969)
F. von Hippel and J. K. Kim, Phys. Rev. Letters 20, 1303 (1968)
S. Fubini and G. Furlan, Ann. Phys. (N. Y.) 48, 322 (1968) A. de Alfaro and C. Rossetti, Nuovo Cimento Suppl. 6, 575 (1968)
A. P. Balachandran, M. Gundzik, and F. Nicodemi, Nuovo Cimento 44A, 1275 (1966) Y. Tomozawa, ibid. 46A, 707 (1967) S. Weinberg, Phys. Rev. Letters 17, 616 (1966)
Omitted endnote
Omitted endnote
T. K. Kuo and M. Sugawara, Phys. Rev. 163, 1716 (1967)
Omitted endnote
Omitted endnote
J. D. Bjorken, Phys. Rev. 148, 1467 (1966)
S. L. Adler, Phys. Rev. Letters 14, 1051 (1965) Phys. Rev. 140, B736 (1965) C. H. Chan and F. T. Meiere, ibid. 175, 2222 (1968)
M. Gell-Mann, Phys. Rev. 125, 1067 (1962)
M. Ademello and R. Gatto, Phys. Rev. Letters 13, 264 (1965)
M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) J. Ellis, Nucl. Phys. B13, 153 (1969)
H. Sugawara, Phys. Rev. Letters 21, 772 (1968)
M. Lévy, Nuovo Cimento 52A, 23 (1967)
Y. Nambu, Phys. Rev. Letters 4, 380 (1960)
V. K. Samaranayake and W. S. Woolcock, Phys. Rev. Letters 15, 936 (1965) S. Goldhaber, W. Chinowsky, G. Goldhaber, T. O'Halloran, T. F. Stubbs, G. M. Pjerrou, D. H. Stork, and H. K. Ticho, 9, 135 (1962) J. K. Kim (unpublished) Phys. Rev. Letters 19, 1074 (1967) [1,2]
J. J. deSwart, Rev. Mod. Phys. 35, 916 (1963)
Omitted endnote
Omitted endnote
([4])
[18] L. D. Roper, R. M. Wright, and B. T. Feld [Phys. Rev. 138, B190 (1965)]
Omitted endnote
S. Weinberg, [4]
M. Gell-Mann (private communication)
R. W. Griffith, thesis, California Institute of Technology (unpublished) C. H. Chan and F. T. Meiere, Phys. Rev. Letters 22, 737 (1969)

[c1] F. von Hippel and J. K. Kim, Phys. Rev. Letters 22, 740 (1969)

[c2] F. von Hippel and J. K. Kim, Phys. Rev. Letters 20, 1303 (1968)

[c3] S. Fubini and G. Furlan, Ann. Phys. (N. Y.) 48, 322 (1968) A. de Alfaro and C. Rossetti, Nuovo Cimento Suppl. 6, 575 (1968)

[c4] A. P. Balachandran, M. Gundzik, and F. Nicodemi, Nuovo Cimento 44A, 1275 (1966) Y. Tomozawa, ibid. 46A, 707 (1967) S. Weinberg, Phys. Rev. Letters 17, 616 (1966)

[c5] Omitted endnote

[c6] Omitted endnote

[c7] T. K. Kuo and M. Sugawara, Phys. Rev. 163, 1716 (1967)

[c8] Omitted endnote

[c9] Omitted endnote

[c10] J. D. Bjorken, Phys. Rev. 148, 1467 (1966)

[c11] S. L. Adler, Phys. Rev. Letters 14, 1051 (1965) Phys. Rev. 140, B736 (1965) C. H. Chan and F. T. Meiere, ibid. 175, 2222 (1968)

[c12] M. Gell-Mann, Phys. Rev. 125, 1067 (1962)

[c13] M. Ademello and R. Gatto, Phys. Rev. Letters 13, 264 (1965)

[c14] M. Gell-Mann, R. J. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) J. Ellis, Nucl. Phys. B13, 153 (1969)

[c15] H. Sugawara, Phys. Rev. Letters 21, 772 (1968)

[c16] M. Lévy, Nuovo Cimento 52A, 23 (1967)

[c17] Y. Nambu, Phys. Rev. Letters 4, 380 (1960)

[c18] V. K. Samaranayake and W. S. Woolcock, Phys. Rev. Letters 15, 936 (1965) S. Goldhaber, W. Chinowsky, G. Goldhaber, T. O'Halloran, T. F. Stubbs, G. M. Pjerrou, D. H. Stork, and H. K. Ticho, 9, 135 (1962) J. K. Kim (unpublished) Phys. Rev. Letters 19, 1074 (1967) [1,2]

[c19] J. J. deSwart, Rev. Mod. Phys. 35, 916 (1963)

[c20] Omitted endnote

[c21] Omitted endnote

[c22] ([4])

[c23] [18] L. D. Roper, R. M. Wright, and B. T. Feld [Phys. Rev. 138, B190 (1965)]

[c24] Omitted endnote

[c25] S. Weinberg, [4]

[c26] M. Gell-Mann (private communication)

[c27] R. W. Griffith, thesis, California Institute of Technology (unpublished) C. H. Chan and F. T. Meiere, Phys. Rev. Letters 22, 737 (1969)

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Nature of $SU (3) \times SU (3)$ Symmetry Breaking—Results from a Systematic Test of the Soft-Meson Theorems

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Nature of $SU (3) \times SU (3)$ Symmetry Breaking — Results from a Systematic Test of the Soft-Meson Theorems

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Nature of SU(3)×SU(3) Symmetry Breaking—Results from a Systematic Test of the Soft-Meson Theorems

Abstract

Erratum

Nature of SU(3)×SU(3) Symmetry Breaking — Results from a Systematic Test of the Soft-Meson Theorems

References (27)

Nature of $SU (3) \times SU (3)$ Symmetry Breaking—Results from a Systematic Test of the Soft-Meson Theorems

Nature of $SU (3) \times SU (3)$ Symmetry Breaking — Results from a Systematic Test of the Soft-Meson Theorems