<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Δ</mi><mi>I</mi><mo>=</mo><mn>1</mn><mn></mn></math></span> Mass Differences and <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi><mo>→</mo><mn>3</mn><mi>π</mi></math></span> Decay

J. Schechter; Y. Ueda

doi:10.1103/PhysRevD.4.733

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$Δ I = 1$ Mass Differences and $η \to 3 π$ Decay

J. Schechter and Y. Ueda

Physics Department, Syracuse University, Syracuse, New York 13210

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Phys. Rev. D 4, 733 – Published 1 August, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.733

Abstract

The octet baryon $Δ I = 1$ mass shifts, kaon electromagnetic mass shift, and $η \to 3 π$ decay amplitude are all correlated in the framework of the linear $SU (3)$ $σ$ model. It is shown how this model provides a natural realization of the "tadpole" idea of Coleman and Glashow. An attempt is made to resolve the long-standing mystery associated with the $η \to 3 π$ process, and the rare mode $η^{'} \to 3 π$ is also calculated. Finally, it is shown that the chiral-symmetry-breaking and isospin-nonconserving coefficients in the Lagrangian have the same order of magnitude.

References (24)

J. Schechter and Y. Ueda, Phys. Rev. D 3, 168 (1971)
J. Schechter and Y. Ueda, Phys. Rev. D 3, 176 (1971)
J. Schechter and Y. Ueda, Phys. Rev. D 3, 2874 (1971)
M. Gell-Mann, R. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) S. Glashow and S. Weinberg, Phys. Rev. Letters 20, 224 (1968) R. Dashen, Phys. Rev. 183, 1245 (1969)
Y. Nambu and G. Jona Lasinio, Phys. Rev. 122, 345 (1961) ibid.124, 246 (1961)
Haim Harari, Phys. Rev. Letters 17, 1303 (1966) S. Okubo, ibid. 18, 256 (1967)
Riazuddin, Phys. Rev. 114, 1184 (1959) V. Barger and E. Kazes, Nuovo Cimento 28, 385 (1963) T. Das, G. S. Guralnik, V. S. Mathur, F. E. Low, and J. E. Young, Phys. Rev. Letters 18, 759 (1967)
S. Coleman and S. Glashow, Phys. Rev. 134, B671 (1964)
W. A. Bardeen and B. W. Lee, Phys. Rev. 177, 2389 (1969) S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)
N. Cabibbo and L. Maiani, Phys. Rev. D 1, 707 (1970)
R. Gatto, G. Sartori, and M. Tonin, Phys. Letters 28B, 128 (1968)
R. J. Oakes, Phys. Letters 29B, 683 (1969)
R. H. Socolow, Phys. Rev. 137, B1221 (1965) J. H. Wojtaszek, R. E. Marshak, and Riazuddin, ibid. 136, B1053 (1964)
Omitted endnote
Omitted endnote
Particle Data Group, Rev. Mod. Phys. 42, 87 (1970)
D. G. Sutherland, Phys. Letters 23, 384 (1966)
Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 161, 1612 (1967)
S. Bose and A. Zimmerman, Nuovo Cimento 47, 669 (1967) D. G. Sutherland, Nucl. Phys. B2, 433 (1967) H. Osborn and D. J. Wallace, B20, 23 (1970)
S. K. Yun, Phys. Rev. 173, 1764 (1968) L. Clavelli, Nuovo Cimento 52A, 73 (1967)
[Columbia-Berkeley-Purdue-Wisconsin-Yale collaboration, Phys. Rev. 149, 1049 (1966)]
S. Weinberg, Phys. Rev. Letters 18, 188 (1967) [9]
Omitted endnote
Omitted endnote

[c1] J. Schechter and Y. Ueda, Phys. Rev. D 3, 168 (1971)

[c2] J. Schechter and Y. Ueda, Phys. Rev. D 3, 176 (1971)

[c3] J. Schechter and Y. Ueda, Phys. Rev. D 3, 2874 (1971)

[c4] M. Gell-Mann, R. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968) S. Glashow and S. Weinberg, Phys. Rev. Letters 20, 224 (1968) R. Dashen, Phys. Rev. 183, 1245 (1969)

[c5] Y. Nambu and G. Jona Lasinio, Phys. Rev. 122, 345 (1961) ibid.124, 246 (1961)

[c6] Haim Harari, Phys. Rev. Letters 17, 1303 (1966) S. Okubo, ibid. 18, 256 (1967)

[c7] Riazuddin, Phys. Rev. 114, 1184 (1959) V. Barger and E. Kazes, Nuovo Cimento 28, 385 (1963) T. Das, G. S. Guralnik, V. S. Mathur, F. E. Low, and J. E. Young, Phys. Rev. Letters 18, 759 (1967)

[c8] S. Coleman and S. Glashow, Phys. Rev. 134, B671 (1964)

[c9] W. A. Bardeen and B. W. Lee, Phys. Rev. 177, 2389 (1969) S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)

[c10] N. Cabibbo and L. Maiani, Phys. Rev. D 1, 707 (1970)

[c11] R. Gatto, G. Sartori, and M. Tonin, Phys. Letters 28B, 128 (1968)

[c12] R. J. Oakes, Phys. Letters 29B, 683 (1969)

[c13] R. H. Socolow, Phys. Rev. 137, B1221 (1965) J. H. Wojtaszek, R. E. Marshak, and Riazuddin, ibid. 136, B1053 (1964)

[c14] Omitted endnote

[c15] Omitted endnote

[c16] Particle Data Group, Rev. Mod. Phys. 42, 87 (1970)

[c17] D. G. Sutherland, Phys. Letters 23, 384 (1966)

[c18] Y. T. Chiu, J. Schechter, and Y. Ueda, Phys. Rev. 161, 1612 (1967)

[c19] S. Bose and A. Zimmerman, Nuovo Cimento 47, 669 (1967) D. G. Sutherland, Nucl. Phys. B2, 433 (1967) H. Osborn and D. J. Wallace, B20, 23 (1970)

[c20] S. K. Yun, Phys. Rev. 173, 1764 (1968) L. Clavelli, Nuovo Cimento 52A, 73 (1967)

[c21] [Columbia-Berkeley-Purdue-Wisconsin-Yale collaboration, Phys. Rev. 149, 1049 (1966)]

[c22] S. Weinberg, Phys. Rev. Letters 18, 188 (1967) [9]

[c23] Omitted endnote

[c24] Omitted endnote

Physical Review D

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$Δ I = 1$ Mass Differences and $η \to 3 π$ Decay

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ΔI=1 Mass Differences and η→3π Decay

Abstract

References (24)

$Δ I = 1$ Mass Differences and $η \to 3 π$ Decay