Neutral-Pion Decay and the Weak-Coupling Limit

Michael D. Scadron

doi:10.1103/PhysRevD.2.213

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Neutral-Pion Decay and the Weak-Coupling Limit

Michael D. Scadron

Physics Department, Northwestern University, Evanston, Illinois 60201

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Phys. Rev. D 2, 213 – Published 1 July, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.213

Abstract

An exact version of Pagels's sum rule for neutral-pion decay is derived for massless pions. It is inconsistent, however, in the weak-coupling limit. If we modify this limit by including the $σ$ meson, then the sum rule is consistent and also yields the physically reasonable relation $κ_{p} = - κ_{n}$ .

References (26)

J. Bell and R. Jackiw, Nuovo Cimento 60A, 47 (1969)
S. L. Adler, Phys. Rev. 177, 2426 (1969)
J. Steinberger, Phys. Rev. 76, 180 (1949)
M. L. Goldberger and S. B. Treiman, Nuovo Cimento 9, 451 (1958)
H. Pagels, Phys. Rev. 158, 1566 (1967)
H. D. I. Abarbanel and M. L. Goldberger, Phys. Rev. 165, 1594 (1968) S. R. Choudhury and R. Rajaraman, ibid. 169, 1218 (1968)
G. C. Fox and D. Z. Freedman, Phys. Rev. 182, 1628 (1969)
Y. Nambu, Phys. Rev. Letters 4, 380 (1960) S. Weinberg, ibid. 16, 879 (1966) S. Mandelstam, Phys. Rev. 168, 1884 (1968) J. D. Bjorken and M. Nauenberg, Ann. Rev. Nucl. Sci. 18, 229 (1968)
H. F. Jones and M. D. Scadron, Nucl. Phys. B10, 17 (1969) Imperial College Report No. ICTP/67/26, 1968 (unpublished)
Omitted endnote
A. Hearn and E. Leader, Phys. Rev. 126, 789 (1962)
Omitted endnote
D. Z. Freedman, Phys. Rev. 168, 1822 (1968) S. R. Choudhury and D. Z. Freedman, ibid. 168, 1739 (1968)
S. D. Drell and A. C. Hearn, Phys. Rev. Letters 16, 908 (1966)
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L. M. Brown (private communication)
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Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)
S. Okubo, Phys. Rev. 179, 1629 (1969)
F. J. Gilman, Phys. Rev. 184, 1964 (1969)
K. Yamamoto, Phys. Rev. 169, 1353 (1968)
W. A. Bardeen and W. K. Tung, Phys. Rev. 173, 1423 (1968)
F. D. Gault and M. D. Scadron, Imperial College Report No. ICTP/67/33, 1968 (unpublished)

[c1] J. Bell and R. Jackiw, Nuovo Cimento 60A, 47 (1969)

[c2] S. L. Adler, Phys. Rev. 177, 2426 (1969)

[c3] J. Steinberger, Phys. Rev. 76, 180 (1949)

[c4] M. L. Goldberger and S. B. Treiman, Nuovo Cimento 9, 451 (1958)

[c5] H. Pagels, Phys. Rev. 158, 1566 (1967)

[c6] H. D. I. Abarbanel and M. L. Goldberger, Phys. Rev. 165, 1594 (1968) S. R. Choudhury and R. Rajaraman, ibid. 169, 1218 (1968)

[c7] G. C. Fox and D. Z. Freedman, Phys. Rev. 182, 1628 (1969)

[c8] Y. Nambu, Phys. Rev. Letters 4, 380 (1960) S. Weinberg, ibid. 16, 879 (1966) S. Mandelstam, Phys. Rev. 168, 1884 (1968) J. D. Bjorken and M. Nauenberg, Ann. Rev. Nucl. Sci. 18, 229 (1968)

[c9] H. F. Jones and M. D. Scadron, Nucl. Phys. B10, 17 (1969) Imperial College Report No. ICTP/67/26, 1968 (unpublished)

[c10] Omitted endnote

[c11] A. Hearn and E. Leader, Phys. Rev. 126, 789 (1962)

[c12] Omitted endnote

[c13] D. Z. Freedman, Phys. Rev. 168, 1822 (1968) S. R. Choudhury and D. Z. Freedman, ibid. 168, 1739 (1968)

[c14] S. D. Drell and A. C. Hearn, Phys. Rev. Letters 16, 908 (1966)

[c15] B. Fried, Phys. Rev. 88, 1142 (1952) H. A. Bethe, S. Schweber, and F. DeHoffman, Mesons and Fields (Row and Peterson, Evanston, Ill., 1956), Vol. II, p. 292

[c16] S. L. Adler and Y. Dothan, Phys. Rev. 151, 1267 (1966)

[c17] M. Gell-Mann and M. Lévy, Nuovo Cimento 16, 705 (1960)

[c18] L. M. Brown (private communication)

[c19] S. Gasiorowicz and D. A. Geffen, Rev. Mod. Phys. 41, 531 (1969)

[c20] M. A. B. Bég, Phys. Rev. Letters 17, 333 (1966)

[c21] Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)

[c22] S. Okubo, Phys. Rev. 179, 1629 (1969)

[c23] F. J. Gilman, Phys. Rev. 184, 1964 (1969)

[c24] K. Yamamoto, Phys. Rev. 169, 1353 (1968)

[c25] W. A. Bardeen and W. K. Tung, Phys. Rev. 173, 1423 (1968)

[c26] F. D. Gault and M. D. Scadron, Imperial College Report No. ICTP/67/33, 1968 (unpublished)

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Neutral-Pion Decay and the Weak-Coupling Limit

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