Zero-Mass Divergences in Expansions about Chiral and Scale Symmetry

Douglas W. McKay; William F. Palmer

doi:10.1103/PhysRevD.5.858

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Zero-Mass Divergences in Expansions about Chiral and Scale Symmetry

Douglas W. McKay

William F. Palmer^*

University of Kansas, Lawrence, Kansas 66044

The Ohio State University, Columbus, Ohio 43210

^*Work supported in part by the U. S. Atomic Energy Commission.

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Phys. Rev. D 5, 858 – Published 15 February, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.858

Abstract

Singularities of expansions in the symmetry-breaking parameters of chiral- and scale-asymmetric theories are studied, in the tree approximation, in polynomial Lagrangian models. The singularities are related to the appearance of zero-mass scalar fields, not necessarily Goldstone particles, at the radius of convergence of the expansion. Methods of avoiding these singularities are presented.

References (25)

Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) J. Goldstone, Nuovo Cimento 19, 154 (1961) J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962) R. Brout, Nuovo Cimento 47A, 932 (1967) P. de Mottoni and E. Fabri, ibid. 54A, 42 (1968) L. Michel and L. A. Radicati, in Proceedings of the Fifth Coral Gables Conference on Symmetry Principles at High Energies, University of Miami, 1968, edited by A. Perlmutter, C. Hurst, and B. Kurşunoğlu (Benjamin, New York, 1968)
R. Dashen, Phys. Rev. 183, 1245 (1969) R. Dashen and M. Weinstein, ibid. 183, 1261 (1969) ibid.188, 2330 (1969) Phys. Rev. Letters 22, 1337 (1969) R. Dashen, Phys. Rev. D 3, 1879 (1971) T. P. Cheng and R. Dashen, Phys. Rev. Letters 26, 594 (1971)
L.-F. Li and H. Pagels, Phys. Rev. Letters 26, 1204 (1971) ibid.27, 1089 (1971)
P. Carruthers and R. W. Haymaker, Phys. Rev. Letters 27, 455 (1971)
P. Carruthers and R. W. Haymaker, Phys. Rev. D 4, 1815 (1971)
P. Carruthers and R. W. Haymaker, Phys. Rev. D 4, 1808 (1971)
R. Olshansky, Phys. Rev. D 4, 2440 (1971)
M. Lévy, Nuovo Cimento 52A, 23 (1967) W. A. Bardeen and B. W. Lee, Phys. Rev. 177, 2389 (1969) S. Gasiorowicz and D. Geffen, Rev. Mod. Phys. 41, 531 (1969) G. Cicogna, F. Strocchi, and R. Vergara Caffarelli, Phys. Rev. Letters 22, 497 (1969) Phys. Rev. D 1, 1197 (1970) J. C. Bane and K. T. Mahanthappa, Phys. Rev. Letters 25, 779 (1970) ibid.25, 1396(E) (1970) Phys. Rev. D 3, 1446 (1971)
William F. Palmer, Ohio State University Report No. C00-1545-82, 1970 (unpublished)
J. Schecter and Y. Ueda, Phys. Rev. D 3, 168 (1971)
J. Schecter and Y. Ueda, Phys. Rev. D 3, 2874 (1971)
S. Okubo and V. Mathur, Phys. Rev. D 1, 2046 (1970) ibid.1, 3468 (1970)
G. Cicogna, Phys. Rev. D 1, 1786 (1970)
R. Arnowitt, M. H. Friedman, P. Nath, and R. Suitor, Phys. Rev. Letters 26, 104 (1971) K. Schilcher, Phys. Rev. D 4, 237 (1971)
[1] [4,5]
Omitted endnote
[8] [9,23]
P. Carruthers, Phys. Rev. D 2, 2265 (1970)
[6]
[9,23]
Omitted endnote
V. Mathur, Phys. Rev. Letters 27, 452 (1971)
[8]
M. Gell-Mann, R. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968)
D. McKay and W. Palmer, Phys. Rev. D 4, 1018 (1971)

[c1] Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961) J. Goldstone, Nuovo Cimento 19, 154 (1961) J. Goldstone, A. Salam, and S. Weinberg, Phys. Rev. 127, 965 (1962) R. Brout, Nuovo Cimento 47A, 932 (1967) P. de Mottoni and E. Fabri, ibid. 54A, 42 (1968) L. Michel and L. A. Radicati, in Proceedings of the Fifth Coral Gables Conference on Symmetry Principles at High Energies, University of Miami, 1968, edited by A. Perlmutter, C. Hurst, and B. Kurşunoğlu (Benjamin, New York, 1968)

[c2] R. Dashen, Phys. Rev. 183, 1245 (1969) R. Dashen and M. Weinstein, ibid. 183, 1261 (1969) ibid.188, 2330 (1969) Phys. Rev. Letters 22, 1337 (1969) R. Dashen, Phys. Rev. D 3, 1879 (1971) T. P. Cheng and R. Dashen, Phys. Rev. Letters 26, 594 (1971)

[c3] L.-F. Li and H. Pagels, Phys. Rev. Letters 26, 1204 (1971) ibid.27, 1089 (1971)

[c4] P. Carruthers and R. W. Haymaker, Phys. Rev. Letters 27, 455 (1971)

[c5] P. Carruthers and R. W. Haymaker, Phys. Rev. D 4, 1815 (1971)

[c6] P. Carruthers and R. W. Haymaker, Phys. Rev. D 4, 1808 (1971)

[c7] R. Olshansky, Phys. Rev. D 4, 2440 (1971)

[c8] M. Lévy, Nuovo Cimento 52A, 23 (1967) W. A. Bardeen and B. W. Lee, Phys. Rev. 177, 2389 (1969) S. Gasiorowicz and D. Geffen, Rev. Mod. Phys. 41, 531 (1969) G. Cicogna, F. Strocchi, and R. Vergara Caffarelli, Phys. Rev. Letters 22, 497 (1969) Phys. Rev. D 1, 1197 (1970) J. C. Bane and K. T. Mahanthappa, Phys. Rev. Letters 25, 779 (1970) ibid.25, 1396(E) (1970) Phys. Rev. D 3, 1446 (1971)

[c9] William F. Palmer, Ohio State University Report No. C00-1545-82, 1970 (unpublished)

[c10] J. Schecter and Y. Ueda, Phys. Rev. D 3, 168 (1971)

[c11] J. Schecter and Y. Ueda, Phys. Rev. D 3, 2874 (1971)

[c12] S. Okubo and V. Mathur, Phys. Rev. D 1, 2046 (1970) ibid.1, 3468 (1970)

[c13] G. Cicogna, Phys. Rev. D 1, 1786 (1970)

[c14] R. Arnowitt, M. H. Friedman, P. Nath, and R. Suitor, Phys. Rev. Letters 26, 104 (1971) K. Schilcher, Phys. Rev. D 4, 237 (1971)

[c15] [1] [4,5]

[c16] Omitted endnote

[c17] [8] [9,23]

[c18] P. Carruthers, Phys. Rev. D 2, 2265 (1970)

[c19] [6]

[c20] [9,23]

[c21] Omitted endnote

[c22] V. Mathur, Phys. Rev. Letters 27, 452 (1971)

[c23] [8]

[c24] M. Gell-Mann, R. Oakes, and B. Renner, Phys. Rev. 175, 2195 (1968)

[c25] D. McKay and W. Palmer, Phys. Rev. D 4, 1018 (1971)

Physical Review D

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Zero-Mass Divergences in Expansions about Chiral and Scale Symmetry

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