Regge Poles for Large Coupling Constants. II

Hung Cheng; Tai Tsun Wu

doi:10.1103/PhysRevD.5.3192

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Regge Poles for Large Coupling Constants. II

Hung Cheng^*,†

Tai Tsun Wu^†

Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Gordon McKay Laboratory, Harvard University, Cambridge, Massachusetts 02138
Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

^*Work supported in part by the National Science Foundation under Grant No. GP 13775.
^†John S. Guggenheim Memorial Fellow.

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Phys. Rev. D 5, 3192 – Published 15 June, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.3192

Abstract

Since we define the Pomeranchon to be the leading singularity of the "potential," and find that a high-energy particle resembles an expanding black disk if this singularity is located at $J > 1$ , we study as a model the generation of such a singularity by the ladder diagrams in $φ^{3}$ theory. We find that, when the coupling constant is sufficiently large, there are Regge poles located at $J > 1$ . Thus the Pomeranchon in this model is a Regge pole with $α (0) > 1$ . This conclusion is reached by solving the Bethe-Salpeter equation to determine, in the strong coupling limit, the positions of the Regge (or Toller) poles at $t = 0$ . We find a family of approximately equally spaced Toller poles. The position of the leading singularity, but not the spacing, depends critically on whether the exchanged particle is massless or massive. Some numerical results are presented.

References (28)

H. Cheng and T. T. Wu, Phys. Rev. Letters 24, 1456 (1970)
H. Cheng and T. T. Wu, this issue, Phys. Rev. D 5, 3170 (1972) (to be published)
H. Cheng and T. T.Wu Phys. Rev. Letters 23, 1311 (1969)
J. L. Day et al., Phys. Rev. Letters 23, 1055 (1969)
H. Cheng and T. T. Wu, Phys. Letters 34B, 647 (1971)
H. Cheng and T. T. Wu, Phys. Rev. D 3, 2195 (1971)
H. Cheng and T. T. Wu, Phys. Rev. Letters 22, 666 (1969)
H. Cheng and T. T. Wu, Phys. Rev. 186, 1611 (1969). Sec. 7
H. Cheng and T. T. Wu, Phys. Rev. D 3, 2397 (1971)
T. Regge, Nuovo Cimento 14, 951 (1959)
G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 7, 394 (1961)
G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 8, 41 (1962)
H. Cheng and T. T. Wu, Phys. Rev. Letters 24, 759 (1970)
H. Cheng and T. T. Wu, preceding paper, Phys. Rev. D 5, 3189 (1972)
G. C. Wick, Phys. Rev. 96, 1124 (1954)
R. E. Cutkosky, Phys. Rev. 96, 1135 (1954)
D. Freedman and J. M. Wang, Phys. Rev. Letters 17, 569 (1966)
M. L. Goldberger and C. E. Jones, Phys. Rev. 150, 1269 (1966)
D. Freedman and J. M. Wang, Phys. Rev. 153, 1596 (1967)
D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962)
G. Cosenza, L. Sertorio, and M. Toller, Nuovo Cimento 35, 913 (1965)
Higher Transcendental Functions (Bateman Manuscript Project), edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. I, Chap. II
E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951) Y. Nambu, Progr. Theoret. Phys. (Kyoto) 5, 614 (1950) M. Gell-Mann and F. Low, Phys. Rev. 84, 350 (1951) J. Schwinger, Proc. Natl. Acad. Sci. U. S. 37, 455 (1951)
N. Nakaniski, Suppl. Progr. Theoret. Phys. (Kyoto) No. 43 (1969)
Eq. (1) on p. 110 of [22]
Eq. (1) on p. 108 of [22]
Chap. VI of [22]
Eq. (17) and Eq. (18) on p. 194 of Vol. II of [22]

[c1] H. Cheng and T. T. Wu, Phys. Rev. Letters 24, 1456 (1970)

[c2] H. Cheng and T. T. Wu, this issue, Phys. Rev. D 5, 3170 (1972) (to be published)

[c3] H. Cheng and T. T.Wu Phys. Rev. Letters 23, 1311 (1969)

[c4] J. L. Day et al., Phys. Rev. Letters 23, 1055 (1969)

[c5] H. Cheng and T. T. Wu, Phys. Letters 34B, 647 (1971)

[c6] H. Cheng and T. T. Wu, Phys. Rev. D 3, 2195 (1971)

[c7] H. Cheng and T. T. Wu, Phys. Rev. Letters 22, 666 (1969)

[c8] H. Cheng and T. T. Wu, Phys. Rev. 186, 1611 (1969). Sec. 7

[c9] H. Cheng and T. T. Wu, Phys. Rev. D 3, 2397 (1971)

[c10] T. Regge, Nuovo Cimento 14, 951 (1959)

[c11] G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 7, 394 (1961)

[c12] G. F. Chew and S. C. Frautschi, Phys. Rev. Letters 8, 41 (1962)

[c13] H. Cheng and T. T. Wu, Phys. Rev. Letters 24, 759 (1970)

[c14] H. Cheng and T. T. Wu, preceding paper, Phys. Rev. D 5, 3189 (1972)

[c15] G. C. Wick, Phys. Rev. 96, 1124 (1954)

[c16] R. E. Cutkosky, Phys. Rev. 96, 1135 (1954)

[c17] D. Freedman and J. M. Wang, Phys. Rev. Letters 17, 569 (1966)

[c18] M. L. Goldberger and C. E. Jones, Phys. Rev. 150, 1269 (1966)

[c19] D. Freedman and J. M. Wang, Phys. Rev. 153, 1596 (1967)

[c20] D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962)

[c21] G. Cosenza, L. Sertorio, and M. Toller, Nuovo Cimento 35, 913 (1965)

[c22] Higher Transcendental Functions (Bateman Manuscript Project), edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. I, Chap. II

[c23] E. E. Salpeter and H. A. Bethe, Phys. Rev. 84, 1232 (1951) Y. Nambu, Progr. Theoret. Phys. (Kyoto) 5, 614 (1950) M. Gell-Mann and F. Low, Phys. Rev. 84, 350 (1951) J. Schwinger, Proc. Natl. Acad. Sci. U. S. 37, 455 (1951)

[c24] N. Nakaniski, Suppl. Progr. Theoret. Phys. (Kyoto) No. 43 (1969)

[c25] Eq. (1) on p. 110 of [22]

[c26] Eq. (1) on p. 108 of [22]

[c27] Chap. VI of [22]

[c28] Eq. (17) and Eq. (18) on p. 194 of Vol. II of [22]

Physical Review D

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Regge Poles for Large Coupling Constants. II

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Regge Poles for Large Coupling Constants. I

References (28)

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