Failure of the Eikonal Approximation for the Vertex Function in a Boson Field Theory

E. Eichten; R. Jackiw

doi:10.1103/PhysRevD.4.439

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Failure of the Eikonal Approximation for the Vertex Function in a Boson Field Theory

E. Eichten^* and R. Jackiw^†

Laboratory for Nuclear Science and Physics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

^*NSF Predoctoral Fellow.
^†Alfred P. Sloan Fellow.

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Phys. Rev. D 4, 439 – Published 15 July, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.439

Abstract

By an explicit calculation of the high-energy behavior of the three-point function in the $λ φ^{3}$ theory, through terms of order $λ^{5}$ , we demonstrate that the eikonal approximation for generalized ladder exchange fails in that model, for this vertex function. In a given order, it underestimates the exact asymptote.

References (13)

Omitted endnote
H. Cheng and T. T. Wu, Phys. Rev. D 2, 2276 (1970) H. D. I. Abarbanel and C. Itzykson, Phys. Rev. Letters 23, 53 (1969)
S. J. Chang and T. M. Yan, Phys. Rev. Letters 25, 1586 (1970) B. Hasslacher, D. K. Sinclair, G. M. Cicuta, and R. L. Sugar, ibid. 25, 1591 (1970)
G. Tiktopoulos and S. B. Treiman, Phys. Rev. D 3, 1037 (1971)
R. Jackiw, Ph.D. thesis, Cornell University, 1966 (unpublished) Ann. Phys. (N. Y.) 48, 292 (1968)
J. Primack, Ph.D. thesis, Stanford University, 1970 (unpublished) P. M. Fishbane and J. D. Sullivan, Phys. Rev. D 4, 458 (1971) E. Eichten, ibid. 4, 439 (1971) T. Appelquist and J. Primack (unpublished)
M. Cassandro and M. Cini, Nuovo Cimento 34, 1719 (1964) [5,6]
Omitted endnote
S. Weinberg, Phys. Rev. 150, 1313 (1966)
G. Tiktopoulos, Phys. Rev. 131, 2373 (1963)
[5] [9]
[5] [5] [5]
Omitted endnote

[c1] Omitted endnote

[c2] H. Cheng and T. T. Wu, Phys. Rev. D 2, 2276 (1970) H. D. I. Abarbanel and C. Itzykson, Phys. Rev. Letters 23, 53 (1969)

[c3] S. J. Chang and T. M. Yan, Phys. Rev. Letters 25, 1586 (1970) B. Hasslacher, D. K. Sinclair, G. M. Cicuta, and R. L. Sugar, ibid. 25, 1591 (1970)

[c4] G. Tiktopoulos and S. B. Treiman, Phys. Rev. D 3, 1037 (1971)

[c5] R. Jackiw, Ph.D. thesis, Cornell University, 1966 (unpublished) Ann. Phys. (N. Y.) 48, 292 (1968)

[c6] J. Primack, Ph.D. thesis, Stanford University, 1970 (unpublished) P. M. Fishbane and J. D. Sullivan, Phys. Rev. D 4, 458 (1971) E. Eichten, ibid. 4, 439 (1971) T. Appelquist and J. Primack (unpublished)

[c7] M. Cassandro and M. Cini, Nuovo Cimento 34, 1719 (1964) [5,6]

[c8] Omitted endnote

[c9] S. Weinberg, Phys. Rev. 150, 1313 (1966)

[c10] G. Tiktopoulos, Phys. Rev. 131, 2373 (1963)

[c11] [5] [9]

[c12] [5] [5] [5]

[c13] Omitted endnote

Physical Review D

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Failure of the Eikonal Approximation for the Vertex Function in a Boson Field Theory

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