Analytic Properties of Three-Particle Amplitudes in the Scattering-Angle Variable

Y. Avishai

doi:10.1103/PhysRevD.4.400

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Analytic Properties of Three-Particle Amplitudes in the Scattering-Angle Variable

Y. Avishai

Argonne National Laboratory, Argonne, Illinois 60439

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Phys. Rev. D 4, 400 – Published 15 July, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.400

Abstract

The elastic amplitude describing a scattering of a free particle on a two-particle bound state is here considered as a function of $cos θ$ , where $θ$ is the scattering angle. The two-body interactions were taken to be $s$ -wave and separable. Our results are: (1) The on-shell amplitude is analytic inside a Lehmann ellipse for all real energies, except for a finite interval on the negative $E$ axis, and (2) for negative energy, the off-shell amplitude is analytic in the whole $cos θ$ plane, apart from possible real left and right cuts, and in the Lehmann ellipse. Its asymptotic behavior in $cos θ$ is determined by the leading Regge trajectory.

References (16)

M. H. Rubin, R. L. Sugar, and G. Tiktopoulos, Phys. Rev. 146, 1130 (1966) ibid.159, 1348 (1967) ibid.162, 1555 (1967)
G. Immirzi, Nuovo Cimento 34, 1361 (1964)
J. B. Hartle and R. L. Sugar, Phys. Rev. 169, 1104 (1968)
A. N. Mitra, Nucl. Phys. 32, 529 (1962) C. A. Lovelace, Phys. Rev. 135, B1225 (1964)
R. Aaron and Vigdor L. Teplitz, Phys. Rev. 167, 1284 (1967)
I. Drummond, Phys. Rev. 140, B1368 (1965)
A. Anselm et al., Ann. Phys. (N. Y.) 37, 227 (1966)
R. D. Amado, Phys. Rev. 132, 485 (1963)
J. H. Hetherington and L. H. Schick, Phys. Rev. 135, B935 (1965)
Y. Avishai, Phys. Rev. D 3, 3232 (1971)
Bateman Manuscript Project, Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. 2, p. 162
Omitted endnote
V. De Alfaro and T. Regge, Potential Scattering (North-Holland, Amsterdam, 1965), Chap. 9
S. Mandelstam [Lawrence Radiation Laboratory Report No. UCRL-17250 (unpublished)]
G. Tiktopoulos, Phys. Rev. 133, 1231 (1964)
Z. Nehari, Conformal Mapping (McGraw-Hill, New York, 1952), p. 269

[c1] M. H. Rubin, R. L. Sugar, and G. Tiktopoulos, Phys. Rev. 146, 1130 (1966) ibid.159, 1348 (1967) ibid.162, 1555 (1967)

[c2] G. Immirzi, Nuovo Cimento 34, 1361 (1964)

[c3] J. B. Hartle and R. L. Sugar, Phys. Rev. 169, 1104 (1968)

[c4] A. N. Mitra, Nucl. Phys. 32, 529 (1962) C. A. Lovelace, Phys. Rev. 135, B1225 (1964)

[c5] R. Aaron and Vigdor L. Teplitz, Phys. Rev. 167, 1284 (1967)

[c6] I. Drummond, Phys. Rev. 140, B1368 (1965)

[c7] A. Anselm et al., Ann. Phys. (N. Y.) 37, 227 (1966)

[c8] R. D. Amado, Phys. Rev. 132, 485 (1963)

[c9] J. H. Hetherington and L. H. Schick, Phys. Rev. 135, B935 (1965)

[c10] Y. Avishai, Phys. Rev. D 3, 3232 (1971)

[c11] Bateman Manuscript Project, Higher Transcendental Functions, edited by A. Erdélyi (McGraw-Hill, New York, 1953), Vol. 2, p. 162

[c12] Omitted endnote

[c13] V. De Alfaro and T. Regge, Potential Scattering (North-Holland, Amsterdam, 1965), Chap. 9

[c14] S. Mandelstam [Lawrence Radiation Laboratory Report No. UCRL-17250 (unpublished)]

[c15] G. Tiktopoulos, Phys. Rev. 133, 1231 (1964)

[c16] Z. Nehari, Conformal Mapping (McGraw-Hill, New York, 1952), p. 269

Physical Review D

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Analytic Properties of Three-Particle Amplitudes in the Scattering-Angle Variable

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