High-Energy Elastic and Inelastic Scattering in <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> Theory

Shau-Jin Chang; Tung-Mow Yan

doi:10.1103/PhysRevD.4.537

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High-Energy Elastic and Inelastic Scattering in $ϕ^{3}$ Theory

Shau-Jin Chang^*

Tung-Mow Yan^†

Department of Physics, University of Illinois, Urbana, Illinois 61801

Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14850

^*Work supported in part by the National Science Foundation under Grant No. NSF GP 19433.
^†Work supported in part by the National Science Foundation.

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Phys. Rev. D 4, 537 – Published 15 July, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.537

Abstract

We study high-energy elastic and inelastic processes in a $ϕ^{3}$ theory based on the following model: For the elastic-scattering amplitude we first sum the leading terms in each order of perturbation of the $t$ -channel straight ladders, plus those obtained by interchange of the Mandelstam variables $s$ and $u$ . We then perform the $s$ -channel iteration with the $t$ -channel ladders as single units. We are only interested in the physical regions in which the incident particles retain their large momenta. This procedure leads to the eikonalization of the $t$ -channel ladders. For the inelastic production amplitude, the dominant contribution comes from diagrams with any number of totally open ladders (i.e., multiperipheral chains) modified by unopen ones. The main results are: (a) The total cross section approaches zero, approaches a constant, or increases as ${(lns)}^{2}$ according as the coupling constant is smaller than, equal to, or larger than a critical value. (b) Elastic and inelastic differential cross sections are computed, and they have many nice features, as suggested by the absorption model. (c) Nonforward $s$ -channel unitarity is explicitly verified. (d) One-particle and multiparticle spectra, the average multiplicity, the number distribution of the final particles, etc., are obtained. The implications of these results to hadron physics are discussed.

References (25)

D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962) K. Wilson, Acta Phys. Austriaca 17, 37 (1963)
R. P. Feynman, Phys. Rev. Letters 23, 1415 (1969) in High Energy Collisions, edited by C. N. Yang (Gordon and Breach, New York, 1969)
J. Benecke, T. T. Chou, C. N. Yang, and E. Yen, Phys. Rev. 188, 2159 (1969)
R. J. Eden et al., The Analytic S-Matrix (Cambridge Univ. Press, Cambridge, England, 1966)
S. Weinberg, Phys. Rev. 150, 1313 (1966)
H. Cheng and T. T. Wu, Phys. Rev. Letters 24, 1456 (1970)
S. J. Chang and S. Ma, Phys. Rev. 180, 1506 (1969) ibid.188, 2385 (1969)
S. J. Chang and P. M. Fishbane, Phys. Rev. D 2, 1104 (1970) ibid.3, 1047 (1971)
M. Lévy and J. Sucher, Phys. Rev. 186, 1656 (1969) R. L. Sugar and R. Blankenbecler, ibid. 183, 1387 (1969)
S. D. Drell, D. J. Levy, and T. M. Yan, Phys. Rev. Letters 22, 774 (1969) Phys. Rev. 187, 2159 (1969)
B. W. Lee and R. F. Sawyer, Phys. Rev. 127, 2266 (1962) [4]
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, Phys. Rev. Letters 25, 1591 (1970)
M. Froissart, Phys. Rev. 123, 1053 (1961)
G. V. Frolov, V. N. Gribov, and L. N. Lipatov, Phys. Letters 31B, 34 (1970)
[8]
Omitted endnote
Omitted endnote
R. Arnold, Phys. Rev. 153, 1523 (1967) S. Frautschi and B. Margolis, Nuovo Cimento 56A, 1155 (1969)
I. J. Muzinich, G. Tiktopoulos, and S. B. Treiman, Phys. Rev. D 3, 1041 (1971) G. Tiktopoulos and S. B. Treiman, ibid. 3, 1037 (1971) G. M. Cicuta and R. L. Sugar, ibid. 3, 970 (1971) B. Hasslacher and D. K. Sinclair, ibid. 3, 1770 (1971) H. Fried, ibid. 3, 2010 (1971)
H. Cheng and T. T. Wu, Phys. Letters 34B, 647 (1971)
T. T. Chou and C. N. Yang, Phys. Rev. 170, 1591 (1968) ibid.175, 1832 (1968) B. Lee, Phys. Rev. D 1, 2361 (1970)
H. Cheng and T. T. Wu, Phys. Rev. D 1, 2775 (1970)
S. J. Chang, Phys. Rev. D 2, 2886 (1970)
K. Wilson, Cornell University report, 1970 (unpublished)

[c1] D. Amati, A. Stanghellini, and S. Fubini, Nuovo Cimento 26, 896 (1962) K. Wilson, Acta Phys. Austriaca 17, 37 (1963)

[c2] R. P. Feynman, Phys. Rev. Letters 23, 1415 (1969) in High Energy Collisions, edited by C. N. Yang (Gordon and Breach, New York, 1969)

[c3] J. Benecke, T. T. Chou, C. N. Yang, and E. Yen, Phys. Rev. 188, 2159 (1969)

[c4] R. J. Eden et al., The Analytic S-Matrix (Cambridge Univ. Press, Cambridge, England, 1966)

[c5] S. Weinberg, Phys. Rev. 150, 1313 (1966)

[c6] H. Cheng and T. T. Wu, Phys. Rev. Letters 24, 1456 (1970)

[c7] S. J. Chang and S. Ma, Phys. Rev. 180, 1506 (1969) ibid.188, 2385 (1969)

[c8] S. J. Chang and P. M. Fishbane, Phys. Rev. D 2, 1104 (1970) ibid.3, 1047 (1971)

[c9] M. Lévy and J. Sucher, Phys. Rev. 186, 1656 (1969) R. L. Sugar and R. Blankenbecler, ibid. 183, 1387 (1969)

[c10] S. D. Drell, D. J. Levy, and T. M. Yan, Phys. Rev. Letters 22, 774 (1969) Phys. Rev. 187, 2159 (1969)

[c11] B. W. Lee and R. F. Sawyer, Phys. Rev. 127, 2266 (1962) [4]

[c12] S. J. Chang and T. M. Yan, Phys. Rev. Letters 25, 1586 (1970)

[c13] B. Hasslacher, D. K. Sinclair, G. M. Cicuta, and R. L. Sugar, Phys. Rev. Letters 25, 1591 (1970)

[c14] M. Froissart, Phys. Rev. 123, 1053 (1961)

[c15] G. V. Frolov, V. N. Gribov, and L. N. Lipatov, Phys. Letters 31B, 34 (1970)

[c16] [8]

[c17] Omitted endnote

[c18] Omitted endnote

[c19] R. Arnold, Phys. Rev. 153, 1523 (1967) S. Frautschi and B. Margolis, Nuovo Cimento 56A, 1155 (1969)

[c20] I. J. Muzinich, G. Tiktopoulos, and S. B. Treiman, Phys. Rev. D 3, 1041 (1971) G. Tiktopoulos and S. B. Treiman, ibid. 3, 1037 (1971) G. M. Cicuta and R. L. Sugar, ibid. 3, 970 (1971) B. Hasslacher and D. K. Sinclair, ibid. 3, 1770 (1971) H. Fried, ibid. 3, 2010 (1971)

[c21] H. Cheng and T. T. Wu, Phys. Letters 34B, 647 (1971)

[c22] T. T. Chou and C. N. Yang, Phys. Rev. 170, 1591 (1968) ibid.175, 1832 (1968) B. Lee, Phys. Rev. D 1, 2361 (1970)

[c23] H. Cheng and T. T. Wu, Phys. Rev. D 1, 2775 (1970)

[c24] S. J. Chang, Phys. Rev. D 2, 2886 (1970)

[c25] K. Wilson, Cornell University report, 1970 (unpublished)

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High-Energy Elastic and Inelastic Scattering in $ϕ^{3}$ Theory

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High-Energy Elastic and Inelastic Scattering in ϕ3 Theory

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References (25)

High-Energy Elastic and Inelastic Scattering in $ϕ^{3}$ Theory