Scattering Amplitudes in Quantum Electrodynamics at Infinite Energy, and Possible Implications for Hadron Physics

Shau-Jin Chang; Paul M. Fishbane

doi:10.1103/PhysRevD.2.1104

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Scattering Amplitudes in Quantum Electrodynamics at Infinite Energy, and Possible Implications for Hadron Physics

Shau-Jin Chang and Paul M. Fishbane

Physics Department, University of Illinois, Urbana, Illinois 61801

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Phys. Rev. D 2, 1104 – Published 15 September, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.1104

Abstract

We study in pure quantum electrodynamics the scattering amplitudes at infinite energy due to multiphoton exchange, with interactions among the exchange photons. Such processes, elastic or inelastic, lead to logarithmic dependence on $s$ . The $\ln s$ dependence is found to be associated with the invariance of subgraphs under a boost along the direction of the high-energy collision. Theoretically, our results lead towards a more efficient way of handling a large class of diagrams, and a better understanding of $j$ -plane cut behavior. We speculate that several features of our results generalize to hadron physics. Among these are features in common with the limiting fragmentation hypothesis, and the appearance of pionization in a many-fireball structure. Finally, in the absence of radiative corrections, we demonstrate that the $e^{-}$ , $e^{\mp}$ elastic scattering amplitude can be expressed as an eikonal form, with $χ (b)$ being generated by the sum of all connected pieces.

Comments & Replies

Comments on Eikonalization at High Energy

Shau-Jin Chang and Paul M. Fishbane

Phys. Rev. D 3, 1047 (1971)

References (30)

T. T. Chou and C. N. Yang, Phys. Rev. 170, 1591 (1968) ibid.175, 1832 (1968)
R. J. Glauber, in Lectures in Theoretical Physics, edited by W. E. Britten and L. G. Dunham (Interscience, New York, 1959), Vol. 1
J. Benecke, T. T. Chou, C. N. Yang, and E. Yen, Phys. Rev. 188, 2159 (1969)
B. W. Lee and R. F. Sawyer, Phys. Rev. 127, 2266 (1962)
H. Cheng and T. W. Wu, Phys. Rev. Letters 22, 666 (1969) Phys. Rev. 182, 1852 (1969) ibid.182, 1868 (1969) ibid.182, 1873 (1969) ibid.182, 1899 (1969)
S. J. Chang and S. Ma, Phys. Rev. Letters 22, 1334 (1969) Phys. Rev. 188, 2385 (1969) H. Cheng and T. T. Wu, ibid. 186, 1611 (1969)
H. D. I. Abarbanel and C. Itzykson, Phys. Rev. Letters 23, 53 (1969) F. Englert et al., Nuovo Cimento 64A, 561 (1969) M. Lévy and J. Sucher, Phys. Rev. 186, 1656 (1969)
M. Lévy, Phys. Rev. 130, 791 (1963) R. Torgerson, ibid. 143, 1194 (1966)
V. N. Gribov and I. Ya Pomeranchuk, Phys. Letters 2, 239 (1962)
Proceedings of the 1969 Regge Cut Conference, edited by P. M. Fishbane and L. M. Simmons (Univ. of Wisconsin, Madison, 1969)
H. Cheng and T. T. Wu, Phys. Rev. Letters 22, 1405 (1969)
G. V. Frolov, V. N. Gribov, and L. N. Lipatov, Phys. Letters 31B, 34 (1970)
M. Gell-Mann, M. L. Goldberger, and F. E. Low, Rev. Mod. Phys. 36, 640 (1964)
M. Koshiba, in Proceedings of the Third International Conference on High-Energy Collisions (Gordon and Breach, New York, 1969) Proceedings of the Tenth International Conference on Cosmic Rays [Can. J. Phys. 46, No. 10, Pts. 2-4 (1968)]
Omitted endnote
S. J. Chang and S. Ma, Phys. Rev. 180, 1506 (1969) ibid.188, 2385 (1969)
A. N. Chester, Phys. Rev. 140, B85 (1965) R. Torgerson, ibid. 143, 1194 (1966)
(Sec. III) [6,8]
S. Weinberg, Phys. Rev. 150, 1313 (1966)
P. V. Landshoff and J. C. Polkinghorne [Phys. Rev. 181, 1989 (1969)]
[16]
S. J. Chang, Phys. Rev. D 1, 2977 (1970) Y. P. Yao, ibid. 1, 2971 (1970)
H. Cheng and T. T. Wu, Phys. Rev. 186, 1611 (1969)
Omitted endnote
R. J. Eden et al., The Analytic S-Matrix (Cambridge U. P., London, 1966)
B. Lee, Phys. Rev. D 1, 2361 (1970)
[28]
S. J. Chang and P. M. Fishbane, Phys. Rev. Letters 24, 847 (1970) Phys. Rev. D 2, 1084 (1970)
R. P. Feynman, Phys. Rev. Letters 23, 1415 (1969)
C. N. Yang, in Proceedings of the Northwestern Symposium, 1970 (unpublished)

[c1] T. T. Chou and C. N. Yang, Phys. Rev. 170, 1591 (1968) ibid.175, 1832 (1968)

[c2] R. J. Glauber, in Lectures in Theoretical Physics, edited by W. E. Britten and L. G. Dunham (Interscience, New York, 1959), Vol. 1

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

[c4] B. W. Lee and R. F. Sawyer, Phys. Rev. 127, 2266 (1962)

[c5] H. Cheng and T. W. Wu, Phys. Rev. Letters 22, 666 (1969) Phys. Rev. 182, 1852 (1969) ibid.182, 1868 (1969) ibid.182, 1873 (1969) ibid.182, 1899 (1969)

[c6] S. J. Chang and S. Ma, Phys. Rev. Letters 22, 1334 (1969) Phys. Rev. 188, 2385 (1969) H. Cheng and T. T. Wu, ibid. 186, 1611 (1969)

[c7] H. D. I. Abarbanel and C. Itzykson, Phys. Rev. Letters 23, 53 (1969) F. Englert et al., Nuovo Cimento 64A, 561 (1969) M. Lévy and J. Sucher, Phys. Rev. 186, 1656 (1969)

[c8] M. Lévy, Phys. Rev. 130, 791 (1963) R. Torgerson, ibid. 143, 1194 (1966)

[c9] V. N. Gribov and I. Ya Pomeranchuk, Phys. Letters 2, 239 (1962)

[c10] Proceedings of the 1969 Regge Cut Conference, edited by P. M. Fishbane and L. M. Simmons (Univ. of Wisconsin, Madison, 1969)

[c11] H. Cheng and T. T. Wu, Phys. Rev. Letters 22, 1405 (1969)

[c12] G. V. Frolov, V. N. Gribov, and L. N. Lipatov, Phys. Letters 31B, 34 (1970)

[c13] M. Gell-Mann, M. L. Goldberger, and F. E. Low, Rev. Mod. Phys. 36, 640 (1964)

[c14] M. Koshiba, in Proceedings of the Third International Conference on High-Energy Collisions (Gordon and Breach, New York, 1969) Proceedings of the Tenth International Conference on Cosmic Rays [Can. J. Phys. 46, No. 10, Pts. 2-4 (1968)]

[c15] Omitted endnote

[c16] S. J. Chang and S. Ma, Phys. Rev. 180, 1506 (1969) ibid.188, 2385 (1969)

[c17] A. N. Chester, Phys. Rev. 140, B85 (1965) R. Torgerson, ibid. 143, 1194 (1966)

[c18] (Sec. III) [6,8]

[c19] S. Weinberg, Phys. Rev. 150, 1313 (1966)

[c20] P. V. Landshoff and J. C. Polkinghorne [Phys. Rev. 181, 1989 (1969)]

[c21] [16]

[c22] S. J. Chang, Phys. Rev. D 1, 2977 (1970) Y. P. Yao, ibid. 1, 2971 (1970)

[c23] H. Cheng and T. T. Wu, Phys. Rev. 186, 1611 (1969)

[c24] Omitted endnote

[c25] R. J. Eden et al., The Analytic S-Matrix (Cambridge U. P., London, 1966)

[c26] B. Lee, Phys. Rev. D 1, 2361 (1970)

[c27] [28]

[c28] S. J. Chang and P. M. Fishbane, Phys. Rev. Letters 24, 847 (1970) Phys. Rev. D 2, 1084 (1970)

[c29] R. P. Feynman, Phys. Rev. Letters 23, 1415 (1969)

[c30] C. N. Yang, in Proceedings of the Northwestern Symposium, 1970 (unpublished)

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Scattering Amplitudes in Quantum Electrodynamics at Infinite Energy, and Possible Implications for Hadron Physics

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Comments on Eikonalization at High Energy

References (30)

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