Low-<span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math></span> Theorems for Charged-Pion Photoproduction

J. A. Campbell; Robert Beck Clark; D. Horn

doi:10.1103/PhysRevD.2.217

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Low- $t$ Theorems for Charged-Pion Photoproduction

J. A. Campbell^* and Robert Beck Clark

D. Horn^†

Center for Particle Theory, University of Texas, Austin, Texas 78712

California Institute of Technology, Pasadena, California 91109

^*Also a member of the Department of Computer Science, University of Texas, Austin, Tex.
^†On leave from Tel-Aviv University, Tel-Aviv, Israel.

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Phys. Rev. D 2, 217 – Published 1 July, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.217

Abstract

Low- $t$ theorems for charged-pion photoproduction are proven on the basis of gauge-invariance restrictions. They can be simply formulated by means of the minimal gauge-invariant extension of pion exchange (MPE). It is shown that whereas MPE leads in $γ N \to π^{\pm} N$ only to weak restrictions for $\frac{d σ}{dt}$ near the forward direction ( $| t | ≲ μ^{2}$ ), it does actually account for all the structure observed in $γ p \to π^{-} Δ^{+ +}$ in this $t$ domain. Results for these reactions as well as the other charge modes of $γ N \to π^{\pm} Δ$ are discussed and compared with experiment.

References (16)

D. Horn and M. Jacob, Nuovo Cimento 56A, 83 (1968)
J. S. Ball, Phys. Rev. 124, 2014 (1961)
F. S. Henyey, Phys. Rev. 170, 1619 (1968) T. Ebata and K. E. Lassila, Phys. Rev. Letters 21, 250 (1968) W. A. Bardeen and W.-K. Tung, Phys. Rev. 173, 1423 (1968)
B. Richter, in Proceedings of the Third International Symposium on Electron and Photon Interactions at High Energies, Stanford Linear Accelerator Center, 1967 (Clearing House of Federal Scientific and Technical Information, Washington, D. C., 1968), p. 313
A. M. Boyarski, F. Bulos, W. Busza, R. Diebold, S. D. Ecklund, G. E. Fischer, J. R. Rees, and B. Richter, Phys. Rev. Letters 20, 300 (1968)
J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)
H. Harari, rapporteur talk, in Proceedings of the Fourth International Symposium on Electron and Photon Interactions at High Energies (Daresbury Nuclear Physics Laboratory, Daresbury, England, 1969), p. 107
A. C. Hearn, Nuovo Cimento 21, 333 (1961)
M. Scadron and H. F. Jones, Phys. Rev. 173, 1734 (1968)
A. C. Hearn, in Interactive Systems for Experimental Applied Mathematics, edited by M. Klerer and J. Reinfelds (Academic, New York, 1968), pp. 79-90
J. A. Campbell, J. Comput. Phys. 2, 412 (1968)
Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)
P. Stichel and M. Scholz, Nuovo Cimento 34, 1381 (1965)
I. Bender, H. G. Dosch, and H. J. Rothe, Nuovo Cimento 63A, 162 (1969) E. Gotsman, Phys. Rev. 186, 1543 (1969)
A. M. Boyarski, R. Diebold, S. D. Ecklund, G. E. Fischer, Y. Murata, B. Richter, and W. S. C. Williams, Phys. Rev. Letters 22, 148 (1969)
A. M. Boyarski, R. Diebold, S. D. Ecklund, G. E. Fischer, Y. Murata, B. Richter, and M. Sands, in Proceedings of the Fourth International Symposium on Electron and Photon Interactions at High Energies (Daresbury Nuclear Physics Laboratory, Daresbury, England, 1969) private communication

[c1] D. Horn and M. Jacob, Nuovo Cimento 56A, 83 (1968)

[c2] J. S. Ball, Phys. Rev. 124, 2014 (1961)

[c3] F. S. Henyey, Phys. Rev. 170, 1619 (1968) T. Ebata and K. E. Lassila, Phys. Rev. Letters 21, 250 (1968) W. A. Bardeen and W.-K. Tung, Phys. Rev. 173, 1423 (1968)

[c4] B. Richter, in Proceedings of the Third International Symposium on Electron and Photon Interactions at High Energies, Stanford Linear Accelerator Center, 1967 (Clearing House of Federal Scientific and Technical Information, Washington, D. C., 1968), p. 313

[c5] A. M. Boyarski, F. Bulos, W. Busza, R. Diebold, S. D. Ecklund, G. E. Fischer, J. R. Rees, and B. Richter, Phys. Rev. Letters 20, 300 (1968)

[c6] J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1965)

[c7] H. Harari, rapporteur talk, in Proceedings of the Fourth International Symposium on Electron and Photon Interactions at High Energies (Daresbury Nuclear Physics Laboratory, Daresbury, England, 1969), p. 107

[c8] A. C. Hearn, Nuovo Cimento 21, 333 (1961)

[c9] M. Scadron and H. F. Jones, Phys. Rev. 173, 1734 (1968)

[c10] A. C. Hearn, in Interactive Systems for Experimental Applied Mathematics, edited by M. Klerer and J. Reinfelds (Academic, New York, 1968), pp. 79-90

[c11] J. A. Campbell, J. Comput. Phys. 2, 412 (1968)

[c12] Particle Data Group, Rev. Mod. Phys. 41, 109 (1969)

[c13] P. Stichel and M. Scholz, Nuovo Cimento 34, 1381 (1965)

[c14] I. Bender, H. G. Dosch, and H. J. Rothe, Nuovo Cimento 63A, 162 (1969) E. Gotsman, Phys. Rev. 186, 1543 (1969)

[c15] A. M. Boyarski, R. Diebold, S. D. Ecklund, G. E. Fischer, Y. Murata, B. Richter, and W. S. C. Williams, Phys. Rev. Letters 22, 148 (1969)

[c16] A. M. Boyarski, R. Diebold, S. D. Ecklund, G. E. Fischer, Y. Murata, B. Richter, and M. Sands, in Proceedings of the Fourth International Symposium on Electron and Photon Interactions at High Energies (Daresbury Nuclear Physics Laboratory, Daresbury, England, 1969) private communication

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Low- $t$ Theorems for Charged-Pion Photoproduction

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Low-t Theorems for Charged-Pion Photoproduction

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References (16)

Low- $t$ Theorems for Charged-Pion Photoproduction