Separation of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Δ</mi></math> Exchanges in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>N</mi></math> Scattering and Deduction of Amplitude Zeros

V. Barger; M. G. Olsson

doi:10.1103/PhysRevD.5.2736

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Separation of $N$ and $Δ$ Exchanges in $π N$ Scattering and Deduction of Amplitude Zeros

V. Barger^* and M. G. Olsson

Physics Department, University of Wisconsin, Madison, Wisconsin 53706

^*John Simon Guggenheim Foundation Fellow.

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Phys. Rev. D 5, 2736 – Published 1 June, 1972

DOI: https://doi.org/10.1103/PhysRevD.5.2736

Abstract

Linear combinations of $π N$ differential cross sections and polarizations are used to isolate the $I_{u} = \frac{1}{2}$ and $I_{u} = \frac{3}{2}$ exchange amplitudes directly from data. For $I_{u} = \frac{1}{2}$ exchange the cross section has a zero at $u = - 0.15$ ${(G e V / c)}^{2}$ and the polarization becomes large and negative for $| u | > 0.25$ ${(G e V / c)}^{2}$ . Our phenomenological analysis indicates that in the dip region the $I_{u} = \frac{1}{2}$ amplitude is inconsistent with appreciable secondary trajectories or absorptive corrections. For $I_{u} = \frac{3}{2}$ exchange we infer that the imaginary $s$ -channel helicity-flip amplitude has a zero near $u = - 0.15$ ${(G e V / c)}^{2}$ , consistent with peripherality for $Δ$ exchange. We also derive a sum rule relating the $π N$ differential cross sections at 180° to the Regge-trajectory difference $α_{Δ} - α_{N}$ .

References (11)

J. Orear et al., Phys. Rev. Letters 21, 389 (1968) J. P. Boright et al., ibid. 24, 964 (1970) Cornell Laboratory of Nuclear Studies Report No. 120, 1970 (unpublished) D. P. Owen et al., Phys. Rev. 181, 1794 (1969)
CERN-IPN (Orsay)-Oxford Collaboration (unpublished) CERN-IPN (Orsay)-Oxford Collaboration, preliminary results (unpublished)
[4,7]
E. Berger and G. Fox, Nucl. Phys. B26, 1 (1970)
([2])
G. V. Dass, J. Froyland, F. Halzen, A. Martin, C. Michael, and S. Roy, Phys. Letters 36B, 339 (1971)
V. Barger and D. Cline, Phenomenological Theories of High Energy Scattering (Benjamin, New York, 1969)
J. D. Stack, Phys. Rev. Letters 16, 286 (1966)
Omitted endnote
S. Chu and A. Hendry, Phys. Rev. Letters 25, 313 (1970) H. Harari, in Proceedings of the International Conference on Duality and Symmetry in Hadron Physics, edited by E. Gotsman (Weizmann Science Press of Israel, Jerusalem, 1971)
Omitted endnote

[c1] J. Orear et al., Phys. Rev. Letters 21, 389 (1968) J. P. Boright et al., ibid. 24, 964 (1970) Cornell Laboratory of Nuclear Studies Report No. 120, 1970 (unpublished) D. P. Owen et al., Phys. Rev. 181, 1794 (1969)

[c2] CERN-IPN (Orsay)-Oxford Collaboration (unpublished) CERN-IPN (Orsay)-Oxford Collaboration, preliminary results (unpublished)

[c3] [4,7]

[c4] E. Berger and G. Fox, Nucl. Phys. B26, 1 (1970)

[c5] ([2])

[c6] G. V. Dass, J. Froyland, F. Halzen, A. Martin, C. Michael, and S. Roy, Phys. Letters 36B, 339 (1971)

[c7] V. Barger and D. Cline, Phenomenological Theories of High Energy Scattering (Benjamin, New York, 1969)

[c8] J. D. Stack, Phys. Rev. Letters 16, 286 (1966)

[c9] Omitted endnote

[c10] S. Chu and A. Hendry, Phys. Rev. Letters 25, 313 (1970) H. Harari, in Proceedings of the International Conference on Duality and Symmetry in Hadron Physics, edited by E. Gotsman (Weizmann Science Press of Israel, Jerusalem, 1971)

[c11] Omitted endnote

Physical Review D

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Separation of $N$ and $Δ$ Exchanges in $π N$ Scattering and Deduction of Amplitude Zeros

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Separation of N and Δ Exchanges in πN Scattering and Deduction of Amplitude Zeros

Abstract

References (11)

Separation of $N$ and $Δ$ Exchanges in $π N$ Scattering and Deduction of Amplitude Zeros