Angular Distributions from Multiparticle Production Models

Donald E. Lyon, Jr; Clifford Risk; Don M. Tow

doi:10.1103/PhysRevD.3.104

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Angular Distributions from Multiparticle Production Models

Donald E. Lyon, Jr.

Clifford Risk and Don M. Tow

Department of Physics, University of Michigan, Ann Arbor, Michigan 48104

Lawrence Radiation Laboratory, University of California, Berkeley, California 94720

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Phys. Rev. D 3, 104 – Published 1 January, 1971

DOI: https://doi.org/10.1103/PhysRevD.3.104

Abstract

Using $\exp (- A {p_{T}}^{2}) \frac{d^{3} p}{E}$ as the momentum distribution of secondaries produced in ultrahigh-energy collisions—a result predicted by the multiperipheral model, by Feynman's parton model, and by Cheng and Wu's consideration of hadrons as extended objects with many internal degrees of freedom—we obtain the characteristic features of the angular distribution. We discuss the dependence on incident energy, mass of secondaries, and the value of $A$ . We find that the c.m. angular distribution on the variable $η_{c . m .} = - \ln tan \frac{1}{2} θ_{c . m .}$ . has a two-bump structure, whereas the lab angular distribution in $η = - \ln tan θ_{l}$ is flat. This difference leads us to a discussion of the transformation between c.m. and lab angular distributions. We find that the usual relativistic approximation of the exact transformation leads to incorrect results. Finally, we point out that these momentum and angular distributions approach limiting distributions.

References (13)

L. Bertocchi, S. Fubini, and M. Tonin, Nuovo Cimento 25, 626 (1962) D. Amati, A. Stanghellini, and S. Fubini, ibid. 26, 896 (1962)
J. S. Ball and G. Marchesini, Phys. Rev. 188, 2508 (1969) D. M. Tow, Phys. Rev. D 2, 154 (1970) G. F. Chew, T. W. Rogers, and D. R. Snider, ibid. 2, 765 (1970)
G. F. Chew and A. Pignotti, Phys. Rev. 176, 2112 (1968) G. F. Chew, M. L. Goldberger, and F. E. Low, Phys. Rev. Letters 22, 208 (1969) I. G. Halliday, Nuovo Cimento 60A, 177 (1969) I. G. Halliday and L. M. Saunders, ibid. 60A, 494 (1969) P. D. Ting, LRL Report No. UCRL-19802, 1970 (unpublished)
R. P. Feynman, in Proceedings of the Third International Conference High-Energy Collisions, Stony Brook, 1969, edited by C. N. Yang (Gordon and Breach, New York, 1969)
H. Cheng and T. T. Wu, Phys. Rev. Letters 23, 1311 (1969)
K. N. Erickson, thesis, Colorado State University, 1970 (unpublished) L. W. Jones et al., report presented at the sixth Interamerican Seminar on Cosmic Rays, La Paz, Bolivia, 1970 (unpublished)
Omitted endnote
L. Caneschi, D. E. Lyon, Jr., and Clifford Risk, Phys. Rev. Letters 25, 774 (1970)
[2]
Omitted endnote
O. Czyzewski and A. Krzywicki, Nuovo Cimento 30, 603 (1963) E. I. Daibog and I. L. Rozental, Yadern Fiz. 10, 818 (1969) [Soviet J. Nucl. Phys. 10, 473 (1970)]
P. Ciok et al., Nuovo Cimento 8, 166 (1958) ibid.10, 741 (1958) G. Cocconi, Phys. Rev. 111, 1699 (1958) K. Niu, Nuovo Cimento 10, 944 (1958)
J. Benecke, T. T. Chou, C. N. Yang, and E. Yen, Phys. Rev. 188, 2159 (1969)

[c1] L. Bertocchi, S. Fubini, and M. Tonin, Nuovo Cimento 25, 626 (1962) D. Amati, A. Stanghellini, and S. Fubini, ibid. 26, 896 (1962)

[c2] J. S. Ball and G. Marchesini, Phys. Rev. 188, 2508 (1969) D. M. Tow, Phys. Rev. D 2, 154 (1970) G. F. Chew, T. W. Rogers, and D. R. Snider, ibid. 2, 765 (1970)

[c3] G. F. Chew and A. Pignotti, Phys. Rev. 176, 2112 (1968) G. F. Chew, M. L. Goldberger, and F. E. Low, Phys. Rev. Letters 22, 208 (1969) I. G. Halliday, Nuovo Cimento 60A, 177 (1969) I. G. Halliday and L. M. Saunders, ibid. 60A, 494 (1969) P. D. Ting, LRL Report No. UCRL-19802, 1970 (unpublished)

[c4] R. P. Feynman, in Proceedings of the Third International Conference High-Energy Collisions, Stony Brook, 1969, edited by C. N. Yang (Gordon and Breach, New York, 1969)

[c5] H. Cheng and T. T. Wu, Phys. Rev. Letters 23, 1311 (1969)

[c6] K. N. Erickson, thesis, Colorado State University, 1970 (unpublished) L. W. Jones et al., report presented at the sixth Interamerican Seminar on Cosmic Rays, La Paz, Bolivia, 1970 (unpublished)

[c7] Omitted endnote

[c8] L. Caneschi, D. E. Lyon, Jr., and Clifford Risk, Phys. Rev. Letters 25, 774 (1970)

[c9] [2]

[c10] Omitted endnote

[c11] O. Czyzewski and A. Krzywicki, Nuovo Cimento 30, 603 (1963) E. I. Daibog and I. L. Rozental, Yadern Fiz. 10, 818 (1969) [Soviet J. Nucl. Phys. 10, 473 (1970)]

[c12] P. Ciok et al., Nuovo Cimento 8, 166 (1958) ibid.10, 741 (1958) G. Cocconi, Phys. Rev. 111, 1699 (1958) K. Niu, Nuovo Cimento 10, 944 (1958)

[c13] J. Benecke, T. T. Chou, C. N. Yang, and E. Yen, Phys. Rev. 188, 2159 (1969)

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Angular Distributions from Multiparticle Production Models

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