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Multiperipheral Integral Equation for Forward Scattering and Its Properties

Stephen Pinsky*

William I. Weisberger†

  • Department of Nuclear Physics, Weizmann Institute of Science, Rehovoth, Israel

  • Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540

  • *Present address: University of Utah, Salt Lake City, Utah 84112.
  • †Permanent Address: Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, N. Y. 11790.
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Phys. Rev. D 2, 2365 – Published 15 November, 1970

DOI: https://doi.org/10.1103/PhysRevD.2.2365

Abstract

We study a multiperipheral integral equation for forward scattering. Positivity of the kernel enables us to show that the leading asymptotic behavior of the forward elastic amplitude at high energy is determined by a nondegenerate factorizable J-plane pole. An iteration formula for numerical calculation of the position of the leading pole is given. The constraints imposed by demanding self-consistency between the positions and the residues of the leading input and output poles are examined. The average multiplicity of secondaries grows logarithmically with total barycentric energy in the multiperipheral model. The coefficient of logarithmic growth is given explicitly in terms of the integral kernel. Conditions on the kernel are stated which guarantee that the leading output trajectory has positive slope at t=0. In the strong-ordering or weak-coupling limit the trajectories are classified according to an additional quantum number m, analogous to Toller's M quantum number. Only m=0 trajectories contribute to the total cross section.

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References (16)

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Phys. Rev. D 2, 2365– Published 15 November, 1970
  • Received 8 December 1969

© 1970 American Physical Society

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