Persistence of the Castillejo-Dalitz-Dyson Ambiguity in Relativistic Crossing-Symmetric Amplitudes

D. Atkinson and Robert Lee Warnock
Phys. Rev. 188, 2098 – Published 25 December 1969
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Abstract

The relativistic equations expressing analyticity, crossing, and unitarity are analyzed without approximations. An infinite family of solutions is constructed, corresponding to a Castillejo-Dalitz-Dyson (CDD) ambiguity in the s wave. This ambiguity is in addition to the one resulting from arbitrary inelastic functions. The amplitudes constructed have nonvanishing single spectral functions, and this implies that a Kronecker δ is present in the angular-momentum plane. This relation between CDD poles and the Kronecker δ is proved only within a certain limited range of the coupling strength. A computational program for reaching the interesting domain of large couplings is outlined. In the latter domain it is not expected that all CDD poles entail Kronecker δ's in the l plane.

  • Received 11 August 1969

DOI:https://doi.org/10.1103/PhysRev.188.2098

©1969 American Physical Society

Authors & Affiliations

D. Atkinson*

  • Argonne National Laboratory, Argonne, Illinois 60439

Robert Lee Warnock

  • Illinois Institute of Technology, Chicago, Illinois 60616 and Argonne National Laboratory, Argonne, Illinois 60439

  • *Present address: CERN, Geneva.

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Issue

Vol. 188, Iss. 5 — December 1969

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