Singularities of Scattering Amplitudes on Unphysical Sheets and Their Interpretation

Phys. Rev. 123, 692 – Published 15 July 1961
R. Blankenbecler, M. L. Goldberger, S. W. MacDowell, and S. B. Treiman


The analytic structure of two-particle scattering amplitudes on the unphysical sheet of the Riemann surface reached by crossing the two-particle cut is discussed. The singularities of the amplitudes there are shown to be poles and their physical interpretation is studied. The way in which bound states appear on the physical sheet in the Mandelstam representation, both as isolated poles and as cuts, is traced in detail. The properties of partial wave amplitudes and of the full amplitude as a function of energy and angle and of energy and momentum transfer are discussed. Finally, a few remarks are made in connection with unstable states.


  • Received 1 March 1961
  • Published in the issue dated July 1961

© 1961 The American Physical Society

Authors & Affiliations

R. Blankenbecler, M. L. Goldberger, S. W. MacDowell*, and S. B. Treiman

  • Palmer Physical Laboratory, Princeton University, Princeton, New Jersey

  • *Present address: Centro Brasileiro de Pesquisas, Fisicas, av Venceslau Braz. 71, Estado da Guanabara, Brasil.
  • Supported in part by the Air Force Office of Scientific Research, Air Research and Development Command.

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