Consistency Conditions on Models for High‐Energy Scattering

From unitarity, analyticity in t, and analyticity in E, a variety of conditions can be derived for the high‐energy behavior of a crossing symmetric two‐body scattering amplitude F(E,t). These conditions are studied as consistency conditions for a class of models for high‐energy scattering based on s...

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Bibliographic Details
Published in:Journal of mathematical physics 1967-01, Vol.8 (2), p.320-325
Main Author: Eden, R. J.
Format: Article
Language:English
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Summary:From unitarity, analyticity in t, and analyticity in E, a variety of conditions can be derived for the high‐energy behavior of a crossing symmetric two‐body scattering amplitude F(E,t). These conditions are studied as consistency conditions for a class of models for high‐energy scattering based on smoothly varying functions. For this class of models they lead to: (1) the Froissart bound without making explicit use of Martin's enlargement of the Lehmann ellipse, (2) conditions on the phase of the amplitude and its derivative with respect to t in the forward direction. As an example of the use of the phase conditions, it is shown how the Lehmann ellipse can be enlarged to give analyticity in the circle |t| < R, where R is fixed. Although the method is different, this result is closely related to the general results of Martin, but with our smoothness assumptions a little more detail can be stated about the behavior of F(E,t).
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1705198