2019 Impact factor 4.389
Particles and Fields
Eur. Phys. J. C 10, 159-173
DOI 10.1007/s100529900086

One-channel Roy equations revisited

J. Gasser1 - G. Wanders2

1 Institut für Theoretische Physik, Universität Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland (e-mail: gasser@itp.unibe.ch)
2 Institut de Physique Théorique, Université de Lausanne, CH-1015 Lausanne, Switzerland (e-mail: gerard.wanders@ipt.unil.ch)

Received: 25 March 1999 / Published online: 15 July 1999

The Roy equation in the single-channel case is a nonlinear, singular integral equation for the phase shift in the low-energy region. We first investigate the infinitesimal neighborhood of a given solution, and then present explicit expressions for amplitudes that satisfy the nonlinear equation exactly. These amplitudes contain free parameters that render the non-uniqueness of the solution manifest. They display, however, an unphysical singularity at the upper end of the interval considered. This singularity disappears and uniqueness is achieved if one uses analyticity properties of the amplitudes that are not encoded in the Roy equation.

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