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
Abstract
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.
Copyright Springer-Verlag
