DOI 10.1007/s100520000459
The role of the input in Roy's equations for
-
scattering
G. Wanders
Institut de Physique Théorique, Université de Lausanne,
1015 Lausanne, Switzerland (e-mail: gerard.wanders@ipt.unil.ch)
Received: 9 May 2000 / Published online: 31 August 2000 - © Springer-Verlag 2000
Abstract
The Roy equations determine the S- and P-wave
-
phase shifts on a low energy interval. They allow
the derivation
of threshold parameters from experimental data. We examine the
solutions of
these equations that are in the neighborhood of a given solution
by means of a
linearization procedure. An updated survey of known results on
the dimension
of the manifold of solutions is presented. The solution is unique
for a low
energy interval with upper end at 800MeV. We determine its
response
to small
variations of the input: S-wave scattering lengths and absorptive
parts above
800MeV. We confirm the existence of a universal curve of solutions
in the
plane of the S-wave scattering lengths and provide a control
of the decrease
of the influence of the input absorptive parts with increasing
energy. A
general result on the suppression of unphysical singularities
at the upper end
of the low energy interval is established and its practical implications
are
discussed.
Copyright Società Italiana di Fisica, Springer-Verlag 2000