2018 Impact factor 4.843
Particles and Fields
Eur. Phys. J. C 17, 323-336
DOI 10.1007/s100520000459

The role of the input in Roy's equations for $\pi$-$\pi$ 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 $\pi$-$\pi$ 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