On the manifold of solutions of Roy's equations for pion-pion scattering: the neighbourhood of the physical p-wave

The pion-pion P-wave below 1 GeV given by experiment is assumed to be a solution of Roy's P-wave equation. It is shown that it is not an isolated solution but belongs to a manifold of solutions. In a particular way of formalizing the problem, this manifold is a two-dimensional one. The solutions which are in the neighbourhood of the physical amplitude exhibit a resonance whose position and width differ slightly from those of the rho meson. These results are obtained by applying a general method giving the solution of a Roy-type equation which are infinitesimally close to a given one. (Auth.)