Solution of ap-Wave Equation for Pion-Pion Scattering

Abstract

A fixed-momentum-transfer dispersion relation is used in a self-consistent calculation of the $\rho$ meson. An expansion of the scattering amplitude in terms of a new variable, introduced by a conformal transformation, forms the starting point of the present calculation, and this expansion converges throughout the physical region. A self-consistent $p$-wave resonance is found at 340 MeV. It is concluded that the $\rho$ meson is not capable of producing itself self-consistently and that some other mechanism is responsible for the 750-MeV $p$-wave resonance observed in the $\pi -\pi$ system.