Low-Momentum-Transfer Pion-Pion Scattering

Abstract

High-energy effects at low momentum transfer, both in the direct and in the crossed channel, are introduced into a self-consistent calculation of low-energy $\pi -\pi$ scattering. These effects are assumed to be dominated by top-level Regge trajectories. The general method consists of combining the generalized Chew-Mandelstam and Ball-Wong techniques with self-consistency. It can be extended to complex angular momenta and thereby used to calculate the parameters of the assumed Regge trajectories. A rough selfconsistent calculation gives a mass of 712 MeV and a half-width of about 75 MeV for the $\rho$ meson, and a value of 15 mb for the total cross section at very high energies.