New Representation of the Scattering Amplitude

Abstract

A new representation of the scattering amplitude that has good analytic properties, Regge asympotic behavior, and an arbitrary double-spectral boundary is proposed. The representation automatically yields partial waves with the correct threshold behavior for both their real and imaginary parts. The presence of the correct double-spectral boundary should be very important in decay problems, where an unstable external particle considerably modifies the analytic properties of the amplitude. This representation in its simplest version is applied to pion-pion scattering. Unitarity is enforced near threshold. By using the (degenerate) $\ensuremath{\rho}$- and $f$-meson trajectories, the $\ensuremath{\rho}$ width, and the Adler self-consistency condition, the three isotopic scattering lengths, the $f$ width, and the Regge-scale mass are predicted.