Scattering Lengths and Medium and High Energy $\pi \pi$ Scattering

Abstract

Medium and high energy absorptive parts contribute to dispersive expressions for D- wave scattering lengths, $a_2^0$ and $a_2^2$. For the model employed by Basdevant, Frogatt and Peterson we find the D- wave driving term contributions to the D- wave scattering lengths are $1.8\cdot 10^{-4}$ to $a_2^0$ and $0.4\cdot 10^{-4}$ to $a_2^2$, roughly $10\%$ and $30\%$ of their respective central experimental values. Inequivalent sets of sum rules are used as a compelling test of the consistency of the model for which crossing symmetry is not guaranteed. Results for the F- wave scattering length $a_3^1$ are presented, completing the recent Roy equation analysis of \pipi scattering in the range for $a_0^0$ favored by standard chiral perturbation theory.

31 pages plain latex to be run twice with 3 embedded figures using epsf