Lower bound on inelasticity in pion-pion scattering

Assuming that the pion-pion scattering amplitude and its absorptive part are analytic inside an ellipse in the complex t plane with foci t = 0, u = 0 and right extremity t = 4m(pi)(2) + epsilon, (epsilon > 0)-except for cuts prescribed by the Mandelstam representation for t >= 4m(pi)(2), u >= 4m(pi)(2), and bounded by s(N) on the boundary of this domain- we prove that for s -> infinity, sigma(inel)(s) > const/s(5/2) exp [- root s/4 (N + 5/2) ln s].