Lower bound on inelasticity in pion-pion scattering

Abstract

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=4m²_π+ε, (ε>0)—except for cuts prescribed by the Mandelstam representation for t≥4m²_π, u≥4m²_π, and bounded by sN on the boundary of this domain—we prove that for s→∞, σ_inel(s)>const/s^5/2exp[−√s/4(N+5/2)ln s].