Asymptotic total cross-sections and positivity in meson-meson scattering

Abstract

Starting from the recent experimental analysis of elastic ππ and Kπ scatterings, we derive for both processes the (unique) analytic function which best approximates the data, satisfies the requirement imposed by unitarity and generates a constant asymptotic total cross-section. Assuming that the asymptotic regime sets up particularly quickly at imaginary ν≃(s−u)/4, we predict the values of these cross-sections. Our prediction is σ∞ππ≃σ∞κπ≃(9÷12) mb.