Dispersive approach to off-mass-shell ππ amplitudes

Abstract

It is shown that ππ amplitudes with one pion off its mass shell are determined by a set of linear integral equations in terms of physical amplitudes once off-shell adsorptive parts are known in the inelastic region. We show how this can be used in practice to obtain off-shell amplitudes in the low energy region. The arbitrariness of off-shell extensions is discussed; it is suppressed in the soft pion limit owing to Adler's self-consistency condition. Applications of our method to Adler-Weisberger type relations, and to off-shell effects in Chew-Low extrapolation experiments are discussed.