A treatment of meson pair production in γγ collisions including inelasticity and current algebra

Abstract
We have considered two problems posed by dispersive approaches to γγ → ππ and γγ → KK^- amplitudes, namely the introduction of inelastic unitarity and the ambiguity in partial wave dispersion relation subtractions. Introducing an (R, φ) representation for ππ amplitudes, we hare transformed inelastic unitarity into an inhomogeneous Hilbert-Riemann problem, completely defined by one subtraction and by the knowledge of meson-meson partial amplitudes ; subtractions have then been fixed imposing off-mass-shell current algebra limits both for one and two massless external mesons. Predictions on the S wave amplitudes have also been derived from the recent analysis of meson-meson scattering by Protopopescu et al.