Model-independent lower bounds for massless-particle scattering

We examine massless pion-pion, neutrino-neutrino, and light-by-light scattering within the context of a dispersion approach to the interaction of massless particles. We assume the existence of a fixed-t dispersion relation with a finite number of subtractions for t≤0, unitarity, crossing symmetry, and the convergence of helicity expansions in the physical region. All three processes have a zero at threshold in the forward amplitude; for massless pions it is the Adler zero and for neutrinos and photons it is a kinematic zero. We demonstrate that the forward scattering amplitudes and total cross sections have the asymptotic lower bounds |F(s, 0)|≥ const and σtₒt(s)≥ const/s². We obtain the same result for scattering of neutrinos on electrons. We also generalize the upper bounds obtained by Dolgov, Zakharov, and Okun for lepton-lepton scattering to massless π-π and light-by-light scattering.