A rigorous lower bound on the scattering amplitude at large angle

We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angles. This is based on the interplay of the analyticity of the amplitude and the positivity properties of its absorptive part. The assumptions are minimal, namely, those of local quantum field theory (in the case when dispersion relations hold). In the Appendix A, lower bounds for the forward particle-particle and particle-antiparticle amplitudes are obtained. This is of independent interest.