Abstract
We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angle. 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 Appendix A, lower bounds for the forward particle-particle and particle-antiparticle amplitudes are obtained. This is of independent interest.
Highlights
In 1963, Cerulus and one of us (A.M.) obtained a lower bound on the scattering amplitude at large angles [1]
We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angles
Things are not as simple as that because the lower bound on the scattering amplitude is only for discrete values of the energy; even if we assume that everything is continuous, we do not know if, precisely, for these discrete values, the absorptive part in the ellipse is bounded by s2
Summary
In 1963, Cerulus and one of us (A.M.) obtained a lower bound on the scattering amplitude at large angles [1]. Things are not as simple as that because the lower bound on the scattering amplitude is only for discrete values of the energy; even if we assume that everything is continuous, we do not know if, precisely, for these discrete values, the absorptive part in the ellipse is bounded by s2. To overcome this problem we replace the scattering amplitude by an average over some energy interval.
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