# A rigorous lower bound on the scattering amplitude at large angle

## TL;DR

This paper establishes a rigorous lower bound on the scattering amplitude at large angles in two-body processes, leveraging analyticity and positivity properties within local quantum field theory.

## Contribution

It provides the first rigorous lower bound on large-angle scattering amplitudes under minimal assumptions, advancing theoretical understanding in quantum field theory.

## Key findings

- Lower bounds for large-angle scattering amplitudes are proven.
- Appendix derives bounds for forward particle-particle and particle-antiparticle amplitudes.
- Results rely on analyticity and positivity, with minimal assumptions.

## 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.