New lower bounds on scattering amplitudes: non-locality constraints

TL;DR

This paper extends known bounds on elastic scattering amplitudes, allowing for exponential growth and deriving new limits in the Regge regime, with implications for quantum gravity and non-locality in high-energy physics.

Contribution

It introduces generalized lower bounds on scattering amplitudes under broader assumptions, including exponential growth, and explores their implications for non-locality and ultraviolet completions.

Findings

Derived a more general lower bound allowing exponential growth.

Established new bounds in the Regge regime for elastic scattering.

Discussed implications for gravitational scattering and non-locality.

Abstract

Under reasonable working assumptions including the polynomial boundedness, one proves the well-known Cerulus-Martin lower bound on how fast an elastic scattering amplitude can decrease in the hard-scattering regime. In this paper we consider two non-trivial extensions of the previous bound. (i) We generalize the assumption of polynomial boundedness by allowing amplitudes to exponentially grow for some complex momenta and prove a more general lower bound in the hard-scattering regime. (ii) We prove a new lower bound on elastic scattering amplitudes in the Regge regime, in both cases of polynomial and exponential boundedness. A bound on the Regge trajectory for negative momentum transfer squared is also derived. We discuss the relevance of our results for understanding gravitational scattering at the non-perturbative level and for constraining ultraviolet completions. In particular, we use the new bounds as probes of non-locality in black-hole formation, perturbative string theory, classicalization, Galileons, and infinite-derivative field theories, where both the polynomial boundedness and the Cerulus-Martin bound are violated.