High Energy Scattering in Higher Dimensional Theories

TL;DR

This paper explores the high energy scattering amplitudes in higher-dimensional spacetimes, deriving new bounds and establishing zero-free regions in the complex t-plane, advancing understanding of scattering behavior beyond four dimensions.

Contribution

It introduces new bounds on scattering amplitudes in higher dimensions and proves the existence of zero-free regions in the complex t-plane, extending previous results.

Findings

Derived a new bound on scattering amplitudes for |t|<T_0

Proved the existence of a zero-free region in the complex t-plane

Established stronger bounds for the absorptive amplitude in a specific domain

Abstract

The high energy behavior of scattering amplitudes in spacetime dimensions, $D>4$, is investigated. The bound on total cross sections, $\sigma_t \le Constant~(los s)^{D-2}$, $D\ge 4$ has been obtained in the past under usual assumptions. I derive new bound on scattering amplitudes in the region $|t|<T_0$, $t$ being momentum transfer squared. and $T_0$ is a constant. The existence of a zero-free region for the amplitude in complex t-plane, is proved. I prove stronger upper and lower bounds for the absorptive amplitude in the domain $0<t<T_0$.