High Energy Scattering in Higher Dimensional Theories

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 $\mathrm{\mid }t\mathrm{\mid }<T_0$, $t$ 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 $0<t<T_0$.