Gravitational scattering in the ADD model at high and low energies

Gravitational scattering in the ADD model is considered at both sub- and transplanckian energies using a common formalism. By keeping a physical cut-off in the KK tower associated with virtual KK exchange, such as the cut-off implied by a finite brane width, troublesome divergences are removed from the calculations in both energy ranges. The scattering behavior depends on three different energy scales: the fundamental Planck mass, the collision energy and the inverse brane width. The result for energies low compared to the effective cut-off (inverse brane width) is a contact-like interaction. At high energies the gravitational scattering associated with the extra dimensional version of Newton’s law is recovered.