Gravitational Scattering in the ADD-model Revisited

Gravitational scattering in the ADD-model is studied and it is argued that no cut-off is needed for the exchange of virtual Kaluza–Klein modes. By introduction of a small coordinate in the extra dimensions a unique form of the Kaluza–Klein-summed propagator is found for an odd number of extra dimensions. The matrix element corresponding to this propagator can also (as opposed to the cut-offed version) be Fourier transformed to position space, giving back the extra-dimensional version of Newton’s law. For an even number of extra dimensions the propagator is found by requiring that Newton’s law should be recovered.