Classical ultra-relativistic scattering in ADD

TL;DR

This paper computes the classical differential cross-section for high-energy small-angle gravitational scattering in models with extra dimensions, showing finiteness and connection to quantum eikonal approximation.

Contribution

It provides a finite, non-perturbative classical calculation of gravitational scattering in models with extra dimensions, linking it to quantum ladder graph summation.

Findings

Finite classical differential cross-section obtained without ultraviolet cutoff.

Correspondence established between classical and quantum eikonal amplitudes.

Results reproduce known cases when extra dimensions are absent.

Abstract

The classical differential cross-section is calculated for high-energy small-angle gravitational scattering in the factorizable model with toroidal extra dimensions. The three main features of the classical computation are: (a) It involves summation over the infinite Kaluza-Klein towers but, contrary to the Born amplitude, it is finite with no need of an ultraviolet cutoff. (b) It is shown to correspond to the non-perturbative saddle-point approximation of the eikonal amplitude, obtained by the summation of an infinite number of ladder graphs of the quantum theory. (c) In the absence of extra dimensions it reproduces all previously known results.