Virtual gravitons and brane field scattering in the RS model with a small curvature

TL;DR

This paper analyzes how virtual Kaluza-Klein gravitons influence high-energy scattering in the Randall-Sundrum model with small curvature, deriving an analytical amplitude expression that accounts for graviton widths.

Contribution

It provides a new analytical expression for the scattering amplitude involving virtual KK gravitons in the RS model with small curvature, considering nonzero graviton widths.

Findings

Replacing the resonance series with a continuous mass distribution is incorrect outside trans-Planckian energies.

The derived amplitude expression accurately accounts for narrow low-mass graviton resonances.

The approach clarifies the limitations of continuum approximations in the RS model.

Abstract

The contribution of virtual s-channel Kaluza-Klein (KK) gravitons to high energy scattering of the SM fields in the Randall-Sundrum (RS) model with two branes is studied. The small curvature option of the RS model is considered in which the KK gravitons are narrow low-mass spin-2 resonances. The analytical tree-level expression for a process-independent gravity part of the scattering amplitude is derived, accounting for nonzero graviton widths. It is shown that one cannot get a correct result, if a series of graviton resonances is replaced by a continuous mass distribution, in spite of the small graviton mass splitting. Such a replacement appeared to be justified only in the trans-Planckian energy region.