Spin-2 Kaluza-Klein scattering in a stabilized warped background
R. Sekhar Chivukula (Department of Physics and Astronomy, University of California, 9500 Gilman Drive, San Diego, California 92093, USA); Dennis Foren (Department of Physics and Astronomy, University of California, 9500 Gilman Drive, San Diego, California 92093, USA); Kirtimaan A. Mohan (Department of Physics and Astronomy, Michigan State University, 567 Wilson Road, East Lansing, Michigan 48824, USA); Dipan Sengupta (Department of Physics and Astronomy, University of California, 9500 Gilman Drive, San Diego, California 92093, USA, ARC Centre of Excellence for Dark Matter Particle Physics, Department of Physics, University of Adelaide, South Australia 5005, Australia); Elizabeth H. Simmons (Department of Physics and Astronomy, University of California, 9500 Gilman Drive, San Diego, California 92093, USA)
Scattering amplitudes involving massive spin-2 particles typically grow rapidly with energy. In this paper we demonstrate that the anomalous high-energy growth of the scattering amplitudes cancel for the massive spin-2 Kaluza-Klein modes arising from compactified five-dimensional gravity in a stabilized warped geometry. Generalizing previous work, we show that the two sum rules which enforce the cancellations between the contributions to the scattering amplitudes coming from the exchange of the (massive) radion and those from the exchange of the tower of Goldberger-Wise scalar states (admixtures of the original gravitational and scalar fields of the theory) still persist in the case of the warping which would be required to produce the hierarchy between the weak and Planck scales in a Randall-Sundrum model. We provide an analytic proof of one combination of these generalized scalar sum rules and show how the sum rule depends on the Einstein equations determining the background geometry and the mode-equations and normalization of the tower of physical scalar states. Finally, we provide a consistent and self-contained derivation of the equations governing the physical scalar modes, and we list, in appendixes, the full set of sum rules ensuring proper high-energy growth of all massive spin-2 scattering amplitudes.
