A Universal Kaluza-Klein Graviton Cascade Rate

Abstract

We obtain a general decay rate between Kaluza-Klein (KK) gravitons, resolving an ambiguity in the literature concerning these decays. The amplitude is determined not only by the mass $m_n$ of the decaying particle, but also by the momentum $q$ of the decay products in the parent's rest frame, and is suppressed relative to the expression commonly used in the literature by $(q/m_n)^2$. Phase space gives a general $q^5$-dependent decay rate obtained earlier in Randall-Sundrum models. We identify the cancellation that gives this result as a consequence of the massless 5D graviton, and argue for its universality even with scalar-induced KK violation by absorbing non-minimally coupled scalar fields into the warp-factor. This has significant implications for the potential for cascading dark matter models, and can be used to rule out existing Dark Dimension models, because the rapid cascade that was needed to evade constraints is severely suppressed. The amplitude is established by an explicit calculation that accounts for the backreaction of fields and branes and applies broadly to non-minimal diffeomorphism invariant two-derivative couplings between scalar fields and gravity.