Abstract
The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.
Highlights
The production of spin-2 particles from matter has not received as much attention
This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions
The breakdown of the theory at high energies is already expected at the Lagrangian level but studies of the scattering amplitudes of spin-2 fields show a rapid growth in the high energy limit that indicates the break-down of perturbativity at scales much lower than the fundamental scale of the theory
Summary
We analyze a simplified version of the Randall-Sundrum model [6] with a toy matter sector instead of the full Standard Model field content. Our matter Lagrangian consists of a single scalar with only gravitational interactions. This setup is sufficient to make the point we are interested in and we expect that our key observations will carry over to a more realistic construction with minor modifications. Our somewhat compressed introduction of the Randall-Sundrum model follows [15]; for a more in-depth introduction see for example [27,28,29]
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