Unitarity in KK-graviton production, a case study in warped extra-dimensions

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.

Dark matter interacting via a massive spin-2 mediator in warped extra-dimensions

“…These clashing expectations can be resolved by realizing that the 4D theory that arises from the KK-decomposition of extra dimensions does not just contain a single spin-2 field but a tower of KK-gravitons and their interactions instead. We recently analyzed the high energy limit of KK-graviton production in warped extra-dimensions and found that the contribution of the other KK-gravitons conspire to cancel the contributions that grow faster than s 1 [18]. 2 Naturally, this will have an impact on the DM production rates and can change the amount of produced in the early Universe considerably.…”

“…the 5D graviton, and a scalar perturbation r, the so-called radion. A detailed discussion of this expansion and the resulting Lagrangian up to third order in the fields can for example be found in [18,21]. Second, one utilizes a Kaluza-Klein decomposition of the 5D graviton…”

“…In addition, we need the three-point interactions between gravitons and radions and the next higher term in the expansion of the interaction with matter. The Langrangian and the Feynman rules for these can be found in [18]. Here we only briefly comment on the coefficients of these interactions.…”

“…A set of representative Feynman diagrams for the case of annihilations into two gravitons is shown in figure 4. The relevant Feynman rules and expressions for the coefficients of the graviton/radion interactions are reported in the appendix of [18]. Treating processes with external gravitons correctly is subtle.…”

“…Treating processes with external gravitons correctly is subtle. In the following, we briefly recapitulate the results of [18] where we discussed the challenges associated with graviton production in the Randall-Sundrum in detail, see also [20,21] for a related discussion on graviton scattering.…”