Dark Matter in an Evanescent Three-Brane Randall-Sundrum Scenario

TL;DR

This work explores DM in an evanescent three-brane Randall–Sundrum model where DM resides on a deep IR (DIR) brane while the SM sits on a separate IR brane, enabling DM to freeze out via annihilations into radions and KK gravitons. The study derives the radion and KK graviton spectra and their couplings, computes annihilation channels (DMDM→rr, DMDM→rG_n, DMDM→G_nG_m, plus DMDM→SM), and analyzes cosmological and collider constraints to identify viable regions. It finds that thermal freeze-out can reproduce the observed DM abundance for a broad but constrained parameter space with $10\ \text{TeV} \lesssim \Lambda_{IR} \lesssim 10^3$ TeV and $0.1\ \text{TeV} \lesssim m_{DM} \lesssim$ a few TeV, with bulk channels often dominating over SM channels. The work highlights that future direct detection experiments and collider discoveries of radion/KK resonances could not only test this scenario but also hint at the underlying brane structure by revealing multiple resonances and their couplings.

Abstract

Apart from its gravitational interactions, dark matter (DM) has remained so far elusive in laboratory searches. One possible explanation is that the relevant interactions to explain its relic abundance are mainly gravitational. In this work we consider an extradimensional Randall-Sundrum scenario with a TeV-PeV IR brane, where the Standard Model is located, and a GeV-TeV deep IR (DIR) one, where the DM lies. When the curvatures of the bulk to the left and right of the IR brane are very similar, the tension of the IR brane is significantly smaller than that of the other two branes, and therefore we term it \evanescent". In this setup, the relic abundance of DM arises from the freezeout mechanism, thanks to DM annihilations into radions and gravitons. Focusing on a scalar singlet DM candidate, we compute and apply current and future constraints from direct, indirect and collider-based searches. Our findings demonstrate the viability of this scenario and highlight its potential testability in upcoming experiments. We also discuss the possibility of inferring the number of branes if the radion and several Kaluza-Klein graviton resonances are detected at a future collider.

Figures (14)

• Figure 1: Schematic representation of the three-brane setup used in this work in conformal coordinates.
• Figure 2: Couplings of the KK gravitons with matter in the IR brane (SM), $\Lambda_{\rm IR}^n$, as a function of the KK mode $n$ for different fixed values of $\Lambda_{\rm DIR}$, $\Lambda_{\rm IR}$ and $m_{1}$. The continuous blue line corresponds to the analytical function for $\Lambda_{\rm IR}^{n}$ in Eq. \ref{['eq:LambdaIR']} and takes physical values at the discrete blue dots, each one representing a KK mode. The orange dashed curves corresponds to the analytical approximation valid for $\xi x_n\ll1$.
• Figure 3: Branching ratios of the radion as a function of its mass. The lifetime $\tau$, shown in the right axis, is calculated for $\Lambda_{\rm IR}=100\, \text{TeV}$.
• Figure 4: Similar to Fig. \ref{['fig:decaysr']} for the decays of the first KK graviton for different values of $\Lambda_{\rm IR},\,\Lambda_{\rm DIR}$.
• Figure 5: Feynman diagrams for DM annihilations into SM particles.