Is the Lightest Kaluza-Klein Particle a Viable Dark Matter Candidate?

TL;DR

This work analyzes whether the Lightest Kaluza-Klein Particle (LKP) in universal extra dimensions (UED) can be a viable dark matter candidate. It develops relic-density predictions for two principal LKPs, the first KK photon $B^{(1)}$ and the first KK neutrino $\nu^{(1)}$, using standard freeze-out formalism and incorporating coannihilation with near-degenerate KK leptons via the effective cross-section framework. The study finds TeV-scale $B^{(1)}$ and $\nu^{(1)}$ can yield the correct relic density $\Omega_M \sim 0.33$, with specific mass windows that shift when coannihilation is included (e.g., $m_{KK}$ roughly in the range 0.6–1.1 TeV for $B^{(1)}$ with coannihilation, and 0.95–1.25 TeV for $\nu^{(1)}$ in the three-flavor case). It also discusses generalizations to six dimensions and outlines detection implications, underscoring that KK parity stabilizes the LKP and that TeV-scale LKPs could be probed at future colliders and indirect/d direct-detection experiments. The results provide a concrete, predictive DM scenario within a minimal extension of the SM, tying the dark matter scale to the compactification radius $R^{-1}$ of order TeV.

Abstract

In models with universal extra dimensions (i.e. in which all Standard Model fields, including fermions, propagate into compact extra dimensions) momentum conservation in the extra dimensions leads to the conservation of Kaluza--Klein (KK) number at each vertex. KK number is violated by loop effects because of the orbifold imposed to reproduce the chiral Standard Model with zero modes, however, a KK parity remains at any order in perturbation theory which leads to the existence of a stable lightest KK particle (LKP). In addition, the degeneracy in the KK spectrum is lifted by radiative corrections so that all other KK particles eventually decay into the LKP. We investigate cases where the Standard Model lives in five or six dimensions with compactification radius of TeV$^{-1}$ size and the LKP is the first massive state in the KK tower of either the photon or the neutrino. We derive the relic density of the LKP under a variety of assumptions about the spectrum of first tier KK modes. We find that both the KK photon and the KK neutrino, with masses at the TeV scale, may have appropriate annihilation cross sections to account for the dark matter, $Ω_M \sim 0.3$.

Figures (12)

• Figure 1: Prediction for $\Omega_{B^{(1)}} h^2$ as a function of the KK mass (when neglecting coannihilation). The upper horizontal region delimits the values of $\Omega h^2$ above which the contribution from ${B^{(1)}}$ to the energy density would overclose the universe. The lower horizontal band denotes the region $\Omega =0.33\pm0.035$ (using $h=0.69\pm 0.06$) and defines the KK mass window if all the dark matter is to be accounted for by the $B^{(1)}$ LKP.
• Figure 2: Prediction for $\Omega_{\nu^{(1)}} h^2$ as a function of the KK mass. The solid lines are for $\nu^{(1)}$ alone (in the one and three family cases) and the dotted ones correspond to the cases where coannihilation with degenerate $e^{(1)}_L$ is included.
• Figure 3: Prediction for $\Omega_{B^{(1)}} h^2$ as in Figure \ref{['fig:omegaphoton']}. The solid line is the case for $B^{(1)}$ alone, and the dashed and dotted lines correspond to the case in which there are one (three) flavors of nearly degenerate $e^{(1)}_R$. For each case, the black curves (upper of each pair) denote the case $\Delta=0.01$ and the red curves (lower of each pair) $\Delta=0.05$.
• Figure 4: Feynman diagrams for $B^{(1)} B^{(1)}$ annihilation into fermions.
• Figure 5: Feynman diagrams for $B^{(1)} B^{(1)}$ annihilation into Higgs scalar bosons.