The Abundance of Kaluza-Klein Dark Matter with Coannihilation

TL;DR

This work computes the thermal relic abundance of the KK photon in five-dimensional Universal Extra Dimensions, explicitly incorporating coannihilation with all near-degenerate first-level KK states. By solving the Boltzmann equation with an effective cross section that weights all relevant (co)annihilation channels, the authors show that coannihilation can significantly alter the relic density when mass splittings are small (|δ| ≲ 0.2), broadening the KK photon mass range compatible with cosmological data. The study analyzes three spectra, including a CMS-inspired radiative correction spectrum, and finds that degeneracy with strongly interacting KK states can push the viable KK photon mass up to several TeV, while degeneracy with leptons alone yields a lower bound near ~540–570 GeV. Overall, the results highlight the critical role of the level-1 KK mass spectrum in determining dark matter viability and provide a framework to connect collider-accessible spectra with cosmological relic density observations.

Abstract

In Universal Extra Dimension models, the lightest Kaluza-Klein (KK) particle is generically the first KK excitation of the photon and can be stable, serving as particle dark matter. We calculate the thermal relic abundance of the KK photon for a general mass spectrum of KK excitations including full coannihilation effects with all (level one) KK excitations. We find that including coannihilation can significantly change the relic abundance when the coannihilating particles are within about 20% of the mass of the KK photon. Matching the relic abundance with cosmological data, we find the mass range of the KK photon is much wider than previously found, up to about 2 TeV if the masses of the strongly interacting level one KK particles are within five percent of the mass of the KK photon. We also find cases where several coannihilation channels compete (constructively and destructively) with one another. The lower bound on the KK photon mass, about 540 GeV when just right-handed KK leptons coannihilate with the KK photon, relaxes upward by several hundred GeV when coannihilation with electroweak KK gauge bosons of the same mass is included.

Figures (4)

• Figure 1: Relic abundance of KK dark matter as a function of mass after including no coannihilation (black; right-most solid line), coannihilation of $B^{(1)}$ with all leptons (blue; left-most pair of solid and dashed lines), and all electroweak particles (red; middle pair of solid and dashed lines), assuming in each case that all coannihilating particles have the same mass $m_{\gamma^{(1)}}(1+\delta)$. The solid (dashed) lines show the values for $\delta = 0.01$$(0.05)$ for the cases with coannihilation. Notice that for the case including KK electroweak gauge bosons, the abundance as a function of mass is smaller for the smaller mass splitting $\delta = 0.01$, unlike the case with just KK leptons, since the effects of coannihilation of these two sets of KK particles somewhat compensate for each other in the relic abundance calculation.
• Figure 2: Relic abundance of KK dark matter as a function of mass after including coannihilation of $B^{(1)}$ with all non-strongly interacting particles and quarks (blue), and all level one particles (red) assuming in each case that all coannihilating particles have the same mass $m_{\gamma^{(1)}} (1 + \delta)$. The solid and dashed lines show the values for $\delta = 0.01$, and $\delta = 0.05$.
• Figure 3: Magnitudes of all cross sections, using $m_{KK}=1$ TeV, $x_f=25$, and all couplings taken at the scale $M_Z$. Here each color represents a particular particle species (see legend), and the x-axis indicates with which particle the (co)annihilation is occurring. For example, a blue dot above the text $e_L$ is the coannihilation cross section of $B^{(1)} \equiv \gamma^{(1)}$ with $e_L$. Only 2 families of fermions are shown, as this is sufficient to show the difference between annihilation between members of the same family, and coannihilation between members of different families. The annihilation cross sections for fermions, $W$ and its scalar counterpart $w$ have been weighted by a factor of $1/2$ to account for the two helicities. In general the coannihilation cross sections are smaller than the annihilation ones, (and more numerous) so that usually adding more coannihilating particles decreases the effective cross section. However, as the SU(2) coupling is stronger than the U(1) coupling, and as it also opens more channels, when scalars and gauge bosons, whose annihilation cross sections are quite large, are added, the average cross section increases.
• Figure 4: The calculated $\gamma^{(1)}$ mass yielding a thermal relic abundance consistent with WMAP observations is shown in the bottom graph using as a function of $\Lambda R$. This result was calculated using a simplified spectrum of the first KK level consisting of four sub-levels that vary logarithmically with $\Lambda R$, shown in the top graph. The ratios are from top to bottom: the KK gluon, the KK quarks, the KK electroweak gauge bosons, and the KK leptons and scalars, divided by the KK photon mass. The black dashed line corresponds to $\delta = 0.05$ for reference. In the bottom graph, including increasing numbers of particles at the first KK level are shown with the four lines labeled in the legend. The solid straight black line (the line at the top on the far right) shows the the case without coannihilation for reference. All level one KK particles except for the leptons and scalars become rapidly irrelevant to the relic abundance calculation once $\Lambda R \gtrsim 100$.