Significant effects of second KK particles on LKP dark matter physics

TL;DR

In universal extra dimensions, second KK states can significantly modify LKP dark matter physics. By computing the annihilation cross section including the $s$-channel resonance from $h^{(2)}$ and solving the Boltzmann equation, the authors show that the annihilation rate is enhanced, reducing the relic density $ obreak \\Omega h^2$ and shifting the WMAP-compatible LKP mass to about $950$ GeV (roughly $900$–$1000$ GeV for $0.5\%<\delta<2\%$). They also discuss how second KK states affect coannihilation, indirect detection signals, and collider phenomenology, highlighting a robust, intrinsic resonance mechanism in UEDs. This work provides a concrete, testable framework linking KK physics to cosmological relic abundance and to potential observational signatures at colliders and in indirect detection experiments.

Abstract

We point out that Kaluza-Klein (KK) dark matter physics is drastically affected by second KK particles. In this work various interesting phenomena caused by the second KK modes are discussed. In particular, we reevaluate the annihilation cross section and thermal relic density of the KK dark matter quantitatively in universal extra dimensions, in which all the standard model particles propagate. In these models, the first KK mode of $B$ boson is a viable dark matter candidate by virtue of KK-parity. We demonstrate that the KK dark matter annihilation cross section can be enhanced, compared with the tree level cross section mediated only by first KK particles. The dark matter mass consistent with the WMAP observation is increased.

Figures (5)

• Figure 1: The resonant $B^{(1)}$ annihilation process mediated by $s$-channel $h^{(2)}$ into a zero mode (SM) particle--anti-particle pair $f\bar{f}$.
• Figure 2: The dominant one-loop diagrams leading to the resonant $B^{(1)}$ pair annihilation process mediated by $h^{(2)}$. Here $t$ is the (zero-mode) top quark, and $t^{(1)}, T^{(1)}$ and $g^{(1)}$ represent the first KK modes of left- and right-handed top quarks and gluon respectively.
• Figure 3: (a) Contour plot of the averaged annihilation cross section (multiplied by the relative velocity) for the LKP, $B^{(1)}$. (b) Contour plot of the ratio of the total averaged cross section to the tree level one. The masses of $B^{(1)}$ and $h^{(2)}$ are represented by $m$ and $m_h^{(2)}$ respectively. Here we set the temperature to be $T=m/25$.
• Figure 4: The predicted dark matter abundance $\Omega h^2$ as a function of the LKP mass $m$ including resonance (Tree + Res.) for $g_* = 100$. Here we set the cutoff scale to be $\Lambda R = 20$ and the mass splitting $\delta = 1\ \%$. For comparison, we show the tree level result (Tree). The $1 \sigma$ region of the relic abundance measured by WMAP is also shown: $\Omega h^2 = 0.110 \pm 0.006$. The allowed mass regions are highlightened in both cases.
• Figure 5: Resonant processes induced by second KK particles which influence (a) coannihilation, (b) indirect detection and (c) collider phenomenology. In the diagrams $e,l$ and $\gamma$ denote the zero mode (SM) electron, charged lepton and photon, $E^{(1)}, L^{(1)}$ and $B^{(1)}$ represent the first KK modes of right- and left-handed charged lepton, $B$ and Higgs boson, and $E^{(2)}, B^{(2)}$ and $W^{(2)}$ stand for the second KK modes of the right-handed charged lepton, $B$ and $W$ bosons.