Kaluza-Klein Dark Matter and the Positron Excess

Abstract

The excess of cosmic positrons observed by the HEAT experiment may be the result of Kaluza-Klein dark matter annihilating in the galactic halo. Kaluza-Klein dark matter annihilates dominantly into charged leptons that yield a large number and hard spectrum of positrons per annihilation. Given a Kaluza-Klein dark matter particle with a mass in the range of 300-400 GeV, no exceptional substructure or clumping is needed in the local distribution of dark matter to generate a positron flux that explains the HEAT observations. This is in contrast to supersymmetric dark matter that requires unnaturally large amounts of dark substructure to produce the observed positron excess. Future astrophysical and collider tests are outlined that will confirm or rule out this explanation of the HEAT data.

Figures (3)

• Figure 1: The positron spectrum from generic particle dark matter annihilations, prior to propagation, for selected annihilation modes with $m_{\rm DM} = 300$ GeV. Solid, dot-dash, dotted and dashed lines correspond to the positron spectrum per annihilation into $\mu^+ \mu^-$, $\tau^+\tau^-$, $b \bar{b}$ and gauge bosons, respectively. Charged lepton final states clearly produce a considerably harder spectrum of positrons than in other modes. The spectrum for annihilation into $e^+ e^-$ (not shown) is trivially a delta function at an energy equal to the dark matter particle mass.
• Figure 2: The positron fraction from annihilation of KKDM is shown as a function of positron energy. The solid and dashed lines represent 300 and 600 GeV $B^{(1)}$s, respectively. The annihilation rate was treated as a free parameter, used for normalization. The dotted line represents the background predicted with no contribution from dark matter annihilation. The error bars shown are from the 1994-95 and 2000 HEAT flights. The propagation parameters $K(E_{e^{+}}) = 3.3 \times 10^{28} (E_{e^{+}}/1\,\rm{GeV})^{0.47} \, \rm{cm}^2/\rm{s}$, $b(E_{e^{+}}) = 10^{-16} (E_{e^{+}}/1\,\rm{GeV})^2 \,\, \rm{GeV/s}$ and $L=4\,$kpc were used.
• Figure 3: The positron fraction from annihilation of KKDM for several choices of propagation parameters. The solid line represents the model with the same propagation parameters as in Fig. \ref{['posfrac1']}. The dashed line is for a model with an energy loss rate smaller by a factor of two. The models represented by dot-dashed and dotted lines use the full energy loss rate but diffusion constants that are $80\%$ and $50\%$ of the value used in Fig. \ref{['posfrac1']}. Lastly, the spectrum with both half the diffusion constant and half the energy loss rate falls almost exactly on top of the solid line. For all cases, $m_{B^{(1)}} = 300$ GeV and $L=4$ kpc were used.