The PAMELA and ATIC Signals From Kaluza-Klein Dark Matter

In this letter, we study the possibility that Kaluza-Klein dark matter in a model with one universal extra dimension is responsible for the recent observations of the PAMELA and ATIC experiments. In this model, the dark matter particles annihilate largely to charged leptons, which enables them to produce a spectrum of cosmic ray electrons and positrons consistent with the PAMELA and ATIC measurements. To normalize to the observed signal, however, large boost factors (~10^3) are required. Despite these large boost factors and significant annihilation to hadronic modes (35%), we find that the constraints from cosmic ray antiproton measurements can be satisfied. Relic abundance considerations in this model force us to consider a rather specific range of masses (approximately 600-900 GeV) which is very similar to the range required to generate the ATIC spectral feature. The results presented here can also be used as a benchmark for model-independent constraints on dark matter annihilation to hadronic modes.

💡 Research Summary

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The paper investigates whether the excess of high‑energy cosmic‑ray electrons and positrons reported by the PAMELA and ATIC experiments can be explained by Kaluza‑Klein (KK) dark matter arising in a model with a single universal extra dimension (UED). In the UED framework every Standard Model field propagates in the extra dimension, leading to a conserved KK parity that renders the lightest KK particle (LKP), usually the first excitation of the hypercharge gauge boson (B¹), stable and a viable dark‑matter candidate.

The authors first review the experimental anomalies: PAMELA observed a rising positron fraction above ~10 GeV, while ATIC measured a pronounced bump in the combined electron‑plus‑positron spectrum around 300–800 GeV. Conventional astrophysical sources (pulsars, secondary production) struggle to reproduce both the magnitude and the spectral shape simultaneously, motivating a particle‑physics origin.

In the UED scenario the LKP annihilates predominantly into charged leptons (≈ 65 % of the total annihilation cross‑section) with a sub‑dominant but non‑negligible hadronic component (≈ 35 % into quark‑antiquark pairs). Because leptonic final states generate hard electrons and positrons, the resulting injection spectrum is naturally hard enough to match the ATIC bump. The authors compute the propagated spectrum using a standard diffusion‑loss model (including spatial diffusion, synchrotron and inverse‑Compton energy losses, and possible re‑acceleration). By fitting the PAMELA positron fraction and the ATIC electron‑plus‑positron flux simultaneously, they find that the annihilation rate must be enhanced by a “boost factor” of order 10³ relative to the canonical thermal relic cross‑section (⟨σv⟩≈3×10⁻²⁶ cm³ s⁻¹). Such a boost could arise from local sub‑halo clumping, Sommerfeld enhancement, or other non‑perturbative effects, but the paper treats it phenomenologically.

A potential obstacle is the production of antiprotons from the hadronic annihilation channel. PAMELA’s antiproton‑to‑proton ratio is consistent with secondary production, leaving little room for an excess. The authors demonstrate that, even with a 35 % hadronic branching ratio and a boost factor of ~10³, the predicted antiproton flux remains within current limits provided one adopts conservative propagation parameters (small diffusion coefficient, strong energy losses). This result hinges on the fact that the antiproton spectrum is softer and more diffused than the electron‑positron signal, reducing its impact at the energies probed by PAMELA.

Thermal freeze‑out calculations impose a narrow mass window for the LKP if it is to account for the observed dark‑matter density (Ω_DM h²≈0.12). The relic abundance is inversely proportional to the annihilation cross‑section; matching the cosmological density while also fitting the cosmic‑ray data forces the LKP mass into the range 600–900 GeV. Remarkably, this interval coincides with the energy region where ATIC observes its spectral feature, providing a compelling convergence of cosmological and astrophysical constraints.

The paper concludes by proposing the KK‑UED model as a benchmark for model‑independent indirect‑detection studies. Because the annihilation proceeds partly into hadrons, future measurements of antiprotons, gamma rays (from π⁰ decay), and neutrinos can be used to place complementary limits on the same parameter space. Upcoming experiments such as AMS‑02, CALET, and DAMPE, with higher precision and extended energy reach, will be able to test the required boost factor, the leptophilic nature of the annihilation, and the narrow mass window.

In summary, the authors show that a KK dark‑matter particle with mass ≈ 600–900 GeV, annihilating mainly into charged leptons, can simultaneously explain the PAMELA positron excess and the ATIC electron‑plus‑positron bump, provided a sizable astrophysical boost is present. The analysis carefully balances the need for a large boost against antiproton constraints and demonstrates that the model remains viable within current data, offering a concrete target for forthcoming indirect‑detection efforts.