Dark Matter Signals from Cascade Annihilations

A leading interpretation of the electron/positron excesses seen by PAMELA and ATIC is dark matter annihilation in the galactic halo. Depending on the annihilation channel, the electron/positron signal could be accompanied by a galactic gamma ray or neutrino flux, and the non-detection of such fluxes constrains the couplings and halo properties of dark matter. In this paper, we study the interplay of electron data with gamma ray and neutrino constraints in the context of cascade annihilation models, where dark matter annihilates into light degrees of freedom which in turn decay into leptons in one or more steps. Electron and muon cascades give a reasonable fit to the PAMELA and ATIC data. Compared to direct annihilation, cascade annihilations can soften gamma ray constraints from final state radiation by an order of magnitude. However, if dark matter annihilates primarily into muons, the neutrino constraints are robust regardless of the number of cascade decay steps. We also examine the electron data and gamma ray/neutrino constraints on the recently proposed “axion portal” scenario.

💡 Research Summary

The paper addresses the excess of high‑energy electrons and positrons reported by the PAMELA satellite and the ATIC balloon experiment, interpreting these anomalies as products of dark‑matter (DM) annihilation in the Galactic halo. Direct annihilation of DM into charged leptons (χχ → ℓ⁺ℓ⁻) is strongly constrained by the accompanying final‑state‑radiation (FSR) gamma‑ray flux measured by atmospheric Cherenkov telescopes such as H.E.S.S. To alleviate these constraints, the authors explore “cascade annihilation” scenarios in which DM first annihilates into a light intermediate state φₙ, which subsequently decays through a chain φₙ → φₙ₋₁ φₙ₋₁ … → φ₁ φ₁, and finally φ₁ → ℓ⁺ℓ⁻ (ℓ = e or μ).

The cascade formalism is developed analytically: for well‑separated mass scales the energy spectrum after n steps can be obtained by iteratively convolving the direct spectrum with a simple kernel (Eq. 1). Each step doubles the multiplicity of final‑state particles (∼2ⁿ) while softening their individual energy distribution, parameterized by x = E/m_DM. The authors compute spectra for 0‑step (direct), 1‑step, and 2‑step cascades for both electron and muon final states (details in Appendices A.1–A.2).

To compare with data, the authors solve the steady‑state diffusion‑loss equation for electrons and positrons in the Milky Way, using three benchmark propagation models (MED, M1, M2) and three halo density profiles (cored isothermal, NFW, Einasto). Background primary and secondary electron/positron fluxes are taken from Ref.