Muon Fluxes and Showers from Dark Matter Annihilation in the Galactic Center

We calculate contained and upward muon flux and contained shower event rates from neutrino interactions, when neutrinos are produced from annihilation of the dark matter in the Galactic Center. We consider model-independent direct neutrino production and secondary neutrino production from the decay of taus, W bosons and bottom quarks produced in the annihilation of dark matter. We illustrate how muon flux from dark matter annihilation has a very different shape than the muon flux from atmospheric neutrinos. We also discuss the dependence of the muon fluxes on the dark matter density profile and on the dark matter mass and of the total muon rates on the detector threshold. We consider both the upward muon flux, when muons are created in the rock below the detector, and the contained flux when muons are created in the (ice) detector. We also calculate the event rates for showers from neutrino interactions in the detector and show that the signal dominates over the background for $150 {\rm GeV} <m_\chi < 1$ TeV for $E_{sh}^{th} = 100$ GeV.

💡 Research Summary

The paper presents a comprehensive calculation of muon and shower event rates arising from neutrinos produced by dark‑matter (DM) annihilation in the Galactic Center (GC). The authors consider both model‑independent direct production of neutrinos (χχ→νν) and secondary neutrinos from the decay of τ leptons, W bosons, and bottom quarks generated in the annihilation process. The neutrino flux at Earth is expressed as

 dφν/dEν = R × ∑_F BF (dN_F^ν/dEν),

where R is the annihilation rate, BF the branching fraction of channel F, and dN_F^ν/dEν the neutrino spectrum for that channel. The annihilation rate depends on the thermally‑averaged cross‑section ⟨σv⟩, a boost factor B (to account for possible Sommerfeld enhancement or sub‑halo clumping), and the line‑of‑sight integral J(ΔΩ) that encodes the DM density profile. Two profiles are examined: the cuspy Navarro‑Frenk‑White (NFW) and a cored isothermal model. Typical J‑factor values are taken from the literature (e.g., JΔΩ≈6 for a 5° cone in the NFW case).

Neutrinos propagate essentially unattenuated to Earth, but their interactions with matter produce muons that can be observed either as upward‑going tracks (muons generated in the rock below a detector) or as contained tracks (muons generated inside the detector volume). The upward muon flux is given by

 dφμ/dEμ = ∫_Eμ^mχ dEν (dφν/dEν) P_surv(Eμ,Eν) (dσ_CC/dEμ) R_μ(Eμ,E_th),

where P_surv accounts for muon energy loss in the rock, R_μ is the muon range, and dσ_CC/dEμ is the charged‑current ν‑N differential cross‑section approximated by a linear form with parameters a and b (Table I). The contained muon flux replaces the range factor with the detector size D (≈1 km for IceCube). The authors also compute shower rates from both charged‑ and neutral‑current interactions, using the same neutrino flux and cross‑sections, with shower energy approximated as E_sh≈Eν−Eμ.

Key results are illustrated in several figures. For a benchmark WIMP mass mχ=500 GeV, a boost factor B=200, and a 5° observation cone, the upward muon flux from the direct νν channel exceeds the atmospheric neutrino background in the energy interval 100–470 GeV. Enlarging the cone to 10° broadens the signal region (≈180–420 GeV) because more DM‑induced neutrinos are collected, while the atmospheric background grows more slowly. The shape of the upward muon spectrum is softer than the original neutrino spectrum due to energy loss during propagation, whereas the contained muon spectrum rises with muon energy up to the kinematic limit set by the parent neutrino energy.

The dependence on the DM mass is explored for mχ=200, 500, 800 GeV. The upward muon flux always falls with increasing muon energy, reflecting the 1/mχ² scaling of the annihilation rate, while the contained muon flux grows with muon energy until the cutoff at Eμ≈mχ. For heavier WIMPs the overall signal diminishes, but the spectral shape remains distinct from the atmospheric background.

Shower events provide a complementary probe. With a shower energy threshold of 100 GeV, the signal dominates the atmospheric background for 150 GeV < mχ < 1 TeV, especially for the NFW profile and moderate boost factors (B≈200–800). This dominance is less sensitive to the cone size because showers are produced inside the detector, and the atmospheric neutrino background is isotropic.

The paper emphasizes several practical implications for neutrino telescopes such as IceCube and the future KM3NeT. Upward‑going muons are most useful for high‑energy (> TeV) WIMPs and large detector volumes, while contained muons and showers are advantageous for sub‑TeV WIMPs where the muon range is comparable to the detector size. The choice of observation cone, detector energy threshold, and assumed DM density profile critically affect the signal‑to‑background ratio. The authors conclude that, given realistic boost factors and density profiles, IceCube should be able to detect or place meaningful limits on DM annihilation in the GC for a broad range of WIMP masses, and that shower analyses can significantly improve sensitivity in the 100 GeV–1 TeV regime.