Neutrino Constraints on the Dark Matter Total Annihilation Cross Section

TL;DR

The paper addresses constraining the total DM self-annihilation cross section via indirect detection by exploiting the Milky Way halo and neutrino final states. It builds a generalized halo density profile $\\rho(r)= \\frac{\\rho_0}{(r/r_s)^\\gamma[1+(r/r_s)^\\alpha]^{(\\beta-\\gamma)/\\alpha}}$ and evaluates the halo line-of-sight factor ${\\cal J}(\\psi)$, decomposing the signal into Halo Angular, Halo Average, and Halo Isotropic components, then compares neutrino-channel signals with the atmospheric background and with the cosmic signal through a redshift multiplier $f(z)$. Key contributions: quantify ${\\cal J}_{Ang} \\simeq 25$, ${\\cal J}_{Ave} \\simeq 5$, ${\\cal J}_{Iso} \\simeq 0.5$, showing halo-based neutrino bounds can beat cosmic bounds by 1–2 orders of magnitude (and potentially 2–4 with substructure). Significance: demonstrates that neutrino-based halo constraints can probe the full DM annihilation cross section space, offering robust bounds and guiding upcoming experiments like Super-Kamiokande and IceCube toward testing thermal-relic cross sections across a broad DM mass range.

Abstract

In the indirect detection of dark matter through its annihilation products, the signals depend on the square of the dark matter density, making precise knowledge of the distribution of dark matter in the Universe critical for robust predictions. Many studies have focused on regions where the dark matter density is greatest, e.g., the Galactic Center, as well as on the cosmic signal arising from all halos in the Universe. We focus on the signal arising from the whole Milky Way halo; this is less sensitive to uncertainties in the dark matter distribution, and especially for flatter profiles, this halo signal is larger than the cosmic signal. We illustrate this by considering a dark matter model in which the principal annihilation products are neutrinos. Since neutrinos are the least detectable Standard Model particles, a limit on their flux conservatively bounds the dark matter total self-annihilation cross section from above. By using the Milky Way halo signal, we show that previous constraints using the cosmic signal can be improved on by 1-2 orders of magnitude; dedicated experimental analyses should be able to improve both by an additional 1-2 orders of magnitude.

Figures (4)

• Figure 1: The dark matter density versus radius for the three profiles considered (Moore, NFW and Kravtsov in order of dotted, dashed and solid lines), based on Eq. (\ref{['eq:fitting']}). The normalizations are chosen to match the large scale properties of the Milky Way. The vertical gray line indicates the solar circle distance, $R_{sc}\simeq 8.5$ kpc. See Table I for the other parameters.
• Figure 2: Line of sight integration ${\cal J}(\psi)$ as a function of the pointing angle $\psi$ (bottom axis) with respect to the Galactic Center direction for the three different profiles considered (Moore, NFW and Kravtsov in order of dotted, dashed and solid thin lines). Its average, ${\cal J}_{\Delta \Omega}$, inside a cone with half angle $\psi$ around the GC as a function of the visible fraction of the whole sky, $\Delta \Omega/4\pi=(1-\cos{\psi})/2$ (top axis), is also presented (thick lines). Note that the left (right) side of the graph is presented in log (linear) scale in $\Delta \Omega/4\pi$.
• Figure 3: The atmospheric neutrino spectrum ($\nu_{\mu} + \bar{\nu}_{\mu}$) and the expected increase in the total received intensity from the annihilations of a $100$ GeV DM particle. While the halo signal is sharply peaked in a narrow band of energy, the cosmic signal spreads over a wider energy range. To define upper limits on the cross section, in each case we use a (different, see Fig. 4) cross section such that the annihilation signal would double the total received intensity in the displayed energy ranges.
• Figure 4: Constraints on the DM total self-annihilation cross section from various components of the Milky Way halo (shaded regions excluded). The constraints from the cosmic signal (dotted line) can be compared to that of the Halo Isotropic (dark shaded) component. The successive improvements of the Halo Average (medium shaded) and Halo Angular (light shaded) components can improve on the cosmic constraint by 1--2 orders of magnitude. The unitarity bound (dot-dashed line) and the cross sections for which annihilations flatten the cusps of DM halos (dashed-line) are also shown; see the text.