Ultimate target for dark matter searches

The combination of $S$-matrix unitarity and the dynamics of thermal freeze-out for massive relic particles (denoted here simply by WIMPs) implies a lower limit on the density of such particles, that provide a (potentially subdominant) contribution to dark matter. This then translates to lower limits to the signal rates for a variety of techniques for direct and indirect detection of dark matter. For illustration, we focus on models where annihilation is $s$-wave dominated. We derive lower limits to the flux of gamma rays from WIMP annihilation at the Galactic center; direct detection of WIMPs; energetic neutrinos from WIMP annihilation in the Sun; and the effects of WIMPs on the angular power spectrum and frequency spectrum of the cosmic microwave background radiation. The results suggest that a variety of dark-matter-search techniques may provide interesting avenues to seek new physics, even if WIMPs do not constitute all the dark matter. While the limits are quantitatively some distance from the reach of current measurements, they may be interesting for long-range planning exercises.

Figure 1

Thermal averaged cross section times relative velocity $⟨\sigma v⟩$ versus WIMP mass $m_{\chi }$. The horizontal gray band shows the canonical cross section for a thermal relic making up the dark matter. The black line is the largest annihilation cross section consistent with unitarity. The purple and cyan curves show an estimate of the smallest $⟨\sigma v⟩$ detectable by CTA with 500 hours of observation time [21], assuming annihilation to ${\tau }^{+}{\tau }^{-}$ or $W^{+}{W}^{-}$ pairs, and assuming that the WIMP makes up all the halo dark matter. The red line shows the smallest inferred $⟨\sigma v⟩$ that would be possible for a subdominant WIMP.

Figure 2

WIMP-proton elastic-scattering cross section versus WIMP mass $m_{\chi }$. Dashed lines show the current upper limits by various experiments, assuming that $\chi$ makes up all the dark matter. Solid blue and red lines denote the minimal effective WIMP-nucleon cross sections inferred from the unitarity limit, for two different values of the actual scattering cross section ${\sigma }_{\chi p}^{\text{actual}}={\mu }_{\chi p}^2/\pi {\mathrm{\Lambda }}^4$, corresponding to $\mathrm{\Lambda }=1\mathrm{TeV}$ and $\mathrm{\Lambda }\simeq m_Z/g_{\mathrm{EW}}$, respectively. The dotted cyan band shows the effective cross section at which coherent scattering from background neutrinos becomes significant [22].