Upper Bound on the Dark Matter Total Annihilation Cross Section

TL;DR

The bound is much stronger than the unitarity bound at the most interesting masses, shows that dark matter halos cannot be significantly modified by annihilations, and can be improved by a factor of 10-100 with existing neutrino experiments.

Abstract

We consider dark matter annihilation into Standard Model particles and show that the least detectable final states, namely neutrinos, define an upper bound on the total cross section. Calculating the cosmic diffuse neutrino signal, and comparing it to the measured terrestrial atmospheric neutrino background, we derive a strong and general bound. This can be evaded if the annihilation products are dominantly new and truly invisible particles. Our bound is much stronger than the unitarity bound at the most interesting masses, shows that dark matter halos cannot be significantly modified by annihilations, and can be improved by a factor of 10--100 with existing neutrino experiments.

Figures (3)

• Figure 1: Annihilation of dark matter into SM final states. Since all final states except neutrinos produce gamma rays (see text), we can bound the total cross section from the neutrino signal limit, i.e., assuming Br("Invisible") $\simeq 100\%$.
• Figure 2: Upper: Diffuse $\bar{\nu} \nu$ annihilation signal for $m_\chi = 10, 10^3,$ and $10^5$ GeV, added to the atmospheric background, both as ($\bar{\nu}_\mu + \nu_\mu$) and versus neutrino energy. As noted, the signals are most accurate for $E_\nu \gtrsim m_\chi/3$. Lower: Ratio of this sum and background. The $\langle \sigma_A v \rangle$ values at each example $m_\chi$ are chosen to be detectable by our conservative criteria; the data and assumed uncertainty scales are also indicated.
• Figure 3: Upper bounds on the dark matter total annihilation cross section in galaxy halos as a function of the dark matter mass, calculated as discussed in the text.