Breit-Wigner Enhancement of Dark Matter Annihilation

Abstract

We point out that annihilation of dark matter in the galactic halo can be enhanced relative to that in the early universe due to a Breit-Wigner tail, if the dark matter annihilates through a pole just below the threshold. This provides a new explanation to the "boost factor" which is suggested by the recent data of the PAMELA, ATIC and PPB-BETS cosmic-ray experiments.

Figures (4)

• Figure 1: A schematic plot that shows dispersion in relative velocity $v_{\rm rel}^2$ and an unphysical pole in the cross section at $v_{\rm rel}^2 < 0$ (below threshold). It is clear that a smaller dispersion $v_0$ gives a larger overlap with the Breit--Wigner tail in the cross section and hence an enhanced averaged cross section.
• Figure 2: The time evolution of the yield $Y$ of the dark matter in terms of the parameter $x = m/T$ for given values of $\delta$ and $\gamma$ (the solid line). In this figure, we assume $\delta>0$ and the pole is not in the physical region. The long-dashed line labeled $Y_{\rm app}$ is the evolution with the approximated cross section in Eq. (\ref{['eq:app']}). The dashed line labeled $Y_\infty$ is the asymptotic solution $Y_{\infty}$ given in Eq. (\ref{['eq:sol']}). The short-dashed line represents the equilibrium yield $Y_{\rm EQ}$. The dash-dotted line labeled $Y_{\rm non-res}$ shows the time evolution of the yield in the usual (non-resonant) freeze-out assuming the same cross section at the low temperature $\sigma_{0}$ used in $Y$ (see Eq. (\ref{['eq:sol2']})). The boost factor is the asymptotic value of $Y/Y_{\rm non-res}$.
• Figure 3: The time evolution of the yield of the dark matter $Y$ for $\delta<0$ (the solid line). Everything else is the same as in Fig. \ref{['fig:boltzmann']}. There is practically no boost for this parameter set.
• Figure 4: The boost factor on the $(\delta,\gamma)$ plane. Thermal average is done numerically without relying on the approximation Eq. (\ref{['eq:app']}).