Can the WIMP annihilation boost factor be boosted by the Sommerfeld enhancement?

TL;DR

The paper investigates whether Sommerfeld enhancement can provide the large DM annihilation boost needed to explain high-energy lepton data (e.g., PAMELA/ATIC) by combining non-perturbative effects with CDM substructure. It derives the Sommerfeld correction for a Yukawa potential, identifies regimes of enhancement and resonances, and shows that multi-state DM can boost leptonic channels. When cold substructure is included, the outer halo can yield a total boost of order $10^4$–$10^5$ near a resonance (e.g., for $m \sim$ a few TeV), with the signal dominated by clumps and saturation limiting sensitivity to unresolved small scales. However, gamma-ray constraints from the outer halo favor leptonic channels and require careful treatment of halo profiles and subhalo concentrations; FERMI could detect the resulting quasi-isotropic gamma-ray background, while the inner Galaxy remains comparatively quiet due to tidal disruption of clumps. The work highlights a viable indirect-detection pathway relying on DM microphysics and outer-halo structure, with clear observational and modeling uncertainties guiding future research.

Abstract

We demonstrate that the Sommerfeld correction to CDM annihilations can be appreciable if even a small component of the dark matter is extremely cold. Subhalo substructure provides such a possibility given that the smallest clumps are relatively cold and contain even colder substructure due to incomplete phase space mixing. Leptonic channels can be enhanced for plausible models and the solar neighbourhood boost required to account for PAMELA/ATIC data is plausibly obtained, especially in the case of a few TeV mass neutralino for which the Sommerfeld-corrected boost is found to be $\sim10^4-10^5.$ Saturation of the Sommerfeld effect is shown to occur below $β\sim 10^{-4},$ thereby constraining the range of contributing substructures to be above $\sim 10^5\rm M_\odot.$ We find that the associated diffuse gamma ray signal from annihilations would exceed EGRET constraints unless the channels annihilating to heavy quarks or to gauge bosons are suppressed. The lepton channel gamma rays are potentially detectable by the FERMI satellite, not from the inner galaxy where substructures are tidally disrupted, but rather as a quasi-isotropic background from the outer halo, unless the outer substructures are much less concentrated than the inner substructures and/or the CDM density profile out to the virial radius steepens significantly.

Figures (5)

• Figure 1: Ladder diagram giving rise to the Sommerfeld enhancement for $\chi\chi\rightarrow X\overline{X}$ annihilation, via the exchange of gauge bosons.
• Figure 2: Sommerfeld enhancement $S$ as a function of the dark matter particle mass $m$, for different values of the particle velocity. Going from bottom to top $\beta=10^{-1},\,10^{-2},\,10^{-3},\,10^{-4},\,10^{-5}$.
• Figure 3: Top panel: Sommerfeld enhancement $S$ as a function of the particle velocity $\beta$ for different values of the dark matter mass. From bottom to top: $m= 2,\,10,\,100,\,4.5\,\mathrm{TeV}$, the last value corresponding to the first resonance in Fig. \ref{['fig:som1']}. The black dashed line shows the $1/v$ behaviour that is expected in the intermediate velocity range (see text for discussion). Bottom panel: Sommerefeld enhancement $S$ as a function of the relative distance from the first resonance shown in Fig. \ref{['fig:som1']}, occurring at $m\simeq 4.5\,\mathrm{TeV}$, for different values of $\beta$. From top to bottom: $\beta=10^{-4},\,10^{-3},\,10^{-2}$.
• Figure 4: Diagram describing the annihilation of two neutralinos into a charged lepton pair, circumventing helicity suppression.
• Figure 5: Contribution to the diffuse galactic photon background from the annihilation of a 5 TeV dark matter particle, for different channels, when both clumpiness and the Sommerfeld enhancement in cold clumps are taken into account, compared with the measurements of the diffuse gamma background from EGRET Strong:2004ry. The label "Hyb1" (solid black line) stands for a hybrid model in which the dark matter annihilates to $\tau$ leptons 90% of the time and to $W$ pairs the rest of the time. The label "Hyb2" (dashed black line) stands for a model in which the dark matter annihilates to leptons and quarks only, with the same cross-section apart from color factors. The latter could be realized through the circumvention of helicity suppression.