Consistent Scenarios for Cosmic-Ray Excesses from Sommerfeld-Enhanced Dark Matter Annihilation

TL;DR

This work analyzes a vector-portal dark matter model with a GeV-scale mediator and a small mass splitting between nearly degenerate states to produce large Sommerfeld enhancements. By solving coupled Boltzmann equations for ground and excited states and computing local boost factors, the authors show relic-density-consistent enhancements can reach $\sim\mathcal{O}(10^2)$–$\mathcal{O}(10^3)$, constrained by CMB observations; for heavier DM and WIMPonium, boosts of $\sim600$–$700$ are possible while remaining compatible with the CMB. The parameter-space exploration demonstrates that PAMELA and Fermi electron/positron data can be accommodated across multiple final states, with a preference for leptonic decays and sub-GeV mediator masses. The results offer testable predictions for Planck polarization, low-energy experiments, and collider searches, and highlight the role of substructure and bound-state formation in pushing viable regions of parameter space.

Abstract

Anomalies in direct and indirect detection have motivated models of dark matter consisting of a multiplet of nearly-degenerate states, coupled by a new GeV-scale interaction. We perform a careful analysis of the thermal freezeout of dark matter annihilation in such a scenario. We compute the range of "boost factors" arising from Sommerfeld enhancement in the local halo for models which produce the correct relic density, and show the effect of including constraints on the saturated enhancement from the cosmic microwave background (CMB). We find that boost factors from Sommerfeld enhancement of up to ~800 are possible in the local halo. When the CMB bounds on the saturated enhancement are applied, the maximal boost factor is reduced to ~400 for 1-2 TeV dark matter and sub-GeV force carriers, but remains large enough to explain the observed Fermi and PAMELA electronic signals. We describe regions in the DM mass-boost factor plane where the cosmic ray data is well fit for a range of final states, and show that Sommerfeld enhancement alone is enough to provide the large annihilation cross sections required to fit the data, although for light mediator masses (less than ~200 MeV) there is tension with the CMB constraints in the absence of astrophysical boost factors from substructure. Additionally, we consider the circumstances under which WIMPonium formation is relevant and find for heavy WIMPs (greater than ~2 TeV) and soft-spectrum annihilation channels it can be an important consideration; we find regions with dark matter mass greater than 2.8 TeV that are consistent with the CMB bounds and have ~600-700 present-day boost factors.

Figures (4)

• Figure 1: Left: Allowed ranges of parameter space for fits within the $1 \sigma$, 90% confidence, and $2 \sigma$ error bars to PAMELA only (in decreasing intensity of red), Fermi only (in decreasing intensity of gray), and for simultaneous fits to both PAMELA and Fermi (in decreasing intensity of purple). Yellow crosses indicate benchmark points. Right: As in left, with curves showing the boost factors for a range of mass splittings $\delta$ such that $\Omega h^2 = 0.1120$ (dashed). Yellow lines, marked with asterisks, are chosen to pass through the benchmark points for cases where the BF varies rapidly with $\delta$. The CMB constraints are met for the solid portions of the curves. Results are shown for 800 GeV $\le m_{\chi} \le$ 3 TeV only. All preferred regions shown here assume $\rho_0 = 0.4$ GeV/cm$^3$ and no contribution to the signal from DM substructure; any substructure correction (e.g. Pieri:2009je) will shift the preferred regions to lower boost factors. The $\delta=0$ curve is intended as a consistency check with previous work, and so annihilation channels involving the dark Higgs were omitted from the computation in this case.
• Figure 2: Contours for the boost factor BF in the local halo as a function of the mediator mass $m_{\phi}$ and mass splitting $\delta$, with $\alpha_D$ chosen to produce the correct relic density. The DM velocity distribution is assumed to be Maxwellian with $\sigma = 150$ km/s. The regions overlaid with red lines are ruled out at $95 \%$ confidence by bounds from WMAP5, taking $f = 0.2$ for hadronic final states, $f = 0.24$ for muons, and $f = 0.7$ for electrons, and weighting these three contributions according to the ($m_\phi$-dependent) branching ratios for decays of the dark gauge boson. Blue-hatched regions illustrate the effect of shifting the WMAP5 constraint: these parts of parameter space would remain ruled out even if the bounds were relaxed by a factor of 4 (e.g. due to degeneracy with some parameter not included in the analysis, although we do not consider this a likely scenario). Upper row: Results for 1.2 TeV dark matter, for three values of the coannihilation parameter $\kappa$. Upper left panel:$\kappa = 1/4$, corresponding to the minimal singly-charged Higgs model described in § \ref{['sec:masssplittingann']}. Upper center panel:$\kappa = 1$ ($\alpha_D = 0.0263$, see text). Upper right panel:$\kappa = 4$ ($\alpha_D = 0.0177$, see text). Lower row: Results for DM mass (lower left panel) 900 GeV, (lower center panel) 1.5 TeV, and (lower right panel) 1.8 TeV, in the $\kappa=1/4$ minimal model. Capture into a bound state, inducing an additional enhancement to late-time annihilation, is kinematically allowed in regions to the left of and below the black-dashed line, but has not been included in the analysis; see Appendix \ref{['sec:wimponium']} for a discussion.
• Figure 3: Benchmark models fitting the PAMELA (first and third rows) and Fermi (second and fourth rows) cosmic-ray excesses, obtained using the GALPROP program.
• Figure 4: The present-day boost factor for the case of a single DM state with $m_\phi$ light enough to permit radiative capture into WIMPonium, as a function of the DM mass $m_\chi$, and the mediator mass $m_\phi$ normalized to the WIMPonium binding energy. $\alpha_D$ is tuned to obtain the correct relic density. Red-hatched regions are ruled out at $95\%$ confidence by constraints from WMAP5, taking the energy deposition fraction $f=0.2$ to be conservative.