Dark Matter Self-Interactions and Light Force Carriers

TL;DR

This work investigates whether a light mediator that enhances dark matter annihilation via the Sommerfeld effect—to explain high-energy cosmic-ray signals—necessarily boosts DM self-interactions. The authors solve a non-perturbative two-body problem with a Yukawa potential to compute the enhanced annihilation and self-scattering cross sections, including resonance effects near bound states. By comparing velocity-averaged cross sections to astrophysical bounds, they find dwarf galaxies provide the strongest constraints, requiring mediator masses around 30–40 MeV for plausible couplings. The study emphasizes the need for velocity-dependent N-body simulations to accurately translate bounds across systems and discusses implications for dark-sector model-building and experimental searches for light mediators.

Abstract

Recent observations from PAMELA, FERMI, and ATIC point to a new source of high energy cosmic rays. If these signals are due to annihilating dark matter, then the annihilation cross section in the present day must be substantially larger than that necessary for thermal freeze-out in the early universe. A new force, mediated by a particle of mass O(100 MeV), leading to a velocity dependent annihilation cross section - a `Sommerfeld enhancement' - has been proposed as a possible explanation. We point out that such models necessarily increase the dark matter (DM) self-scattering cross section, and use observational bounds on the amount of DM-DM scattering allowed in various astrophysical systems to place constraints on the mass and couplings of the light mediator.

Figures (6)

• Figure 1: Non-perturbative "ladder" diagrams corresponding to the formation of a $\chi-\bar{\chi}$ bound state for annihilation (left) and scattering (right).
• Figure 2: The maximum angular momentum $L = m_\chi v b_{\rm max}$ as a function of the mediator mass $m_\phi$ for DM of velocity $v$ colliding head-on. In the left-hand plot we have chosen $\alpha = 0.01$ and in the right-hand plot $\alpha = 0.1$. In both cases $m_\chi=500\,{\rm GeV}$. Each contour line corresponds to an increase of $L$ by one from the previous.
• Figure 3: For $m_\chi=500\ {\rm GeV}$, and $\alpha = 0.01$ (left-hand plot) and $\alpha=0.1$ (right-hand plot) we show the transfer cross section, the numerical results (blue solid line) and our approximate formulae Eqs. (\ref{['eq:sigmaapprox']}) and (\ref{['eq:transferapprox']}) (upper and lower red dotted lines), as well as the Sommerfeld enhancement (blue dashed line) in the annihilation cross section. We have assumed that the DM is colliding head-on with speed 100 km/s.
• Figure 4: For $m_\chi = 500\ {\rm GeV}$, $m_\phi=100\ {\rm MeV}$ and $\alpha = 0.01$ (left-hand plot) and $\alpha=0.1$ (right-hand plot) we plot the transfer cross section for two DM particle colliding head on at speed $v$. The result of the numerical calculation, summing the first five $\ell$-modes, is shown in blue (solid) and the upper and lower red (dotted) curves uses the approximate cross section Eqs. (\ref{['eq:sigmaapprox']}) and (\ref{['eq:transferapprox']}) described in the text.
• Figure 5: $\langle \sigma_{\rm tr} \rangle /m_\chi$ as a function of $m_\phi$, assuming that $m_\chi=500$ GeV, and $\alpha = 0.01$ (left) and $\alpha = 0.1$ (right). A thermal velocity distribution Eq. (\ref{['eq:veldis']}) with dispersion $v_0 = 1000~\hbox{km/s}=3.3\times 10^{-3}c$, characteristic of galaxy clusters, was used. Contributions from modes up to $\ell = 5$ are included in the exact numerical cross section for $m_\phi < 0.2$ GeV, while only $\ell \leq 1$ are included above this mass. The approximate solutions from Eqs. (\ref{['eq:sigmaapprox']}) and (\ref{['eq:transferapprox']}) are also shown (dashed red lines).