Sommerfeld Enhancement from Background Force and the Galactic Center GeV Excess

TL;DR

The paper addresses the Galactic Center GeV gamma-ray excess by proposing a two-component dark matter model in which a finite-density background of an ultralight pseudoscalar $φ$ induces a loop-level, background-enhanced force between the dominant fermionic DM $χ$. This background force yields a large Sommerfeld enhancement of the $χχ̄→ηη$ annihilation, with the enhancement strength scaling with the local $φ$ density and the distance to the Galactic Center. The authors derive a Yukawa-like background potential, compute the corresponding $S_p$ via the Hulthén approximation, and show that the effective enhancement can reach ${ m O}(10^2)$ in the inner Galaxy, allowing a good fit to the Fermi-LAT GC excess for reasonable choices of masses and couplings. This mechanism naturally links the annihilation signal to the DM density profile and opens new parameter space for indirect detection, while also predicting temporal and spatial modulation effects tied to the ultralight background relic. The framework avoids early-Universe constraints through a p-wave channel and late-time production of $φ$, emphasizing the role of background environments in shaping DM phenomenology.

Abstract

We study the impact of background-induced forces on dark matter (DM) annihilation and their implications for indirect detection. In the presence of a finite number density of background particles, loop-level interactions can generate an effective force that is significantly enhanced relative to the vacuum case. We construct a two-component DM model in which the dominant component is a fermionic particle $χ$ and the subdominant component is an ultralight pseudoscalar particle $φ$. The annihilation of $χ$ proceeds through the p-wave channel and produces gamma-ray emission. The finite density of $φ$ particles induces a background-enhanced force between $χ$ particles, leading to a sizable Sommerfeld enhancement of the annihilation. We show that a viable region of parameter space in this model can account for the gamma-ray excess observed in the Galactic Center using Fermi-LAT data. The background-induced force substantially amplifies the Sommerfeld enhancement and thus enlarges the parameter space capable of explaining the excess, highlighting the importance of background effects in astrophysical environments.

Figures (4)

• Figure 1: Feynman diagrams which contribute to the self-interacting potential of $\chi$ via the exchange of a virtual mediator $\eta$ and a background DM particle $\phi$. The wavy lines represent the $\phi$ DM background. The background force can be obtained by substituting the $\phi$ propagators with the background modified propagator in Eq. \ref{['eq:thermalOP']}.
• Figure 2: The effective Sommerfeld enhancement factor $\langle v^2 S_p \rangle$ (upper panel) and the effective coupling $\alpha_{bkg}$ (lower panel) as a function of the distance $r$ from the GC. We choose four benchmark points of the parameters $(m_{\phi},\alpha_{\phi})$, which are $m_\phi = 3 \times 10^{-18}\,$eV and $1.5 \times 10^{-18}\,$eV, and $\alpha_\phi = 10^{-8}$ and $10^{-9}$. In addition, for illustrative purposes, we fix $m_\chi = 100\,$GeV and $m_\eta = 12\,$GeV, and take the fraction of the dominant DM component $\chi$ to be $R = 0.9$.
• Figure 3: The Fermi-LAT data (black points with error bar) and the best-fit result with $m_\chi = 65\,$GeV and $m_\phi = 1.1 \times 10^{-18}\,$GeV (red solid line). For comparison, two alternative parameter sets are also displayed: $m_\chi = 90\,$GeV, $m_\phi = 0.8 \times 10^{-18}\,$GeV (blue dashed line) and $m_\chi = 40\,$GeV, $m_\phi = 2 \times 10^{-18}\,$GeV (green dashed line). For illustration, the remaining model parameters are fixed as $\alpha_\phi = 10^{-8}$, $m_\eta = 12\,$GeV and the DM $\chi$ fraction $R = 0.9$.
• Figure 4: The Feynman diagrams correspond to the background-enhanced force by exchanging one virtual $\eta$ and one DM $\phi$ in our two-component DM model.