Aspects of Sommerfeld Enhancement in the light of Halo gamma-ray excess

TL;DR

This work shows that dark matter models with a light scalar mediator can reconcile a high halo gamma-ray cross section with thermal relic abundance through a velocity-dependent, resonantly enhanced $p$-wave annihilation. The authors develop a dilaton-like DM–mediator coupling that yields $\chi\bar{\chi}\to\varphi\varphi$ followed by $\varphi\to b\bar b$, and they analyze the Sommerfeld enhancement, including nonperturbative resonances and saturation at low velocities. They compute the boosted gamma-ray spectrum from $\varphi$ decays, showing that the Lorentz boost broadens the spectrum to align with the $\sim$20 GeV halo excess, while respecting dwarf constraints and AMS-02 antiproton limits. The model’s viable parameter space is constrained but extends into testable ranges for future experiments (SHiP, MATHUSLA, FASER, FCC-ee), making the light mediator a promising target for both astrophysical and collider probes.

Abstract

We examine Sommerfeld enhancement in dark matter annihilation as a potential origin of the halo-like gamma-ray excess near $E_γ\simeq 20$ GeV reported by Totani. A minimal model with a light CP-even scalar mediator naturally produces a velocity-dependent annihilation cross section consistent with thermal freeze-out, the Milky Way excess, and limits from dwarf spheroidal galaxies.

Figures (8)

• Figure 1: The tree-level annihilation process $\chi \bar{\chi} \to \varphi \varphi$.
• Figure 2: DM annihilation in the presence of the Sommerfeld enhancement induced by long-range potential by $\varphi$. The gray blob indicates the hard process at short ranges shown in Fig. \ref{['fig:hard_process']}. After that the production of a pair of scalar $\varphi$ in on-shell, subsequent decays provide gamma-ray signals.
• Figure 3: Velocity dependence of the annihilation cross section with the illustrative parameter set given in the main text. We show the monochromatic (blue solid) and Maxwellian-weighted (red dashed) $\langle \sigma v \rangle$. Desired values for freeze-out (green marker) and Halo excess (black dot) cross sections are shown. The gray region shows the constraints from dwarf galaxy observations.
• Figure 4: $\langle \sigma v \rangle_{\rm Halo} \simeq 1.09 \times 10^{-24}$ cm$^3$/s for $\chi \bar{\chi} \to \varphi \varphi$. After the production of a pair of scalar $\varphi \varphi$ in on-shell, subsequent decays $\varphi \to b \bar{b}$ gives the gamma-ray spectrum including Lorentz boost effect Boddy:2016fds.
• Figure S1: A schematic representation of the resonant scattering taking place when the kinetic energy ($E_k$) is matching to the binding energy ($E_b = V_0$).