Dark matter Simplified models in the Resonance Region

TL;DR

This paper investigates dark matter simplified models (DMSimps) in the resonant regime where $m_{ m DM}\approx m_{ m med}/2$, showing that viability persists under current relic-density, direct-detection, and indirect-detection bounds when a full Boltzmann treatment is used. It demonstrates how resonance enhances annihilation cross sections, enabling correct relic abundance with small couplings that evade direct-detection limits, and it explores the potential to explain the Fermi-LAT Galactic Center Excess with $s$-wave annihilation. The study covers scalar and vector mediators and DM candidates (scalar, Dirac fermion, vector), highlighting that most of the parameter space is excluded away from resonance, while a narrow resonant funnel remains testable, especially with future experiments like DARWIN. It also presents two natural UV completions that realize $m_{ m med}\approx 2 m_{ m DM}$ without fine-tuning, grounding the resonant region in symmetry-breaking scales. Together, these results map out the resonant landscape of DMSimps, linking relic density, collider/ DD constraints, and possible GCE explanations, and outlining clear experimental targets for discovery or exclusion.

Abstract

The particle-physics nature of dark matter (DM) remains one of the central open questions in modern physics. A widely used framework to investigate DM properties is provided by simplified models (DMSimps), which extend the Standard Model with a DM particle and a mediator that connects the visible and dark sectors. Much of the DMSimps parameter space is already constrained by direct and indirect detection, collider searches, and the measured DM relic abundance. We show, however, that the resonant regime $m_{\rm DM}\simeq m_{\rm med}/2$ remains viable under current bounds and will be stringently tested by forthcoming experiments. Using a full Boltzmann treatment that allows for departures from kinetic equilibrium near resonance, we demonstrate that this regime can reproduce the observed relic density with couplings compatible with direct-detection limits. We also show that models with s-wave-dominated annihilation can explain the Fermi-LAT Galactic Center Excess with couplings consistent with relic-density and direct-detection constraints. Finally, we propose two minimal constructions that naturally realize $m_{\rm med} \approx 2m_{\rm DM}$, making the resonant scenario generic rather than fine-tuned.

Figures (14)

• Figure 1: Branching ratios (top) and velocity-averaged annihilation cross sections (bottom) as functions of the DM mass for a scalar mediator and scalar DM. We fix $m_{S}=200~\mathrm{GeV}$ and $g_X=\lambda=\beta=1$. The hierarchy of channels follows the SM fermion masses (Yukawa couplings); for $m_\chi\lesssim 170~\mathrm{GeV}$ the $b\bar{b}$ channel dominates, while above threshold the $t\bar{t}$ channel becomes important. The $SS$ final state opens for $m_\chi>m_{S}$. Near $m_{\rm S}\simeq 2m_\chi$ the $s$-channel resonance enhances the total cross section, allowing smaller couplings to achieve the correct relic abundance.
• Figure 2: Upper limits on the couplings $\lambda=\beta$ for the pseudoscalar mediator model of Eq. \ref{['eq:pseudoDM']}, obtained by comparing the tree–level (momentum–suppressed) SD and the one–loop SI nuclear cross sections with the LZ data LZ:2024zvo. We fix $m_\psi=50~\mathrm{GeV}$ and show limits as a function of $m_A$.
• Figure 3: Left: ratio $\Omega_{\rm DM}^{\tt fBE}/\Omega_{\rm DM}^{\tt nBE}$ obtained by solving the Boltzmann equation with DRAKE Eq. \ref{['eq:RD1']} under the nBE (kinetic equilibrium assumed) and fBE (full) prescriptions, for a scalar mediator and three DM spins. Right: ratio of the couplings $g=\lambda=\beta$ that reproduce $\Omega_{\rm DM} h^2$ for fBE over nBE. The mediator mass is fixed to $200~\mathrm{GeV}$.
• Figure 4: Upper-left panel: Constraints in the $(m_{\psi},m_{S})$ plane for a simplified model with Dirac DM interacting via an s-channel scalar mediator. In this case, $\lambda=\beta=g_{\rm{DM}}=1.0$. The blue colored curve corresponds to parameter space that provides the correct DM relic density. The gray region denotes the region where DM is over-abundant $\Omega_{\rm{DM}}h^2>0.12$, while the cyan region is for under-abundant DM $\Omega_{\rm{DM}}h^2<0.12$. The red (purple) colored curves corresponds to the current (projected) exclusion limits from LZ ( DARWIN) on $\sigma^{SI}_{\psi p}$, while we mark the exclusion region due to LZ constraints with a light red band. The orange curve represents the viable parameter space that satisfies relic density and LZ direct detection constraints. Upper-right and lower-left panels: Same as the upper-left panel but $g_{DM}=0.1$ and $g_{DM}=0.01$. Lower-right panel: Constraints in the $(g_{DM},m_{\psi})$ plane. The mediator mass is fixed to 200 GeV, which implies a resonant DM mass around $m_{\psi}\sim 100$ GeV. We show the direct detection upper limits based on LZ data LZ:2022ufs (red dot-dashed line) and projections to DARWIN DARWIN:2016hyl (purple dot-dashed line). The blue dot-dashed line corresponds to the correct DM relic density.
• Figure 5: The same as in Fig. \ref{['fig:SmedDDM']} where we report the $y$ axis as $m_{\psi}/m_S$ in order to zoom in the resonance region.