Naturally resonant two-mediator model of self-interacting dark matter with decoupled relic abundance

TL;DR

The paper resolves a longstanding tension in self-interacting dark matter by proposing a minimal, fully thermal two-mediator EFT featuring a light scalar $\phi$ driving velocity-dependent self-interactions and a heavy scalar resonance $\Phi_h$ near $m_{\Phi_h} \approx 2 m_χ$ that resonantly enhances annihilation during freeze-out. This decouples early-universe annihilation from late-time halo dynamics, yielding a narrow island of viability around a benchmark $m_χ=600$ GeV, $m_φ=15$ MeV, $m_{\Φ_h} \approx 1.2$ TeV, with $σ_T/m_χ$ in the dwarf-scale range and suppressed cluster-scale cross-sections. The model makes sharp predictions: a narrow $t\bar t$ resonance at about 1.2 TeV accessible to the HL-LHC, and a spin-independent direct-detection cross section $σ_{\rm SI} \sim 7\times10^{-48}$ cm$^2$ within next-generation reach. An optional UV completion via a walking SU(3)$_H$ theory naturally realizes $m_{\Φ_h} \approx 2 m_χ$ and yields an anomalous dimension $γ \approx 0.5$ that can underpin a density-responsive dark-energy sector, suggesting a unified origin for the dark sector. The EFT framework is self-contained and testable, while its UV completion offers concrete lattice and collider signatures, providing a concrete path from phenomenology to fundamental theory.

Abstract

We propose a minimal, fully thermal mechanism that resolves the long-standing tension between achieving the observed dark-matter relic abundance and explaining the astrophysical signatures of self-interactions. The framework introduces two mediators: a light scalar $φ$ (MeV scale) that yields the required, velocity-dependent self-interactions, and a heavy scalar resonance $Φ_h$ (TeV scale) with mass $m_{Φ_h}\!\approx\!2m_χ$ that opens an $s$-channel resonant annihilation during freeze-out. This clearly decouples early-universe annihilation from late-time halo dynamics. A detailed numerical analysis identified a narrow predictive island of viability. A representative benchmark with $m_χ\!=\!600$~GeV, $m_φ\!=\!15$~MeV, and $m_{Φ_h}\!\simeq\!1.2$~TeV reproduces the relic density and yields $σ_T/m_χ\sim 0.1$--$1~\mathrm{cm}^2\!/\mathrm{g}$ at dwarf-galaxy velocities while satisfying cluster bounds. The model makes sharp, testable predictions: a narrow $t\bar t$ resonance near $1.2$~TeV within HL-LHC reach, and a spin-independent direct-detection signal $σ_{\rm SI}\!\sim\!7\times10^{-48}\,\mathrm{cm}^2$ within next-generation sensitivity. As an optional UV completion, we show that walking $\mathrm{SU}(3)_H$ gauge theory with $N_f=10$ naturally realizes the near-threshold relation $m_{Φ_h}\!\approx\!2m_χ$ and can furnish an effective anomalous dimension $γ\!\approx\!0.5$ which underlies a density-responsive dark-energy sector, suggesting a unified origin for the dark sector.

Figures (4)

• Figure 1: Viable parameter space for self-interacting dark matter with resonant annihilation in the $(m_\phi, y_\chi)$ plane for a fixed dark matter mass of $m_\chi = 600$ GeV. The blue band shows the region satisfying the relic density constraint. The red contours define the target region for self-interactions ($0.1 < \sigma_T/m_\chi < 10$ cm$^2$/g at $v=30$ km/s). The green shaded region marks the intersection where both constraints are simultaneously satisfied. Yellow stars indicate all viable points found, with the large green star marking our final benchmark point. The heavy sector parameters ($m_{\Phi_h} = 1201$ GeV, $g^{\rm DM}_{Y_1} = 0.190$) have been tuned to achieve the correct relic density.
• Figure 2: Scaling relations in the viable parameter space. Left: Light mediator mass versus dark matter mass. Right: Yukawa coupling versus dark matter mass. Green bands show the full viable region satisfying all constraints, circles indicate central values at discrete masses from our scan, and the red star marks our benchmark point. The dashed lines show the best-fit power laws $m_\phi \propto m_\chi^{0.83}$ and $y_\chi \propto m_\chi^{0.51}$.
• Figure 3: Resonant enhancement of dark matter annihilation. Top panel: Relic density $\Omega h^2$ as a function of the resonance parameter $\delta = (m_{\Phi_h}/2m_\chi - 1)$. The solid blue line shows the full micrOMEGAs calculation including thermal and Sommerfeld effects. The gray band indicates the observed Planck 2018 value Planck2018. The red circle marks our benchmark point at $\delta \approx 8.3 \times 10^{-4}$, yielding the correct relic abundance. Bottom panel: The corresponding total enhancement factor $S_{\rm total}$, reaching a peak of over 500 near exact resonance and providing a boost of $143\times$ at our benchmark point.
• Figure 4: Velocity-dependent self-interaction cross-section for our benchmark SIDM model. The solid green line shows $\sigma_T/m_\chi$ for the best-fit parameters ($m_\phi = 15$ MeV, $y_\chi = 0.30$), calculated using micrOMEGAs. Dashed and dotted lines illustrate the effect of varying $m_\phi$ and $y_\chi$. Colored circles mark the cross-sections at astrophysically relevant velocities: dwarf galaxies (10 km/s), MW satellites (30 km/s), and galaxy clusters (1000 km/s). The gray shaded region indicates the target range for solving small-scale structure problems. The gray dotted line shows the $v^{-2}$ scaling expected in the classical regime.