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

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 $\varphi$ (MeV scale) that yields the required, velocity-dependent self-interactions, and a heavy scalar resonance ${\Phi }_h$ (TeV scale) with mass $m_{{\Phi }_h}\approx 2m_{\chi }$ 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 $m_{\chi }=600$~GeV, $m_{\varphi }=15$~MeV, and $m_{{\Phi }_h}\simeq 1.2$~TeV reproduces the relic density and yields ${\sigma }_T/m_{\chi }\sim 0.1$--$1{\mathrm{cm}}^2/\mathrm{g}$ 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 ${\sigma }_{\mathrm{SI}}\sim 7\times 10^{-48}{\mathrm{cm}}^2$ 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 $m_{{\Phi }_h}\approx 2m_{\chi }$ and can furnish an effective anomalous dimension $\gamma \approx 0.5$ which underlies a density-responsive dark-energy sector, suggesting a unified origin for the dark sector.

Comments: Incorporates the published corrigendum [Class. Quantum Grav., doi:10.1088/1361-6382/ae68b4] and additionally corrects a direct-detection unit-conversion factor (1 GeV^-2 -> cm^2) not covered by the corrigendum: the corrected spin-independent cross section is sigma_SI ~ 6.7e-51 cm^2 (below the xenon neutrino floor)