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

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 $\phi$ (MeV scale) that yields the required, velocity-dependent self-interactions, and a heavy scalar resonance ${\mathrm{\Phi }}_h$ (TeV scale) with mass $m_{{\mathrm{\Phi }}_h}\text{\hspace{0.17em}⁣}\approx \text{\hspace{0.17em}⁣}2m_{\chi }$ 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 $m_{\chi }\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}600$~GeV, $m_{\phi }\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}15$~MeV, and $m_{{\mathrm{\Phi }}_h}\text{\hspace{0.17em}⁣}\simeq \text{\hspace{0.17em}⁣}1.2$~TeV reproduces the relic density and yields ${\sigma }_T\mathrm{/}{m}_{\chi }\sim 0.1$–$1{\mathrm{c}\mathrm{m}}^2\text{\hspace{0.17em}⁣}\mathrm{/}\mathrm{g}$ 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 ${\sigma }_{\mathrm{S}\mathrm{I}}\text{\hspace{0.17em}⁣}\sim \text{\hspace{0.17em}⁣}7\times {10}^{-48}{\mathrm{c}\mathrm{m}}^2$ within next-generation sensitivity. As an optional UV completion, we show that walking $\mathrm{S}\mathrm{U}(3{)}_H$ gauge theory with $N_f=10$ naturally realizes the near-threshold relation $m_{{\mathrm{\Phi }}_h}\text{\hspace{0.17em}⁣}\approx \text{\hspace{0.17em}⁣}2m_{\chi }$ and can furnish an effective anomalous dimension $\gamma \text{\hspace{0.17em}⁣}\approx \text{\hspace{0.17em}⁣}0.5$ which underlies a density-responsive dark-energy sector, suggesting a unified origin for the dark sector.