Self-Interacting Sterile Neutrino Cold Dark Matter: Resonant Production Mechanism in the Early Universe

RESUMO

Sterile neutrinos are well-motivated dark matter candidates, but their conventional production through active-sterile mixing is tightly constrained by X-ray searches and structure-formation observations. We propose a distinct production mechanism operating entirely within a sterile sector: two sterile neutrinos, $N_1$ and $N_2$, coupled to a singlet scalar $\phi$, with $N_1$ the dark matter candidate and $N_2$ held in equilibrium through frequent scattering induced by its scalar interaction. Thermal self-energies induced by the $N_2$ and $\phi$ backgrounds generate both a temperature-dependent mass splitting and an off-diagonal mixing between $N_1$ and $N_2$. As the Universe cools, the in-medium levels can undergo a level crossing, leading to resonantly enhanced conversion of the thermal $N_2$ population into $N_1$. We formulate the conversion using a density-matrix kinetic equation that consistently incorporates coherent $N_1$-$N_2$ conversion, collisional decoherence, and thermal repopulation of $N_2$. For a narrow resonance, the integrated conversion probability admits a simple analytic form that coincides with the Landau-Zener result, despite the underlying collisionally damped dynamics. In the weak-conversion regime relevant for freeze-in, this correspondence provides a robust analytic description of the resonant production. We derive the resulting dark matter abundance and identify the conditions for cosmological stability of $N_1$ and for resonant conversion to dominate over direct scattering and decay production. The resulting relic abundance scales as $Y_1\propto g_{12}^2 g_{22}M_{\rm Pl}/m_1$, making the dark matter energy density approximately independent of $m_1$. This mechanism provides a new route to sterile-neutrino dark matter that does not require appreciable active-sterile mixing.