FIMPs in a two-component dark matter model with $Z_2\times Z_4$ symmetry

Abstract

We investigate the FIMP-FIMP regime in a two-component dark matter model with a $Z_2\times Z_4$ symmetry, where a singlet scalar $S$ and a Majorana fermion $\chi$ serve as the dark matter candidates. A singlet scalar $S_0$ with vacuum expectation value $v_0$ generates the fermion mass through the relation $m_{\chi }=y_{sf}{v}_0$. We show that the tiny Yukawa coupling $y_{sf}$ needed to reproduce the observed relic abundance naturally leads to a large symmetry-breaking scale $v_0$, which induces an ultra-feeble portal coupling ${\lambda }_{ds}$ responsible for the production of $S$. We find that ${\lambda }_{ds}$ can reach values of $10^{-25}\lesssim {\lambda }_{ds}\lesssim 10^{-13}$, while gravitational freeze-in provides an irreducible contribution at extremely small couplings. Our results demonstrate that the relic abundance constraint, combined with symmetry breaking and freeze-in dynamics, naturally drives the portal interaction responsible for scalar dark matter production into the ultra-feeble regime.