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If fermionic dark matter (DM) is stabilized by dark $U(1)$ gauge symmetrythat is spontaneously broken into its subgroup $Z_2$, the particle contents ofthe model becomes very rich: DM and excited DM, both of them are Majoranafermions, as well as two dark force mediators, dark photon and dark Higgs bosonare naturally present due to the underlying dark gauge symmetry. In this paper,we study the DM bound state formation processes within this scenario, assumingboth dark photon and dark Higgs are light mediators and including the effectsof excited DM. The Goldstone boson contributions to the potential matrix in theSchr\"{o}dinger equations are found to be important. The emissions of alongitudinal vector boson (or somehow equivalently a Goldstone boson) duringthe DM bound state formations are crucial to induce a significantreannihilation process, reducing the dark matter relic abundance. Most of thestringent constraints for this kind of dark matter considered in the literatureare simply evaded.

Dark Matter Bound State Formation in Fermionic $Z_2$ DM model with Light Dark Photon and Dark Higgs Boson