Dark matter physics in dark $SU(2)$ gauge symmetry with non-Abelian kinetic mixing
We investigate a model of dark sector based on non-Abelian $SU(2)_D$ gauge symmetry. This dark gauge symmetry is broken into discrete $Z_2$ via vacuum expectation values of two real triplet scalars, and an $SU(2)_D$ doublet Dirac fermion becomes $Z_2-$odd particles whose lighter component makes stable dark matter candidate. The standard model and dark sector can be connected via the scalar mixing and the gauge kinetic mixing generated by higher dimensional operators. We then discuss relic density of dark matter and implications to collider physics in the model. The most unique signatures of this model at the LHC would be the dark scalar ($Φ_1^{(')}$) productions where it subsequently decays into : (1) a fermionic dark matter ($χ_l$) and a heavy dark fermion ($χ_h$) pair, $Φ_1^{(')} \to \bar χ_l χ_h(\bar χ_h χ_l) $, followed by $χ_h$ decays into $χ_l$ and non-Abelian dark gauge bosons ($X_i$'s) which decays into SM fermion pair $\bar f_{SM} f_{SM}$ resulting in the reaction $p p \rightarrow Φ_1^{(')} \rightarrow \bar χ_h χ_l (\bar χ_l χ_h) \to f_{SM} \bar f_{SM} χ_l \bar χ_l $, (2) a pair of $X_i$'s followed by $X_i$ decays into a DM pair or the SM fermions resulting in the reaction, $p p \rightarrow Φ_1^{(')} \rightarrow X_i X_i \rightarrow \bar χ_l χ_l f_{SM} \bar f_{SM}$ or even number of $f_{SM} \bar{f}_{SM}$ pairs.