Non-Abelian Vector Boson Dark Matter, its Unified Route and signatures at the LHC

Vector boson dark matter (DM) appears in $SU(2)_N$ extension ($N$ stands for neutral) of Standard Model (SM) where an additional global $U(1)_P$ symmetry is assumed and results in a generalized lepton number defined as: $L=P+T_{3N}$. Breaking of $U(1)_P$ leads to the breaking of $L$ to $(-1)^L$, thus stabilizing DM through modified $R=(-1)^{3B+L+2J}$. This model, already discussed in literature, offers several novel features to elaborate upon. For example, $t$-channel annihilation and dominant $s$-channel direct search, along with co-annihilation, helps the DM to evade stringent direct search bounds from LUX and XENON1T after satisfying relic density constraints. On the other hand, the exotic particles of the model can be produced at the Large Hadron Collider (LHC) yielding multilepton final states. Hadronically quiet four lepton signal with large missing energy, in specific, is shown to provide a smoking gun signature of such a framework. We study the details of $E(6) \to SM \otimes SU(2)_N$ breaking patterns (through D-parity odd/even cases) which yield important phenomenological consequences.