Towards UV Models of Kinetic Mixing and Portal Matter: A More Complex Dark Matter Sector?

Portal Matter, with both SM and dark charges, induces KM between the $U(1)_D$ dark photon and the SM gauge fields offering an attractive mechanism by which light thermal DM can obtain its observed relic density. If DM is fermionic, the CMB informs us that it must be Majorana/pseudo-Dirac in nature to avoid temperature-independent $s$-wave annihilation to SM states. How does this fit into a more complete picture with the SM? A first step along this path may not lie far away in energy due to the RGE running of the dark gauge coupling which can becomes non-perturbative before the $\sim 10$'s of TeV range. This implies that $U(1)_D$ must become embedded in a non-Abelian group, $G_D$, before this occurs. The breaking of this group then produces the PM masses and the heavy gauge fields associated with $G_D$ lead to new interactions between the SM and the dark sector. In the past we have examined a set of distinctive phenomenological features associated with this setup, based upon a number of simplifying assumptions. It behooves us to explore the impact of these assumptions on the predictions for possible experimental tests of these models. In past analyses we assumed that DM is a VL, complex singlet under $G_D$. If this assumption is relaxed, the dark sector must be augmented by additional fermion(s) and the scalar fields needed to break the symmetries while generating the needed Majorana-like mass terms for the DM. Here we analyze the simplest extension of this kind wherein the DM lies in a VL doublet of $G_D$, which we take to have the structure $SU(2)_I\times U(1)_{Y_I}$, leading to new phenomenology. We find that given the current LHC search constraints on the masses of heavy gauge bosons, the production of these new dark states with large rates is unlikely at colliders unless they are produced singly in $gg$-fusion or are resonantly enhanced.