Simple Theory of Chiral Fermion Dark Matter

We propose a theory of chiral fermion dark matter (DM) with an isospin-3/2 fermion of a dark sector $SU(2)_D$ gauge symmetry, which is arguably the simplest chiral theory. An isospin-3 scalar breaks $SU(2)_D$ down to a discrete non-Abelian group $T'$ and generates the DM mass. The $SU(2)_D$ gauge symmetry protects the DM mass and guarantees its stability. We derive consistency conditions for the theory and study its DM phenomenology. In some regions of parameters of the theory a two-component DM scenario is realized, consisting of a fermion and a boson, with the boson being the lightest $T'$ nonsinglet field. In the case of single component fermionic DM, we find that internal consistency of the theory, perturbativity arguments, and the observed relic abundance limit the DM mass to be less than $280$ GeV, except when $s$-channel resonance regions are open for annihilation. For a significant part of the parameter space, the theory can be tested in DM direct detection signals at the LZ and XENONnT experiments.