Abstract
We propose a vector dark matter model with an exotic dark SU(2) gauge group. Two Higgs triplets are introduced to spontaneously break the symmetry. All of the dark gauge bosons become massive, and the lightest one is a viable vector DM candidate. Its stability is guaranteed by a remaining Z2 symmetry. We study the parameter space constrained by the Higgs measurement data, the dark matter relic density, and direct and indirect detection experiments. We find numerous parameter points satisfying all the constraints, and they could be further tested in future experiments. Similar methodology can be used to construct vector dark matter models from an arbitrary SO(N) gauge group.
Highlights
If the dark gauge group is SU(2), it can be spontaneously broken completely through one dark Higgs doublet, with a remaining custodial global SU(2) symmetry ensuring the stability of the three degenerate gauge bosons as vector DM particles [30]
We study a vector DM model with a dark SU(2)D gauge group broken by two real Higgs triplets, which develop a generic configuration of vacuum expectation values (VEVs)
We have discussed a vector DM model based on a dark SU(2)D gauge theory
Summary
Under a SU(2)D gauge transformation, the dark Higgs fields Φa and Xa transform as. where U = exp[iθa(x)T a] with (T a)bc being the generators in the adjoint representation of SU(2)D, and some representation indices have been omitted. Under a SU(2)D gauge transformation, the dark Higgs fields Φa and Xa transform as. From three vectors E, F, and G in such a space, nonzero invariant scalars can only be constructed via either dot products, like E · F = EaFa and G · G = GaGa, or triple products, like (E × F) · G = εabcEaFbGc. Since we only have two triplet Higgs fields Φa and Xa, the related scalar potential terms must be formed by bilinear dot products ΦaΦa, XaXa, and ΦaXa. the model respects an accidental Z2 symmetry, under which the Higgs triplets transform as. Since the Levi-Civita symbol satisfies εabc = det(R)RadRbeRcf εdef for R ∈ O(3)D, the O(3)D invariance of the Lagrangian requires that Aaμ acts as an O(3)D axial vector, whose transformation is.
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