Higgs-Portal Stueckelberg Dark Matter

We study dark photon dark matter $X$ associated with a dark $U(1)_X$ gauge symmetry. To evade laboratory and cosmological constraints on kinetic mixing with the Standard Model $U(1)_Y$, we assign a $Z_2$-odd dark parity to $X$ that forbids such mixing. The leading interactions then arise from gauge-invariant dimension-6 Higgs-portal operators, including both parity-even and parity-odd terms. We assume that the dark matter mass is generated via the Stueckelberg mechanism, which also induces a dimension-4 Higgs-portal operator $(H^\dagger H) X_\mu X^\mu$ and additional dimension-6 operators. We investigate freeze-in production of $X$ from Higgs-pair annihilations after reheating, incorporating both gauge-invariant and Stueckelberg-induced operators. First, we consider the case in which the Wilson coefficients of the gauge-invariant dimension-6 operators, $C$ and $\tilde{C}$, are of order unity. We find that, in this case, the Stueckelberg contributions remain subdominant in dark matter production. This result follows from the requirement that the effective scale implied by perturbative unitarity must exceed the cutoff scale of the effective field theory. Next, we explore a more general situation in which $C$ and $\tilde{C}$ are smaller than unity. In this second case, Stueckelberg-induced operators can become comparable and lead to distinctive features in the dark-matter parameter space, including interference effects. For both cases, we show that there exists a wide parameter space consistent with the observed dark matter relic density.