Feebly coupled vector boson dark matter in effective theory

A model of dark matter (DM) that communicates with the Standard Model (SM) exclusively through suppressed dimension five operator is discussed. The SM is augmented with a symmetry $U(1)_X \otimes Z_2$, where $U(1)_X$ is gauged and broken spontaneously by a very heavy decoupled scalar. The massive $U(1)_X$ vector boson ($X^\mu$) is stabilized being odd under unbroken $Z_2$ and therefore may contribute as the DM component of the universe. Dark sector field strength tensor $X^{\mu\nu}$ couples to the SM hypercharge tensor $B^{\mu\nu}$ via the presence of a heavier $Z_2$ odd real scalar $\Phi$, i.e. $1/\Lambda \; X^{\mu\nu}B_{\mu\nu}\Phi$, with $\Lambda$ being a scale of new physics. The freeze-in production of the vector boson dark matter feebly coupled to the SM is advocated in this analysis. Limitations of the so-called UV freeze-in mechanism that emerge when the maximum reheat temperature $T_\text{RH}$ drops down close to the scale of DM mass are discussed. The parameter space of the model consistent with the observed DM abundance is determined. The model easily and naturally avoids both direct and indirect DM searches. Possibility for detection at the Large Hadron Collider (LHC) is also considered. A Stueckelberg formulation of the model is derived.