  Our contribution sets out to investigate the GeV-scale phenomenology of a
model based on an $SU_{L}(2) \times U_{Y}(1) \times U(1)_{X}$-gauge symmetry.
The model accommodates, as a consequence of the symmetry-breaking pattern, a
light gauge boson at the GeV-scale or below, allowing then to set up a new low
energy physics. The fermion sector includes an exotic candidate to Dark Matter
(DM) and the whole fermionic field content yields, as it is mandatory, the
cancellation of the chiral anomaly. %In this strict sense, we refer to our
proposal as a unified description : two different and exclusive
symmetry-breaking patterns are treated with a single Lagrangian density and a
common symmetry group. Furthermore, The light gauge boson and the exotic
fermion are proposed as candidates to the so-called dark sector of the model
that we try to describe in this contribution. The low-energy spectrum exhibits
a hidden scalar field with mass fixed at the GeV level in the Higgs sector. We
calculate the DM relic density associated with the dark fermion candidate by
considering two annihilation processes in which the light gauge boson works as
a portal for the DM detection. The observed relic density points to a mass of
$3.4$ GeV for the DM fermion, while the light gauge boson mass is $8.0$ GeV. We
also investigate the direct detection of DM in the low energy regime and obtain
the region of parameters allowed by recent discussions on DM limits. Finally,
the correction to the muon magnetic dipole moment is calculated considering the
gauge boson mass at the GeV scale or below.
