  The described Dark Abelian Sector Model (DASM) extends the Standard Model
(SM) by a ``dark'' sector containing a spontaneously broken $U(1)_\text{d}$
gauge group. Keeping this dark sector quite generic we only add one additional
Higgs boson, one Dirac fermion, and right-handed SM-like neutrinos to the SM.
Using the only two singlet operators of the SM with dimension less than 4 (the
$U(1)_\text{Y}$ field-strength tensor and the SM Higgs mass operator
$|\Phi|^2$) as well as the right-handed neutrino fields we open up three
portals to the dark sector. Dark sectors, such as the one of the DASM, that
introduce an additional Higgs boson $\text{H}$ as well as an additional
$\text{Z}'$ gauge boson can have a large influence on the predictions for
electroweak precision observables and even accommodate possible dark matter
candidates. We consider one of the two Higgs bosons to be the known
$125\,\text{GeV}$ Higgs boson and parameterize the extension of the scalar
sector by the mass of the second Higgs boson, the Higgs mixing angle, and a
Higgs self-coupling. We do not assume any mass hierarchy in the gauge sector
and use the mass of the additional $\text{Z}'$ boson and a corresponding
gauge-boson mixing angle to parameterize the extension of the gauge sector. The
fermion sector is parameterized by the mass of the additional fermion and a
fermion mixing angle. We describe an on-shell as well as an
$\overline{\text{MS}}$ renormalization scheme for the DASM sectors and give
explicit results for the renormalization constants at the 1-loop level, and,
thus, prepare the ground for full NLO predictions for collider observables in
the DASM. As a first example, we provide the DASM prediction for the W-boson
mass derived from muon decay.
