  In spontaneously broken gauge theories, transition amplitudes describing
dark-matter (DM) annihilation processes through a resonance may become highly
inaccurate close to a production threshold, if a Breit-Wigner (BW) ansatz with
a constant width is used. To partially overcome this problem, the BW propagator
needs to be modified by including a momentum dependent decay width. However,
such an approach to resonant transition amplitudes generically suffers from
gauge artefacts that may also give rise to a bad or ambiguous high-energy
behaviour for such amplitudes. We address the two problems of gauge dependence
and high-energy unitarity within a gauge-independent framework of resummation
implemented by the so-called Pinch Technique. We study DM annihilation via
scalar resonances in a gauged U(1)$_X$ complex-scalar extension of the Standard
Model that features a massive stable gauge field which can play the role of the
DM. We find that the predictions for the DM abundance may vary significantly
from previous studies based on the naive BW ansatz and propose an alternative
simple approximation which leads to the correct DM phenomenology. In
particular, our results do not depend on the gauge-fixing parameter and are
consistent with considerations from high-energy unitarity.
