  We reanalyze the effective field theory (EFT) approach for the scenario in
which the particles that account for the dark matter (DM) in the universe are
vector states that interact only through the Standard Model-like Higgs boson.
These DM particles are searched for in direct and indirect detection in
astrophysical experiments and in invisible Higgs decays at the LHC. The
constraints obtained in these two search types are complementary and
correlated. In recent years, it has been advocated that the EFT approach is
problematic for small DM mass and that it does not capture all the aspects of
vector DM; one should thus rather interpret the searches in ultraviolet
complete theories that are more realistic. In this note, we show that a more
appropriate definition of the EFT with the introduction of an effective New
Physics scale parameter, can encompass such issues. We illustrate this by
matching the EFT to two examples of ultraviolet completions for it: the U(1)
model with a dark photon and a model that was recently adopted by the LHC
experiments in which vector-like fermions generate an effective interaction
between the Higgs and the DM states at the one-loop level. Additionally, we
find that the region of parameter space that is relevant for DM phenomenology
is well inside the range of validity of the EFT. It thus provides a general
parametrization of the effects of any ultraviolet model in the regime under
exploration, making it the ideal framework for model-independent analyses of
the vector DM Higgs-portal.
