  The Standard Model Effective Field Theory (SMEFT) and the Low Energy
Effective Field Theory (LEFT) can be extended by adding additional spin 0, 1/2
and 1 dark matter particles which are singlets under the Standard Model (SM)
gauge group. We classify all gauge invariant interactions in the Lagrangian up
to terms of dimension six, and present the tree-level matching conditions
between the two theories at the electroweak scale. The most widely studied dark
matter models, such as those based on the Higgs portal or on kinetic mixing
between the photon and a dark photon, are based on dimension-four interactions
with the SM sector. We consider a model with dark vector particles with a
$\mathbb{Z}_2$ symmetry, so that the lightest dark matter particle is stable.
The leading interaction with the SM is through dimension-six operators
involving two dark vector field-strength tensors and the electromagnetic
field-strength tensor. This model is a viable dark matter model in the
freeze-in scenario for a wide range of parameters.
