  High-energy jets recoiling against missing transverse energy (MET) are
powerful probes of dark matter at the LHC. Searches based on large MET
signatures require a precise control of the $Z(\nu\bar\nu)+$jet background in
the signal region. This can be achieved by taking accurate data in control
regions dominated by $Z(\ell^+\ell^-)+$jet, $W(\ell\nu)+$jet and $\gamma+$jet
production, and extrapolating to the $Z(\nu\bar\nu)+$jet background by means of
precise theoretical predictions. In this context, recent advances in
perturbative calculations open the door to significant sensitivity improvements
in dark matter searches. In this spirit, we present a combination of
state-of-the art calculations for all relevant $V+$jets processes, including
throughout NNLO QCD corrections and NLO electroweak corrections supplemented by
Sudakov logarithms at two loops. Predictions at parton level are provided
together with detailed recommendations for their usage in experimental analyses
based on the reweighting of Monte Carlo samples. Particular attention is
devoted to the estimate of theoretical uncertainties in the framework of dark
matter searches, where subtle aspects such as correlations across different
$V+$jet processes play a key role. The anticipated theoretical uncertainty in
the $Z(\nu\bar\nu)+$jet background is at the few percent level up to the TeV
range.
