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 $Z( ubar u)+$jet background in the signal region. This can be achieved by taking accurate data in control regions dominated by $Z(ell^+ell^-)+$jet, $W(ell u)+$jet and $gamma+$jet production, and extrapolating to the $Z( ubar u)+$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 $Z( ubar u)+$jet background is at the few percent level up to the TeV range.
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