  We study the production of dineutrinos in proton-proton collisions, with
large missing transverse energy and an energetic jet as the experimental
signature. Recasting a search from the ATLAS collaboration we work out
constraints on semileptonic four-fermion operators, gluon and electroweak
dipole operators and $Z$-penguins in the SMEFT. All but the $Z$-penguin
operators experience energy-enhancement. Constraints on gluon dipole operators
are the strongest, probing new physics up to 14 TeV, and improve over existing
ones from collider studies. Limits on FCNC four-fermion operators are
competitive with Drell-Yan production of dileptons, and improve on those for
tau final states. For left-handed $|\Delta s|=|\Delta d|=1$ and right-handed
$|\Delta c|=|\Delta u|=1$ transitions these are the best available limits, also
considering rare kaon and charm decays. We estimate improvements for the $3000
\;\mathrm{fb}^{-1}$ High Luminosity Large Hadron Collider.
