  We present a first-principle computation of the jet quenching parameter,
which describes the momentum broadening of a high-energy parton moving through
the deconfined state of QCD matter at high temperature. Following an idea
originally proposed by Caron-Huot, we explain how one can evaluate the soft
contribution to the collision kernel characterizing this real-time phenomenon,
analyzing certain gauge-invariant operators in a dimensionally reduced
effective theory (electrostatic QCD), which can be studied non-perturbatively
via simulations on a Euclidean lattice. Our high-precision numerical
computations at two different temperatures indicate that soft contributions to
the jet quenching parameter are large. After discussing the systematic
uncertainties involved, we present a quantitative estimate for the jet
quenching parameter in the temperature range accessible at heavy-ion colliders,
and compare it to results from phenomenological models as well as to
strong-coupling computations based on the holographic correspondence.
