  In this paper, we examine the strategies and prospects for distinguishing
between traditional dark-matter models and models with non-minimal dark sectors
--- including models of Dynamical Dark Matter (DDM) --- at hadron colliders.
For concreteness, we focus on events with two hadronic jets and large missing
transverse energy at the Large Hadron Collider (LHC). As we discuss, simple
"bump-hunting" searches are not sufficient; probing non-minimal dark sectors
typically requires an analysis of the actual shapes of the distributions of
relevant kinematic variables. We therefore begin by identifying those kinematic
variables whose distributions are particularly suited to this task. However, as
we demonstrate, this then leads to a number of additional subtleties, since
cuts imposed on the data for the purpose of background reduction can at the
same time have the unintended consequence of distorting these distributions in
unexpected ways, thereby obscuring signals of new physics. We therefore proceed
to study the correlations between several of the most popular relevant
kinematic variables currently on the market, and investigate how imposing cuts
on one or more of these variables can impact the distributions of others.
Finally, we combine our results in order to assess the prospects for
distinguishing non-minimal dark sectors in this channel at the upgraded LHC.
