  We show that new physics can show up in dileptonic events through its
radiative contributions to the dilepton invariant mass, leading to unique
"monocline" features in $m_{\ell\ell}$, as well as the angular distribution of
the leptons. We focus in particular on the case of dark matter with scalar
messengers coupling it to the quarks and leptons. Consistent thermal models
require the dark matter to have masses of 100's GeV and have $\gsim 1$
couplings to the Standard Model (SM), implying that radiative corrections to
the SM Drell-Yan rate can be sizeable. We consider the case of Majorana, Dirac,
and pseudo-Dirac dark matter and show that there are regions of parameter space
where the non-existence of a monocline, which starts at roughly twice the dark
matter mass, $m_{\ell\ell} \sim 2 m_\chi$, places the strongest constraint on
the model. We make predictions for the sensitivities at the high luminosity 14
TeV LHC as well as a future 100 TeV proton-proton collider. We find that our
dilepton signal is most sensitive when the mediator and the dark matter are
nearly degenerate and conventional MET-based searches are least sensitive.
