  Collider search for dark matter production has been performed over the years
based on high pT standard model signatures balanced by large missing transverse
energy. The mono-Z boson production with leptonic decay has a clean signature
with the advantage that the decaying electrons and muons can be precisely
measured. This signature not only enables reconstruction of the Z boson rest
frame, but also makes possible recovery of the underlying production dynamics
through the decaying lepton angular distribution. In this work, we exploit full
information carried by the leptonic Z boson decays to set limits on coupling
strength parameters of the dark sector. We study simplified dark sector models
with scalar, vector, and tensor mediators and observe among them different
signatures in the distribution of angular coefficients.Specifically, we show
that angular coefficients can be used to distinguish different scenarios of the
spin-0 and spin-1 models, including the ones with parity-odd and charge
conjugation parity-odd operators. To maximize the statistical power, we perform
a matrix element method study with a dynamic construction of event likelihood
function. We parametrize the test statistic such that sensitivity from the
matrix element is quantified through a term measuring the shape difference. Our
results show that the shape differences provide significant improvements in the
limits, especially for the scalar mediator models. We also present an example
application of a matrix-element-kinematic-discriminator, an easier approach
that is applicable for experimental data.
