  A search is presented for production of dark matter particles recoiling
against a leptonically decaying Z boson in 20.3 fb$^{-1}$ of pp collisions at
$\sqrt{s}$=8 TeV with the ATLAS detector at the Large Hadron Collider. Events
with large missing transverse momentum and two oppositely-charged electrons or
muons consistent with the decay of a Z boson are analyzed. No excess above the
Standard Model prediction is observed. Limits are set on the mass scale of the
contact interaction as a function of the dark matter particle mass using an
effective field theory description of the interaction of dark matter with
quarks or with Z bosons. Limits are also set on the coupling and mediator mass
of a model in which the interaction is mediated by a scalar particle.
