  We examine the case of neutralino dark matter in the focus point region of
the MSSM, in which the scalar sparticles are too heavy to be produced at the
LHC. Whilst it has been previously asserted that the LHC alone would fail to
constrain the properties of the lightest neutralino for such a scenario, we
find that one can obtain good predictions of astrophysical quantities such as
the relic density, annihilation cross-section and direct search cross-sections
by using the shape of the dilepton invariant mass spectrum to constrain
neutralino mixing. We demonstrate our technique using a Bayesian analysis of
the 24 parameter MSSM model space, and in the process introduce a novel way of
improving the LHC results even without assumptions on which new sparticles are
responsible for the kinematic features in the dilepton invariant mass
distribution.
