MSSM dark matter measurements at the LHC without squarks and sleptons

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.