Naturalness Reach of the Large Hadron Collider in Minimal Supergravity
  We re-analyse the prospects of discovering supersymmetry at the LHC, in order to re-express coverage in terms of a fine-tuning parameter and to extend the analysis to scalar masses (m_0) above 2 TeV.   We use minimal supergravity (mSUGRA) unification assumptions for the SUSY breaking parameters. The discovery reach at high m_0 is of renewed interest because this region has recently been found to have a focus point, leading to relatively low fine-tuning, and because it remains uncertain how much of the region can be ruled out due to lack of radiative electroweak symmetry breaking.   The best fine tuning reach is found in a mono-leptonic channel, where for mu>0, A_0=0 and tan beta=10   (within the focus point region), and a top mass of 174 GeV, all points in mSUGRA with m_0 < 4000 GeV, with a fine tuning measure up to 210 (500) are covered by the search, where the definition of fine-tuning excludes (includes) the contribution from the top Yukawa coupling. Even for arbitrarily high m_0, mSUGRA can be discovered through gaugino events, provided the gaugino mass parameter M_1/2 < 460 GeV. In this region, the mono-leptonic channel still provides the best reach. 
B.C. Allanach, J.P.J. Hetherington, M.A. Parker, B.R. Webber