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. Such high values of m_0 have recently been found to have a focus point, leading to relatively low fine-tuning. In addition, improvements in the simulations since the last study mean that this region no longer lacks 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 (corresponding to the focus point), all points in mSUGRA with m_0 < 4000 GeV, with a fine tuning measure up to 300 (570) 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 does not evade detection provided the gaugino mass parameter M_{1/2} < 460 GeV.