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 (m0) above 2 TeV. We use minimal supergravity (mSUGRA) unification assumptions for the SUSY breaking parameters. Such high values of m0 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 μ > 0, A0 = 0 and tan β = 10 (corresponding to the focus point), all points in mSUGRA with m0 < 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 m0, mSUGRA does not evade detection provided the gaugino mass parameter M1/2 < 460 GeV.