Uncertainty in Electroweak Symmetry Breaking in Models With High Scale Supersymmetry Breaking and its Impact on Interpretations of Searches For Supersymmetric Particles

Some regions of parameter space of the minimal supersymmetric standard model (MSSM) with high scale supersymmetry breaking have extreme sensitivity of electroweak symmetry breaking (EWSB) to the top quark mass through renormalisation group evolution effects. This leads to uncertainties in the predictions which need to be taken into account in the interpretation of searches for supersymmetric particles in these regions. As an example, we provide estimates of the current uncertainties on the position in parameter space of the region which does not break electroweak symmetry in the constrained MSSM (CMSSM). The position of the boundary of EWSB can vary by up to 2 TeV in m_0 due to the uncertainties coming from the current measurement errors on the top quark mass and from higher order corrections. In this dangerous region, for fixed CMSSM parameters the neutralino lightest supersymmetric particle mass has an associated large uncertainty of order 100%. These uncertainties therefore have a profound effect on the interpretation of LHC supersymmetric particle searches in terms of the CMSSM. We also show how to ameliorate poor convergence of the iterative numerical algorithm that calculates the MSSM spectrum near the boundary of EWSB.