Sparticle Discovery Potentials in the CMSSM and GUT-less Supersymmetry-Breaking Scenarios

We consider the potentials of the LHC and a linear e^+e^- collider (LC) for discovering supersymmetric particles in variants of the MSSM with soft supersymmetry-breaking mass parameters constrained to be universal at the GUT scale (CMSSM) or at some lower scale M_{in} (GUT-less models), as may occur in some scenarios with mirage unification. Whereas the LHC should be able to discover squarks and/or gluinos along all the CMSSM coannihilation strip where the relic neutralino LSP density lies within the range favoured for cold dark matter, many GUT-less models could escape LHC detection. In particular, if M_{in} < 10^{11} GeV, the LHC would not detect sparticles if the relic density lies within the favoured range. For any given discovery of supersymmetry at the LHC, in such GUT-less models the lightest neutralino mass and hence the threshold for sparticle pair production at a LC increases as M_{in} decreases, and the CMSSM offers the best prospects for measuring sparticles at a LC. For example, if the LHC discovers sparticles with 1 fb^{-1} of data, within the CMSSM a centre-of-mass energy of 600 GeV would suffice for a LC to to produce pairs of neutralinos, if they provide the cold dark matter, whereas over 1 TeV might be required in a general GUT-less model. These required energies increase to 800 GeV in the CMSSM and 1.4 TeV in GUT-less models if the LHC requires 10 fb^{-1} to discover supersymmetry.