Collider Interplay for Supersymmetry, Higgs and Dark Matter

We discuss the potential impacts on the CMSSM of future LHC runs and possible [Formula: see text] and higher-energy proton-proton colliders, considering searches for supersymmetry via  [Formula: see text] events, precision electroweak physics, Higgs measurements and dark matter searches. We validate and present estimates of the physics reach for exclusion or discovery of supersymmetry via [Formula: see text] searches at the LHC, which should cover the low-mass regions of the CMSSM parameter space favoured in a recent global analysis. As we illustrate with a low-mass benchmark point, a discovery would make possible accurate LHC measurements of sparticle masses using the MT2 variable, which could be combined with cross-section and other measurements to constrain the gluino, squark and stop masses and hence the soft supersymmetry-breaking parameters [Formula: see text] and [Formula: see text] of the CMSSM. Slepton measurements at CLIC would enable [Formula: see text] and [Formula: see text] to be determined with high precision. If supersymmetry is indeed discovered in the low-mass region, precision electroweak and Higgs measurements with a future circular [Formula: see text] collider (FCC-ee, also known as TLEP) combined with LHC measurements would provide tests of the CMSSM at the loop level. If supersymmetry is not discovered at the LHC, it is likely to lie somewhere along a focus-point, stop-coannihilation strip or direct-channel A / H resonance funnel. We discuss the prospects for discovering supersymmetry along these strips at a future circular proton-proton collider such as FCC-hh. Illustrative benchmark points on these strips indicate that also in this case FCC-ee could provide tests of the CMSSM at the loop level.