We discuss the potential impacts on the CMSSM of future LHC runs and possible
electron-positron and higher-energy proton-proton colliders, considering
searches for supersymmetry via MET 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 MET 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 m_0, m_{1/2} and
A_0 of the CMSSM. Slepton measurements at CLIC would enable m_0 and m_{1/2} 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 electron-positron 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, 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.Comment: 47 pages, 26 figure