  A recent global fit to the CMSSM incorporating current constraints on
supersymmetry, including missing transverse energy searches at the LHC, BR(B_s
to mu+ mu-) and the direct XENON100 search for dark matter, favours points
towards the end of the stau-neutralino (stau_1- chi) coannihilation strip with
relatively large m_1/2 and 10 < tan beta < 40 and points in the H/A
rapid-annihilation funnel with tan beta ~ 50. The coannihilation points
typically have m_stau_1-m_chi < 5 GeV, and a significant fraction, including
the most-favoured point, has m_stau_1-m_chi < m_tau. In such a case, the stau_1
lifetime would be so long that the stau_1 would be detectable as a long-lived
massive charged particle that may decay inside or outside the apparatus. We
show that CMSSM scenarios close to the tip of the coannihilation strip for tan
beta < 40 are already excluded by LHC searches for massive charged particles,
and discuss the prospects for their detection in the CMS and ATLAS detectors
via time-of-flight measurements, anomalous heavy ionization or decays into one
or more soft charged particles.
