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Looking for supersymmetry: ~1 Tev WIMP and the power of complementarity in LHC and dark matter searches

Some doubts have been expressed about low energy supersymmetry (SUSY) following the first run of the LHC. In this talk I will try to present a more upbeat view based on data, rather than theoretical expectations. In particular, I will make the following points: (a) in my opinion the most attractive candidate for dark matter (DM) is now the lightest neutralino with mass around 1 TeV and with well defined properties (a nearly pure higgsino). This follows primarily from a combination of the properties of the discovered Higgs boson, in particular its mass close to 125 Gev, and the relic density of dark matter, and is most clearly visible in the context of unified, or constrained, SUSY frameworks, although the DM candidate is quite generic; (b) this DM candidate will be nearly fully tested in forthcoming one-tonne DM underground search detectors; (c) the CMSSM will be nearly fully tested in the next few years by a combination of expected data from LHC experiments and from direct DM searches, as well as potentially also by the Cherenkov Telescope Array; (d) if naturalness plays any real role in SUSY (which remains unclear), then the amount of fine tuning, which is very large in simple models like the CMSSM, can be significantly reduced (even down to 1 in 20) with properly selected boundary conditions at the unification scale; (e) the (g-2) muon anomaly can be accommodated not only in the context of the general MSSM but also of some unified SUSY models with some superpartners to be within reach of the LHC.