We analyze the Minimal Supersymmetric extension of the Standard Model that we have after the discovery of the Higgs boson at the LHC, the hMSSM (habemus MSSM?), i.e. a model in which the lighter h boson has a mass of approximately 125 GeV which, together with the non-observation of superparticles at the LHC, indicates that the SUSY-breaking scale MS is rather high, MS≳1 TeV. We first demonstrate that the value Mh≈125 GeV fixes the dominant radiative corrections that enter the MSSM Higgs boson masses, leading to a Higgs sector that can be described, to a good approximation, by only two free parameters. In a second step, we consider the direct supersymmetric radiative corrections and show that, to a good approximation, the phenomenology of the lighter Higgs state can be described by its mass and three couplings: those to massive gauge bosons and to top and bottom quarks. We perform a fit of these couplings using the latest LHC data on the production and decay rates of the light h boson and combine it with the limits from the negative search of the heavier H,A and H± states, taking into account the current uncertainties.
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