Supersymmetric Fits after the Higgs Discovery and Implications for Model Building

The data from the first run of the LHC at 7 and 8 TeV, together with the information provided by other experiments such as precision electroweak measurements, flavour measurements, the cosmological density of cold dark matter and the direct search for the scattering of dark matter particles in the LUX experiment, provide important constraints on supersymmetric models. Important information is provided by the ATLAS and CMS measurements of the mass of the Higgs boson, as well as the negative results of searches at the LHC for events with missing transverse energy accompanied by jets, and the LHCb and CMS measurements off BR($B_s \to \mu^+ \mu^-$). Results are presented from frequentist analyses of the parameter spaces of the CMSSM and NUHM1. The global $\chi^2$ functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs mass and the missing transverse energy search, with best-fit values that are comparable to the $\chi^2$ for the Standard Model. The $95\%$ CL lower limits on the masses of gluinos and squarks allow significant prospects for observing them during the LHC runs at higher energies.