Non-universal SUSY models, $g_\mu-2$, $m_H$ and dark matter

We study the anomalous magnetic moment of the muon, $g_\mu - 2 \equiv 2 a_\mu$, in the context of supersymmetric models beyond the CMSSM, where the unification of either the gaugino masses $M_{1,2,3}$ or sfermion and Higgs masses is relaxed, taking into account the measured mass of the Higgs boson, $m_H$, the cosmological dark matter density and the direct detection rate. We find that the model with non-unified gaugino masses can make a contribution $\Delta a_\mu\sim 20 \times 10^{-10}$ to the anomalous magnetic moment of the muon, for example if $M_{1,2} \sim 600$ GeV and $M_3\sim 8$ TeV. The model with non-universal sfermion and Higgs masses can provide even larger $\Delta a_\mu \sim 24 \times 10^{-10}$ if the sfermion masses for the first and the second generations are $ \sim 400 $ GeV and that of the third is $ \sim 8 $ TeV. We discuss the prospects for collider searches for supersymmetric particles in specific benchmark scenarios illustrating these possibilities, focusing in particular on the prospects for detecting the lighter smuon and the lightest neutralino.