The Higgs Mass beyond the CMSSM

The apparent discovery of a Higgs boson with mass ~125 GeV has had a significant impact on the constrained minimal supersymmetric extension of the Standard Model in which the scalar masses, gaugino masses and tri-linear A-terms are assumed to be universal at the GUT scale (the CMSSM). Much of the low-mass parameter space in the CMSSM has been excluded by supersymmetric particle searches at the LHC as well as by the Higgs mass measurement and the emergent signal for B_s to mu^+ mu^-. Here, we consider the impact of these recent LHC results on several variants of the CMSSM with a primary focus on obtaining a Higgs mass of ~125 GeV. In particular, we consider the one- and two-parameter extensions of the CMSSM with one or both of the Higgs masses set independently of the common sfermion mass, m_0 (the NUHM1,2). We also consider the one-parameter extension of the CMSSM in which the input universality scale M_in is below the GUT scale (the sub-GUT CMSSM). We find that when M_in < M_GUT large regions of parameter space open up where the relic density of neutralinos can successfully account for dark matter with a Higgs boson mass ~125 GeV. In some of these regions essential roles are played by coannihilation processes that are usually less important in the CMSSM with M_in = M_GUT. Finally, we reconsider mSUGRA models with sub-GUT universality, which have the same number of parameters as the CMSSM. Here too, we find phenomenologically viable regions of parameter space, which are essentially non-existent in GUT-scale mSUGRA models. Interestingly, we find that the preferred range of the A-term straddles that predicted by the simplest Polonyi model.