Higgs and Dark Matter Hints of an Oasis in the Desert

Recent LHC results suggest a standard model (SM)-like Higgs boson in the vicinity of 125 GeV with no clear indications yet of physics beyond the SM. At the same time, the SM is incomplete, since additional dynamics are required to accommodate cosmological dark matter (DM). In this paper we show that interactions between weak scale DM and the Higgs which are strong enough to yield a thermal relic abundance consistent with observation can easily destabilize the electroweak vacuum or drive the theory into a non-perturbative regime at a low scale. As a consequence, new physics--beyond the DM itself--must enter at a cutoff well below the Planck scale and in some cases as low as O(10 - 1000 TeV), a range relevant to indirect probes of flavor and CP violation. In addition, this cutoff is correlated with the DM mass and scattering cross-section in a parameter space which will be probed experimentally in the near term. Specifically, we consider the SM plus additional spin 0 or 1/2 states with singlet, triplet, or doublet electroweak quantum numbers and quartic or Yukawa couplings to the Higgs boson. We derive explicit expressions for the full two-loop RGEs and one-loop threshold corrections for these theories.Comment: 29 pages, 13 figure

Four Generations: SUSY and SUSY Breaking

We revisit four generations within the context of supersymmetry. We compute the perturbativity limits for the fourth generation Yukawa couplings and show that if the masses of the fourth generation lie within reasonable limits of their present experimental lower bounds, it is possible to have perturbativity only up to scales around 1000 TeV. Such low scales are ideally suited to incorporate gauge mediated supersymmetry breaking, where the mediation scale can be as low as 10-20 TeV. The minimal messenger model, however, is highly constrained. While lack of electroweak symmetry breaking rules out a large part of the parameter space, a small region exists, where the fourth generation stau is tachyonic. General gauge mediation with its broader set of boundary conditions is better suited to accommodate the fourth generation.Comment: 27 pages, 5 figure

Twenty Years of SUGRA

A brief review is given of the developments of mSUGRA and its extensions since the formulation of these models in 1982. Future directions and prospects are also discussed.Comment: Invited talk at the International Conference BEYOND-2003, Schloss Ringberg, Germany, June 10-14, 2003; 21 pages, Late