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The notion of stringy naturalness-that an observable O 2 is more natural than O 1 if more (phenomenologically acceptable) vacua solutions lead to O 2 rather than O 1 -is examined within the context of the Standard Model (SM) and various SUSY extensions: CMSSM/mSUGRA, high-scale SUSY and radiatively-driven natural SUSY (RNS). Rather general arguments from string theory suggest a (possibly mild) statistical draw towards vacua with large soft SUSY breaking terms. These vacua must be tempered by an anthropic veto of non-standard vacua or vacua with too large a value of the weak scale m weak . We argue that the SM, the CMSSM and various high-scale SUSY models are all expected to be relatively rare occurances within the string theory landscape of vacua. In contrast, models with TeV-scale soft terms but with m weak ∼ 100 GeV and consequent light higgsinos (SUSY with radiatively-driven naturalness) should be much more common on the landscape. These latter models have a statistical preference for m h 125 GeV and strongly interacting sparticles beyond current LHC reach. Thus, while conventional naturalness favors sparticles close to the weak scale, stringy naturalness favors sparticles so heavy that electroweak symmetry is barely broken and one is living dangerously close to vacua with charge-or-color breaking minima, no electroweak breaking or pocket universe weak scale values too far from our measured value. Expectations for how landscape SUSY would manifest itself at collider and dark matter search experiments are then modified compared to usual notions. *

The string theory landscape of vacua solutions provides physicists with some understanding as to the magnitude of the cosmological constant. Similar reasoning can be applied to the magnitude of the soft SUSY breaking terms in supersymmetric models of particle physics: there appears to be a statistical draw towards large soft terms which is tempered by the anthropic requirement of the weak scale lying not too far from ∼ 100 GeV. For a mild statistical draw of m n sof t with n = 1 (as expected from SUSY breaking due to a single F term) then the light Higgs mass is preferred at ∼ 125 GeV while sparticles are all pulled beyond LHC bounds. We confront a variety of LHC and WIMP dark matter search limits with the statistical expectations from a fertile patch of string theory landscape. The end result is that LHC and WIMP dark matter detectors see exactly that which is expected from the landscape: a Standard Model-like Higgs boson of mass 125 GeV but as yet no sign of sparticles or WIMP dark matter. SUSY from the n = 1 landscape is most likely to emerge at LHC in the soft opposite-sign dilepton plus jet plus MET channel. Multi-ton noble liquid WIMP detectors should be able to completely explore the n = 1 landscape parameter space. *

We examine several issues pertaining to statistical predictivity of the string theory landscape for weak scale supersymmetry (SUSY). We work within a predictive landscape wherein superrenormalizable terms scan while renormalizable terms do not. We require stringy naturalness wherein the likelihood of values for observables is proportional to their frequency within a fertile patch of landscape including the minimal supersymmetric standard model as low energy effective theory with a pocket-universe value for the weak scale nearby to its measured value in our universe. In the string theory landscape, it is reasonable that the soft terms enjoy a statistical power-law draw to large values, subject to the existence of atoms as we know them (atomic principle). We argue that gaugino masses, scalar masses, and trilinear soft terms should each scan independently. In addition, the various scalars should scan independently of each other unless protected by some symmetry. The expected nonuniversality of scalar masses-once regarded as an undesirable feature-emerges as an asset within the context of the string landscape picture. In models such as heterotic compactifications on Calabi-Yau manifolds, where the tree-level gauge kinetic function depends only on the dilaton, gaugino masses may scale mildly, while scalar masses and A terms, which depend on all the moduli, may scale much more strongly leading to a landscape solution to the SUSY flavor and CP problems in spite of nondiagonal Kähler metrics. We present numerical results for Higgs and sparticle mass predictions from the landscape within the generalized mirage mediation SUSY model and discuss resulting consequences for LHC SUSY and weakly interacting massive particles dark matter searches.

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