Abstract
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 msoftn 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.
Highlights
Given that quantum corrections to the Higgs mass diverge quadratically with the theory cutoff ΛSM, it seems the Standard Model (SM) with ΛSM mweak would be a rare occurrance within the landscape since one would be required to select only those vacuum solutions with highly fine-tuned scan parameters
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
Rather general arguments regarding the statistics of the landscape of flux vacua in string theory point to a statistical draw towards large soft SUSY breaking terms governed by a power law mnsoft where n = 2nF + nD − 1 involves the number of F and D term SUSY breaking fields in a complicated hidden sector
Summary
The function fSUSY contains the expected statistical distribution of SUSY breaking scales This is related to the mass scale of MSSM soft terms as msoft m2hidden/mP. Susskind posits that an increased weak scale would lead to larger SM particle masses and consequent disruptions in both atomic and nuclear physics From these calculations, it seems reasonable to veto SM-like vacua which lead to a weak scale more than (conservatively) four times its measured value. Θ function in eq (2.6) guarantees that we veto vacua with CCB minima or no EWSB It vetoes properly broken Higgs potentials but where the weak scale is generated at more than four times its measured value
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