Abstract
Perturbative supersymmetry breaking on the landscape of string vacua is expected to favor large soft terms as a power-law or log distribution, but tempered by an anthropic veto of inappropriate vacua or vacua leading to too large a value for the derived weak scale -- a violation of the atomic principle. Indeed, scans of such vacua yield a statistical prediction for light Higgs boson mass m_h~ 125 GeV with sparticles (save possibly light higgsinos) typically beyond LHC reach. In contrast, models of dynamical SUSY breaking (DSB) -- with a hidden sector gauge coupling g^2 scanned uniformly -- lead to gaugino condensation and a uniform distribution of soft parameters on a log scale. Then soft terms are expected to be distributed as $m_{\rm soft}^{-1}$ favoring small values. A scan of DSB soft terms generally leads to $m_h\ll 125$ GeV and sparticle masses usually below LHC limits. Thus, the DSB landscape scenario seems excluded from LHC search results. An alternative is that the exponential suppression of the weak scale is set anthropically on the landscape via the atomic principle.
Highlights
One of the mysteries of nature is the origin of mass scales
Another possibility is nonperturbative SUSY breaking via instanton effects, which leads to an exponential suppression of mass scales
We adopt the ISAJET [56] code for calculation of the Higgs and superparticle mass spectrum [57] based on two-loop renormalization group equation (RGE) running [58] along with sparticle and Higgs masses calculated at the RG
Summary
One of the mysteries of nature is the origin of mass scales. At least in QCD, we have an answer: the hadronic mass scale can arise when the gauge coupling evolves to large values such that the fundamental constituents, the quarks, condense to bound states. The proton mass can be found even in terms of the Planck mass mPl via mproton ≃ mPl expð−8π2=g2Þ, which gives the right answer for g2 ∼ 1.8. Another mass scale begging for explanation is that associated with weak interactions: mweak ≃ mW;Z;h ∼ 100 GeV. Supersymmetrization of the SM eliminates the Higgs mass quadratic divergences so any remaining divergences are merely logarithmic [1,2]: the minimal supersymmetric Standard Model, or MSSM [3], can be viable up to the GUTor even Planck scales. The exponentially suppressed hidden sector mass scale must be put in by hand, so SSB can apparently only accommodate, but not explain, the magnitude of the weak scale.
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