Linking the supersymmetric standard model to the cosmological constant.

String theory has no parameter except the string scale M S , so the Planck scale M Pl, the supersymmetry-breaking scale , the electroweak scale m EW as well as the vacuum energy density (cosmological constant) Λ are to be determined dynamically at any local minimum solution in the string theory landscape. Here we consider a model that links the supersymmetric electroweak phenomenology (bottom up) to the string theory motivated flux compactification approach (top down). In this model, supersymmetry is broken by a combination of the racetrack Kähler uplift mechanism, which naturally allows an exponentially small positive Λ in a local minimum, and the anti-D3-brane in the KKLT scenario. In the absence of the Higgs doublets from the supersymmetric standard model, one has either a small Λ or a big enough , but not both. The introduction of the Higgs fields (with their soft terms) allows a small Λ and a big enough simultaneously. Since an exponentially small Λ is statistically preferred (as the properly normalized probability distribution P(Λ) diverges at Λ = 0+), identifying the observed Λobs to the median value Λ50% yields m EW ∼ 100 GeV. We also find that the warped anti-D3-brane tension has a SUSY-breaking scale ∼ 100 m EW while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector is ≃ m EW.