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 [Image: see text] , 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 [Image: see text] , but not both. The introduction of the Higgs fields (with their soft terms) allows a small Λ and a big enough [Image: see text] simultaneously. Since an exponentially small Λ is statistically preferred (as the properly normalized probability distribution P(Λ) diverges at Λ = 0(+)), identifying the observed Λ(obs) to the median value Λ(50%) yields m(EW) ∼ 100 GeV. We also find that the warped anti-D3-brane tension has a SUSY-breaking scale [Image: see text] ∼ 100 m(EW) while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector is [Image: see text] ≃ m(EW).