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 m_✘susy✘, 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 in the supersymmetric standard model, one has either a small Λ or a big enough m_✘susy✘, but not both. The introduction of the Higgs fields (with their soft terms) allows a small Λ and a big enough m_✘susy✘ 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 M_✘susy✘ ∼ 100 m_EW while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector m_✘susy✘ ≈ m_EW. © The Authors.