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) Lambda 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 Kahler uplift mechanism, which naturally allows an exponentially small positive Lambda 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 Lambda or a big enough m(susy), but not both. The introduction of the Higgs fields (with their soft terms) allows a small Lambda and a big enough m(susy) simultaneously. Since an exponentially small Lambda is statistically preferred (as the properly normalized probability distribution P(Lambda) diverges at Lambda = 0(+)), identifying the observed Lambda(obs) to the median value Lambda(50%) yields m(EW)similar to 100 GeV. We also find that the warped anti-D3-brane tension has a SUSY-breaking scale m(susy) similar to 100 m(EW) while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector is m(susy) similar or equal to m(EW).

Automated summary

The study explores a model linking supersymmetric electroweak phenomenology to string theory motivated flux compactification approach, breaking supersymmetry through various mechanisms to allow for both small Lambda and large m(susy) simultaneously. This model suggests a statistically preferred exponentially small Lambda and a SUSY-breaking scale directly correlating with Higgs fields in the visible sector.