Linking the Supersymmetric Standard Model to the Cosmological Constant

Abstract: String theory has no parameter except the string scale $M_S$, so the Planck scale $M_\text{Pl}$, the supersymmetry-breaking scale, the EW scale $m_\text{EW}$ 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 K\"ahler 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 in the supersymmetric standard model, one has either a small $\Lambda$ or a big enough SUSY-breaking scale, but not both. The introduction of the Higgs fields (with their soft terms) allows a small $\Lambda$ and a big enough SUSY-breaking scale simultaneously. Since an exponentially small $\Lambda$ is statistically preferred (as the properly normalized probability distribution $P(\Lambda)$ diverges at $\Lambda=0^{+}$), identifying the observed $\Lambda_{\rm obs}$ to the median value $\Lambda_{50\%}$ yields $m_{\rm EW} \sim 100$ GeV. We also find that the warped anti-D3-brane tension has a SUSY-breaking scale of $100m_{\rm EW}$ in the landscape while the SUSY-breaking scale that directly correlates with the Higgs fields in the visible sector has a value of $m_{\rm EW}$.