Linking the Supersymmetric Standard Model to the Cosmological Constant

TL;DR

This paper proposes a model linking string theory's landscape to the Standard Model, explaining the small cosmological constant and electroweak scale through flux compactification and supersymmetry breaking mechanisms.

Contribution

It introduces a framework connecting string theory flux compactifications with electroweak phenomenology, explaining the small cosmological constant and electroweak scale simultaneously.

Findings

Small cosmological constant is statistically favored in the landscape.

Electroweak scale around 100 GeV naturally emerges.

SUSY-breaking scales are related to the Higgs sector and anti-D3-brane tension.

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 $m_{\rm EW}$.