String theory has no parameter except the string scale, so a dynamically compactified solution to 4 dimensional spacetime should determine both the Planck scale and the cosmological constant Λ. In the racetrack Kähler uplift flux compactification model in Type IIB theory, where the string theory landscape is generated by scanning over discrete values of all the flux parameters, a statistical preference for an exponentially small Λ is found to be natural [1]. Within this framework and matching the median Λ value to the observed Λ, a mass scale m 100 GeV naturally appears. We explain how the electroweak scale can be identified with this mass scale.

We use the spinor helicity formalism to study KLT-like relations for the inflationary graviton four-point correlation function. New features are observed in this correlation function compared to the graviton scattering amplitude in flat spacetime. After obtaining the general momentum dependence, collinear, squeezed and collapsed limits are considered to further study the features of the correlation function, and the relation to the corresponding flat space scattering amplitude.

Besides the string scale, string theory has no parameter except some quantized flux values; and the string theory Landscape is generated by scanning over discrete values of all the flux parameters present. We propose that a typical (normalized) probability distribution P (Q) of a physical quantity Q (with nonnegative dimension) tends to peak (diverge) at Q = 0 as a signature of string theory. In the Racetrack Kähler uplift model, where P (Λ) of the cosmological constant Λ peaks sharply at Λ = 0, the electroweak scale (not the electroweak model) naturally emerges when the median Λ is matched to the observed value. We check the robustness of this scenario. In a bottom-up approach, we find that the observed quark and charged lepton masses are consistent with the same probabilistic philosophy, with distribution P (m) that diverges at m = 0, with the same (or almost the same) degree of divergence. This suggests that the Standard Model has an underlying string theory description, and yields relations among the fermion masses, albeit in a probabilistic approach (very different from the usual sense). Along this line of reasoning, the normal hierarchy of neutrino masses is clearly preferred over the inverted hierarchy, and the sum of the neutrino masses is predicted to be m ν 0.0592 eV, with an upper bound m ν < 0.066 eV. This illustrates a novel way string theory can be applied to particle physics phenomenology.