Preference for a vanishingly small cosmological constant in supersymmetric vacua in a Type IIB string theory model

We study the probability distribution P(Λ) of the cosmological constant Λ in a specific set of KKLT type models of supersymmetric IIB vacua. We show that, as we sweep through the quantized flux values in this flux compactification, P(Λ) behaves divergent at Λ=0− and the median magnitude of Λ drops exponentially as the number of complex structure moduli h2,1 increases. Also, owing to the hierarchical and approximate no-scale structure, the probability of having a positive Hessian (mass-squared matrix) approaches unity as h2,1 increases.