Linking light scalar modes with a small positive cosmological constant in string theory

Based on the studies in Type IIB string theory phenomenology, we conjecture that a good fraction of the meta-stable de Sitter vacua in the cosmic stringy landscape tend to have a very small cosmological constant A when compared to either the string scale Ms or the Planck scale Mp, i.e., A << M-S(4), << M-P(4),. These low lying de Sitter vacua tend to be accompanied by very light scalar bosons/axions. Here we illustrate this phenomenon with the bosonic mass spectra in a set of Type IIB string theory flux compactification models. We conjecture that small A with light bosons is generic among de Sitter solutions in string theory; that is, the smallness of A and the existence of very light bosons (may be even the Higgs boson) are results of the statistical preference for such vacua in the landscape. We also discuss a scalar field phi(3)/phi(4) model to illustrate how this statistical preference for a small A remains when quantum loop corrections are included, thus bypassing the radiative instability problem.