The Weinberg operator and a lower string scale in orientifold compactifications

We investigate the interplay between the string scale and phenomenological scales in orientifold compactifications. Specifically, we discuss in generality the tension that often arises in accounting for neutrino masses, Yukawa couplings, and a μ-term of the correct order and show that it often constrains the string scale Ms. The discussion focuses on two scenarios where, (1) the observed order of the neutrino masses are accounted for by a D-instanton induced "stringy" Weinberg operator, or (2) effectively via the type I seesaw mechanism with an instanton induced Majorana mass term. In both scenarios, the string scale might be further constrained if the suppression factor of a single D-instanton must account for two of the phenomenological scales. For the sake of concreteness, we present phenomenologically viable quivers which exhibit these effects and perform a systematic analysis of four-stack and five-stack quivers which give rise to the exact MSSM spectrum and account for the order of the neutrino masses via the stringy Weinberg operator.