CP violation in hierarchical Yukawa models

Because 4-dimensional CP is a good symmetry of many higher-dimensional theories, this suggests the possible existence of an universal CP-violating phase originating from the process of compactification. Such a phase, if it existed, would not be easy to uncover since the phases in Yukawa matrices are not simply related to the observed Cabibbo-Kobayashi-Maskawa phase delta. Hierarchical Yukawa models, of the type arising in F-theory GUT models provide an interesting exception. Recently, Heckman and Vafa studied a particular F-theory GUT model with hierarchical Yukawa matrices with complex phases of O(1) and showed, by examining the Jarlskog invariant, that this model leads to sin delta similar to O(1). A more detailed examination of the model, although confirming their results, is seen to be also compatible with having a phase delta(o) = pi/3 imprinted on the Hermitian Yukawa matrices, leading to sin delta similar or equal to sin delta(o).