CP Violation due to Multi Froggatt-Nielsen Fields

We study how to incorporate CP violation in the Froggatt-Nielsen (FN) mechanism. To this end, we introduce non-renormalizable interactions with a flavor democratic structure to the fermion mass generation sector. It is found that at least two iso-singlet scalar fields with a discrete symmetry imposed are necessary to generate CP violation due to the appearance of the relative phase between their vacuum expectation values. In the simplest model, the ratios of quark masses and the Cabibbo-Kobayashi-Maskawa (CKM) matrix including the CP violating phase are determined by the CKM element vertical bar Vus vertical bar and the ratio of two vacuum expectation values of FN fields, R = vertical bar R vertical bar(ie) (a magnitude and a phase). It is demonstrated how the angles phi i (i = 1,..., 3) of the unitarity triangle and the CKM off-diagonal elements vertical bar V-ub vertical bar and vertical bar V-cb vertical bar are predicted as a function of I V,,,, 1, 1 R I and a. Although the predicted value of the CP violating phase does not agree with the experimental data within the simplest model, the basic idea of our scenario would be promising if one wants to construct a more realistic model of flavor and CP violation.