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CP violation due to multi-Froggatt-Nielsen fields

Abstract:

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 |Vus| and the ratio of two vacuum expectation values of FN fields, R=|R|eiα (a magnitude and a phase). It is demonstrated how the angles φi (i=1,...,3) of the unitarity triangle and the CKM off-diagonal elements |V ub| and |Vcb| are pbkp_redicted as a function of |V us|, |R| and α. Although the pbkp_redicted 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. © 2007 Springer-Verlag / Società Italiana di Fisica.