Maki-Nakagawa-Sakata matrix and Froggatt-Nielsen mechanism

Abstract

Flavor mixings together with fermion mass spectra are studied in detail in the $SU(6)\times SU(2{)}_R$ model, in which state-mixings beyond the minimal supersymmetric standard model (MSSM) take place. Characteristic patterns of fermion spectra are attributed to the hierarchical structure of effective Yukawa interactions via the Froggatt-Nielsen mechanism and also to the state-mixings beyond the MSSM. It is shown explicitly that the neutrino mass matrix in the mass diagonal basis for charged leptons has no hierarchical structure. This is due to the cancellation among the hierarchical factors by the seesaw mechanism with the hierarchical Majorana mass matrix of $R$-handed neutrinos. As a consequence, $V_{\mathrm{MNS}}$ exhibits large mixing. It is found that observed values of the Maki-Nakagawa-Sakata matrix elements are reproduced successfully.

Comments: 20 pages, The title has been changed. Several paragraphs have been added. In particular, three novel relations among fermion masses and the CKM mixing matrix have been proposed in Sec.VII. (to be published Phys. Rev. D)