Quark Mass Hierarchy, FCNC and CP violation in a Seesaw model
  The seesaw model of quark masses is studied systematically, focusing on its developments. A framework allowing the top quark mass to be of the order of the electroweak symmetry breaking scale, while the remaining light quarks have much smaller masses, due to the seesaw mechanism, is presented. The violation of the GIM mechanism is shown to be small and the tree level FCNC are suppressed naturally. In this model, there are many particles which could contribute to the FCNC in the one-loop level. Parameters of the model are constrained by using the experimental data on K^0-\bar{K}^0 mixing and \epsilon_K. The rare K meson decays K_{L,S} -> \pi^0 \nu \bar{\nu} and K^+ -> \pi^+ \nu \bar{\nu} are also investigated in the model. In these processes the scalar operators (\bar{s}d)(\bar{\nu}_{\tau}\nu_{\tau}), which are derived from box diagrams in the model, play an important role due to an enhancement factor M_K/m_s in the matrix element <\pi|\bar{s}d|K>. It is emphasized that the K_L decay process through the scalar operator is not the CP violating mode, so B(K_L -> \pi^0 \nu \bar{\nu}) remains non-zero even in the CP conserved limit. The pion energy spectra for these processes are predicted. 
Y. Kiyo, T. Morozumi, P. Parada, M. N. Rebelo and M. Tanimoto