Flavor-changing neutral currents and seesaw masses for quarks

The structure of flavor-changing neutral currents (FCNC’s) which arise when one tries to give masses to quarks through the analogue of the seesaw mechanism for neutrino masses is studied. General conditions for the absence of FCNC’s in the seesaw limit are derived. A specific model where these conditions are satisfied by the tree-level-quark mass matrices is identified. The FCNC’s get generated in this model through radiative corrections to quark masses. These corrections lead to a hierarchy $F_{12}$<$F_{13}$<$F_{23}$ in typical strength $F_{\mathrm{ij}}$ of the neutral-current transition between ith and jth generations. Moreover the flavor-changing transitions between down quarks are suppressed compared to the corresponding transitions between up quarks. As a consequence, the FCNC’s connecting d to s quark are greatly suppressed in conformity with observations such as $K^0$-K${¯}^0$ mixing and the decay $K_L$→${\mu }^{+}$ ${\mu }^{\mathrm{-}}$. In contrast, the transitions between c and t quarks could have observable magnitudes. The branching ratio for Z→t¯c could be as large as ${10}^{\mathrm{-}6}$–${10}^{\mathrm{-}7}$ in the model considered here. The $D^0$-D${¯}^0$ mixing could also be in the vicinity of the present experimental limits.