Dynamical Generation of the CKM Matrix

Abstract

We argue that in dynamical models of fermion masses, which explain the three mass scales of the generations of fermions with three separate heavy scales above the electroweak symmetry breaking scale, the off diagonal CKM matrix elements must be generated at a fourth scale. The simplest form for the additional mass generation is a mechanism that has an $SU(3)_L \otimes SU(3)_R$ family symmetry. We show that such an ansatz can produce the up down mass inversion and the observed Cabibbo angle. If the mass terms for the third family quarks are enhanced by additional interactions the full CKM matrix may be realized. We present a toy model which realizes vacua with these masses.}