Mass hierarchies and a formula for the Cabibbo angle in SU(2) L × U(1)

Abstract

Form the observation that there is a three-fold hierarchy of quark and lepton masses we are led to impose a discrete symmetry on the lagrangian. As a consequence, two quark masses and all mixing angles are predicted with the following results: (i) tan θ c = (m d /m s ) 1 2 ; (ii) m b is predicted correctly; (iii) m t is predicted to be ∼ 20 GeV; (iv) the relation m e/ m μ ≈ m u/ m c emerges automatically; (v) a heavy meson containing a b quark is predicted to decay into charmed particles with a lifetime of ∼ 10 −11 s; (vi) the magnitude of CP violation in K L → 2π automatically is O(10 −3).