Numerical studies on the renormalization of the mass matrices

We study the development of the mass matrix elements (Yukawa couplings) by integrating the renormalization group equations numerically. We find that the masses for a heavy fourth generation converge to values close to 200 GeV, the mass difference m T − m B ≈ (few) GeV. For realistic solutions where the Cabibbo mixing between the fourth and third generations is small, the top quark mass is limited from above by 60 GeV. Finally, we introduce the SU(5) condition for a charged heavy lepton and find that its mass is limited between 43 and 77 GeV.