Supersymmetric grand unified theories: Two-loop evolution of gauge and Yukawa couplings

Abstract

We make a numerical study of gauge and Yukawa unification in supersymmetric grand unified models and examine the quantitative implications of fermion mass Ansätze at the grand unified scale. Integrating the renormalization group equations with α1(MZ) and α2(MZ) as inputs, we find α3(MZ)0.111(0.122) for MSUSY=mt and α3(MZ)0.106(0.116) for MSUSY=1 TeV at one-loop (two-loop) order. Including b and τ Yukawa couplings in the evolution, we find an upper limit of mt200 GeV from Yukawa unification. For given mt175 GeV, there are two solutions for β: one with tanβ>mtmb, and one with sinβ0.78(mt150GeV). Taking a popular Ansatz for the mass matrices at the unified scale, we obtain a lower limit on the top-quark mass of mt150(115) GeV for α3(MZ)=0.11(0.12) and an upper limit on the supersymmetry parameter tanβ50 if α3(MZ)=0.11. The evolution of the quark mixing matrix elements is also evaluated. © 1993 The American Physical Society.