Can Supersymmetric Loops Correct the Fermion Mass Relations in SU(5)?

We investigate three different possibilities for improving the fermion mass relations that arise in grand unified theories (GUTs). Each scenario relies on supersymmetric loop effects alone, without modifying the naive Yukawa unification. First, we consider A-terms that follow the usual proportionality condition. In this case SUSY effects can improve the mass relations, but not completely. Interestingly, imposing Yukawa coupling unification for two families greatly constrains the range of parameters in the MSSM. Secondly, we employ a new ansatz for the tri-linear A-terms that satisfies all experimental and vacuum stability bounds, and can successfully modify the mass relations. Finally, we investigate the use of general (non-proportional) A-terms, with large off-diagonal entries. In this case flavor changing neutral current (FCNC) data present an important constraint. We do not pretend to present a complete, motivated theory of fermion masses. Rather this paper can be viewed as an existence proof, serving to show that Yukawa coupling unification can occur even within the framework of minimal GUTs.