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The minimal Higgs sectors of Supersymmetric Grand Unified Theories (SGUT's) can be extended by introducing higher dimensional (anomaly free) representations. We have found models ith different anomaly free combinations of SU(5) representations which are different in terms or their β functions. It is also interesting to consider the RGE effect associated with the Yukawa coupling that involve the additional Higgs representations. In order to do this we shall consider the 2-loop β functions for the gauge coupling, but will keep only the 1-loop RGE for the new Yukawa couplings, in a SU(5) SGUT model. [ABSTRACT FROM AUTHOR]

We discuss several aspects of the flavor problem in the Supersymmetry. First, in order to quantify the SUSY flavor problem, we generate randomly the entries of the sfermion mass matrices and determine which percentage of the points are consistent with current bounds on the flavor violating transitions, for which we take as an illustration the lepton flavor violating (LFV) decays li → ljγ. In the first instance we apply the mass-insertion method, and study how this percentage changes as one varies the parameters of the model. It is found that for 105 points about 10% of points pass current LFV bounds on μ → eγ provided the sleptons masses are ∼ 10 TeV. While bounds on τ → μγ, eγ are satisfied for almost 100% of points even for sleptons masses as low as 360 GeV. Then, we consider an ansatz for sfermion masses that can be diagonalized exactly, and compare the results obtained previously for τ → μγ. Now, we get that 100% of points satisfy the experimental bounds but with sleptons masses larger than 460 GeV. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]