Sfermion mass degeneracy, superconformal dynamics, and supersymmetric grand unified theories

We discuss issues in a scenario where hierarchical Yukawa couplings are generated through the strong dynamics of superconformal field theories (SCFTs). Independently of the mediation mechanism of supersymmetry breaking, the infrared convergence property of SCFTs can provide an interesting solution to the supersymmetric flavor problem; sfermion masses are suppressed around the decoupling scale of SCFTs and eventually become degenerate to some degree, thanks to family-independent radiative corrections governed by the gaugino masses of the minimal supersymmetric standard model (MSSM). We discuss under what conditions the degeneracy of the sfermion mass can be estimated in a simple manner. We also discuss the constraints from lepton flavor violations. We then explicitly study sfermion mass degeneracy within the framework of grand unified theories coupled to SCFTs. It is found that the degeneracy for right-handed sleptons becomes worse in the conventional SU(5) model than in the MSSM. On the other hand, in the flipped $\mathrm{SU}\mathrm{}\left(5\right)\mathrm{}\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ model, each right-handed lepton is still an SU(5) singlet, whereas the B-ino mass $M_1$ is determined by two independent gaugino masses of $\mathrm{SU}\mathrm{}\left(5\right)\mathrm{}\times \mathrm{U}\mathrm{}\left(1\right).$ These two properties enable us to have an improved degeneracy for the right-handed sleptons. We also speculate on how further improvement can be obtained in the SCFT approach.