Flavor Mixing Signals For Realistic Supersymmetric Unification

The gauge interactions of any supersymmetric extension of the standard model involve new flavor mixing matrices. The assumptions involved in the construction of minimal supersymmetric models, both $SU(3) \times SU(2) \times U(1)$ and grand unified theories, force a large degree of triviality on these matrices. However, the requirement of realistic quark and lepton masses in supersymmetric grand unified theories forces these matrices to be non-trivial. This leads to important new dominant contributions to the neutron electric dipole moment and to the decay mode $p \to K^o\mu^+$, and suggests that there may be important weak scale radiative corrections to the Yukawa coupling matrix of the up quarks. The lepton flavor violating signal $\mu \to e\gamma$ is studied in these theories when $\tan\beta$ is sufficiently large that radiative effects of couplings other than $\lambda_t$ must be included. The naive expectation that large $\tan\beta$ will force sleptons to unacceptably large masses is not borne out: radiative suppressions to the leptonic flavor mixing angles allow regions where the sleptons are as light as 300 GeV, provided the top Yukawa coupling in the unified theory is near the minimal value consistent with $m_t$.