U ( 1 ) textures and lepton flavor violation

$U(1)$ family symmetries have led to successful predictions of the fermion mass spectrum and the mixing angles of the hadronic sector. In the context of the supersymmetric unified theories, they further imply a nontrivial mass structure for the scalar partners, giving rise to new sources of flavor violation. In the present work, lepton flavor nonconserving processes are examined in the context of the minimal supersymmetric standard model augmented by a $U(1)$-family symmetry. We calculate the mixing effects on the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}$ rare decays. All supersymmetric scalar masses involved in the processes are determined at low energies using two loop renormalization group analysis and threshold corrections. Further, various novel effects are considered and found to have important impact on the branching ratios. Thus, a rather interesting result is that when the seesaw mechanism is applied in the $12\ifmmode\times\else\texttimes\fi{}12$ sneutrino mass matrix, the mixing effects of the Dirac matrix in the effective light sneutrino sector are canceled at first order. In this class of models and for the case that soft term mixing is already present at the GUT scale, $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}$ decays are mostly expected to arise at rates significantly smaller than the current experimental limits. On the other hand, the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ rare decays impose important bounds on the model parameters, particularly on the supersymmetric scalar mass spectrum. In the absence of soft term mixing at high energies, the predicted branching ratios for rare decays are, as expected, well below the experimental bounds.