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Solar and Atmospheric Neutrino Oscillations and Lepton Flavor Violation in Supersymmetric Models with Right-handed Neutrinos

Taking the solar and the atmospheric neutrino experiments into account we discuss the lepton flavor violating processes, such as $τ\toμγ$ or $μ\to eγ$, in the minimal supersymmetric standard model with right-handed neutrinos (MSSMRN) and the supersymmetric SU(5) GUT with right-handed neutrinos (SU(5)RN). The predicted branching ratio of $μ\to eγ$ in the MSSMRN with the MSW large angle solution is so large that it goes beyond the current experimental bound if the second-generation right-handed Majorana mass $M_{ν_2}$ is greater than $\sim 10^{13}(\sim 10^{14})$GeV for $\tanβ=30(3)$. When we take the MSW small angle solution, the $μ\to eγ$ rate is at most about 1/100 of that of the MSW large angle solution. The 'just so' solution implies $10^{-5}$ of that of the MSW large angle solution. Also, in the SU(5)RN the large $μ\to eγ$ rate naturally follows from the MSW large angle solution, and the predicted rate is beyond the current experimental bound if the typical right-handed Majorana mass $M_N$ is larger than $\sim 10^{13}(\sim 10^{14})$GeV for $\tanβ=30(3)$, similarly to the MSSMRN. We show the multimass insertion formulas and their applications to $τ\toμγ$ and $μ\to eγ$.