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

Taking the solar and the atmospheric neutrino experiments into account we discuss the lepton flavor violating processes, such as τ → μγ or μ → eγ, in the minimal supersymmetric standard model with the right-handed neutrinos (MSSMRN) and the supersymmetric SU(5) GUT with the righthanded neutrinos (SU(5)RN). The predicted branching ratio of μ → eγ in the MSSMRN with the MSW large angle solution is so large that it goes beyond the current experimental bound if the secondgeneration right-handed Majorana mass Mν2 is greater than ∼ 10 (∼ 10)GeV for tanβ = 30(3). When we take the MSW small angle solution, the μ → eγ rate is at most about 1/100 of that of the MSW large angle solution. The ’just so’ solution implies 10 of that of the MSW large angle solution. Also, in the SU(5)RN the large μ → 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 MN is larger than ∼ 10 (∼ 10)GeV for tan β = 30(3), similarly to the MSSMRN. We show the multi-mass insertion formulas and their applications to τ → μγ and μ → eγ.