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 $\tau\to\mu\gamma$ or $\mu\to e\gamma$, in the minimal supersymmetric standard model with the right-handed neutrinos (MSSMRN) and the supersymmetric SU(5) GUT with the right-handed neutrinos (SU(5)RN). The predicted branching ratio of $\mu\to e\gamma$ 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 $M_{\nu_2}$ is greater than $\sim 10^{13}(\sim 10^{14})$GeV for $\tan\beta=30(3)$. When we take the MSW small angle solution, the $\mu\to e\gamma$ 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 $\mu\to e\gamma$ 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 $\tan\beta=30(3)$, similarly to the MSSMRN. We show the multi-mass insertion formulas and their applications to $\tau\to\mu\gamma$ and $\mu\to e\gamma$.