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 $\overrightarrow{\tau }\mu \gamma$ or $\overrightarrow{\mu }e\gamma ,$ in the minimal supersymmetric standard model with right-handed neutrinos (MSSMRN) and the supersymmetric SU(5) grand unified theory with right-handed neutrinos [SU(5)RN]. The predicted branching ratio of $\overrightarrow{\mu }e\gamma$ in the MSSMRN with the Mikheyev-Smirnov-Wolfenstein (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 $\sim {10}^{13}\left(\sim {10}^{14}\right)\mathrm{GeV}$ for $\tan \beta =30\mathrm{}\left(3\right).$ When we take the MSW small angle solution, the $\overrightarrow{\mu }e\gamma$ 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 $\overrightarrow{\mu }e\gamma$ 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 $\sim {10}^{13}\left(\sim {10}^{14}\right)\mathrm{GeV}$ for $\tan \beta =30\mathrm{}\left(3\right),$ similarly to the MSSMRN. We show the multimass insertion formulas and their applications to $\overrightarrow{\tau }\mu \gamma$ and $\overrightarrow{\mu }e\gamma .$