Solar and atmospheric neutrino oscillations and lepton flavor violation in supersymmetric models with right-handed neutrinos

Abstract

Taking the solar and the atmospheric neutrino experiments into account we discuss the lepton flavor violating processes, such as $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}$ or $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma},$ 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 $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ 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 ${M}_{{\ensuremath{\nu}}_{2}}$ is greater than $\ensuremath{\sim}{10}^{13}(\ensuremath{\sim}{10}^{14})\mathrm{GeV}$ for $\mathrm{tan}\ensuremath{\beta}=30(3).$ When we take the MSW small angle solution, the $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ rate is at most about 1/100 of that of the MSW large angle solution. The ``just so'' solution implies ${10}^{\ensuremath{-}5}$ of that of the MSW large angle solution. Also, in the SU(5)RN the large $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}$ 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 $\ensuremath{\sim}{10}^{13}(\ensuremath{\sim}{10}^{14})\mathrm{GeV}$ for $\mathrm{tan}\ensuremath{\beta}=30(3),$ similarly to the MSSMRN. We show the multimass insertion formulas and their applications to $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\tau}}\ensuremath{\mu}\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\mu}}e\ensuremath{\gamma}.$