Muon anomalous magnetic moment, lepton flavor violation, and flavor changing neutral current processes in supersymmetric grand unified theory with right-handed neutrinos

Motivated by the large mixing angle solutions for the atmospheric and solar neutrino anomalies, flavor changing neutral current processes and lepton flavor violating processes as well as the muon anomalous magnetic moment are analyzed in the framework of SU(5) supersymmetric grand unified theory (SUSY GUT) with right-handed neutrinos. In order to explain realistic mass relations for quarks and leptons, we take into account the effects of higher dimensional operators above the GUT scale. It is shown that the supersymmetric contributions to the $\mathrm{CP}$ violation parameter in $K^0-K^0$ mixing, ${\varepsilon }_K,$ the $\overrightarrow{\mu }e\gamma$ branching ratio, and the muon anomalous magnetic moment become large in a wide range of parameter space. We also investigate the correlations among these quantities. Within the current experimental bound of $B\left(\overrightarrow{\mu }e\gamma \right),$ large SUSY contributions are possible either in the muon anomalous magnetic moment or in ${\varepsilon }_K.$ In the former case, the favorable value of the recent muon anomalous magnetic moment measurement at the BNL E821 experiment can be accommodated. In the latter case, the allowed region of the Kobayashi-Maskawa phase can be different from the prediction within the standard model (SM) and therefore measurements of the $\mathrm{CP}$ asymmetry of the $\overrightarrow{B}J/\psi K_S$ mode and $\Delta m_{B_s}$ could discriminate this case from the SM. We also show that the $\overrightarrow{\tau }\mu \gamma$ branching ratio can be close to the current experimental upper bound and the mixing induced $\mathrm{CP}$ asymmetry of the radiative B decay can be enhanced in the case where the neutrino parameters correspond to the Mikheyev-Smirnov-Wolfenstein small mixing angle solution.