Recent MEG Results and Predictive SO(10) Models

Recent MEG results of a search for the lepton flavor violating (LFV) muon decay, $\mu \to e \gamma$, show 3 events as the best value for the number of signals in the maximally likelihood fit. Although this result is still far from the evidence/discovery in statistical point of view, it might be a sign of a certain new physics beyond the Standard Model. As has been well-known, supersymmetric (SUSY) models can generate the $\mu \to e \gamma$ decay rate within the search reach of the MEG experiment. A certain class of SUSY grand unified theory (GUT) models such as the minimal SUSY SO(10) model (we call this class of models "predictive SO(10) models") can unambiguously determine fermion Yukawa coupling matrices, in particular, the neutrino Dirac Yukawa matrix. Based on the universal boundary conditions for soft SUSY breaking parameters at the GUT scale, we calculate the rate of the $\mu \to e \gamma$ process by using the completely determined Dirac Yukawa matrix in two examples of predictive SO(10) models. If we interpret the 3 events in MEG experiment as a positive signal and combine it with other experimental constraints such as the relic density of the neutralino dark matter and recent results on muon $g-2$, we can pin down a parameter set of the universal boundary conditions. Then, we propose benchmark sparticle mass spectra for each predictive SO(10) model, which will be tested at the Large Hadronic Collider.