The GUT? Neutrino bi-large mixing and proton decay

In this talk, we introduce a new scenario of grand unified theory (GUT) with anomalous $U(1)_A$ gauge symmetry, which can explain doublet-triplet splitting, quark and lepton masses and mixing angles. In neutrino sector, the scenario realizes LMA solution for solar neutrino problem and large $U_{e3}=O(0.1)$. Moreover, the scenario predicts that the main decay mode of proton is from dimension 6 operators and the lifetime of proton must be near the present limit. The realization of gauge coupling unification requires that the cutoff scale of the scenario must be around the usual GUT scale $\Lambda_G\sim 2\times 10^{16}$ GeV, which is smaller than the Planck scale. It may suggest the extra dimension in which gauge fields in visible sector do not propagate. This talk is based on the papers. [maekawa,maekawa2,maekawa3,BM,MY]