The Three Neutrino Scenario

I have discussed in my talk several remaining issues in the standard three-flavor mixing scheme of neutrinos, in particilar, the sign of $\Delta m^2_{13}$ and the leptonic CP violating phase. In this report I focus on two topics: (1) supernova method for determining the former sign, and (2) illuminating how one can detect the signatures for both of them in long-baseline ($\gsim 10$ km) neutrino oscillation experiments. I do this by formulating perturbative frameworks appropriate for the two typical options of such experiments, the high energy and the low energy options with beam energies of $\sim$ 10 GeV and $\sim$ 100 MeV, respectively.