Some Simple Mixing and Mass Matrices for Neutrinos

In this brief note, we suggest that the accumulating neutrino data [1–3], including the recent results from KamLAND [4] and K2K [5], point to a relatively simple neutrino mass matrix. The data can be explained by oscillations between three active neutrinos with the atmospheric neutrino and K2K data explained by oscillation between the muon and the tauon neutrinos, and the solar neutrino and KamLAND data explained by the oscillation between the electron and muon neutrinos. Following standard convention, let us denote the neutrinos current eigenstates, coupled to the charged leptons by the W bosons, by να (α = e, μ, τ) and the neutrino mass eigenstates by νi (i = 1, 2, 3). We will take the neutrinos to be Majorana as seems likely [6], and thus the neutrino mass matrix Mαβ is symmetric in the basis of the current eigenstates. We will also for simplicity assume CP conservation so that M is real. Thus, M is diagonalized by an orthogonal transformation