Neutrino Physics and A 4 matter assignments

It is an experimental fact that atmospheric, solar, reactor and accelerator neutrinos change flavour. The present data [1] give the solar lepton mixing angle sin θ12 = 0.32 with a relative error about of 25%(@3σ), the atmospheric angle sin θ23 = 0.5 with a relative error about of 34%(@3σ) and sin θ13 ≤ 0.05(@3σ). The complex phase has not been measured. Precise future data might confirm the maximality of the atmospheric angle within 10% error. The best fit values agree very well with the so called Tri-Bimaximal (TB) lepton mixing matrix [2] where the atmospheric angle is maximal sin θ23 = 1/2, the solar angle is large sin θ12 = 1/3 and sin 2 θ13 = 0. Assuming the charged lepton mass matrix Ml diagonal, UTB ·Diag [m1,m2,m3] · U T TB takes the form