Why is the 3 x 3 neutrino mixing matrix almost unitary in realistic seesaw models?

A simple extension of the standard model is to introduce n heavy right-handed Majorana neutrinos and preserve its SU(2)L x U(1)Y gauge symmetry. Diagonalizing the (3 + n) x (3 + n) neutrino mass matrix, the authors obtain an exact analytical expression for the effective mass matrix of νe, νμ and ντ. It turns out that the 3 x 3 neutrino mixing matrix V, which appears in the leptonic charged-current weak interactions, must not be exactly unitary. The unitarity violation of V is negligibly tiny; however, if the canonical seesaw mechanism works to reproduce the correct mass scale of light Majorana neutrinos. A similar conclusion can be drawn in the realistic Type-II seesaw models. (authors)