Neutrino masses and mixing with general mass matrices

We consider the most general neutrino masses and mixings including Dirac ma ss terms, M-D, as well as Majorana masses, M-R and M-L. Neither the Majoran a nor the Dirac mass matrices are expected to be diagonal in the eigenbasis of weak interactions, and so the resulting eigenstates of the Hamiltonian are admixtures of SU(2)(L) singlet and doublet fields of different "generat ions." We show that for three generations each of doubler and singlet neutr inos, diagonalization of the Hamiltonian to obtain the propagating eigensta tes in the general case requires diagonalization of a 12 x 12 Hermitian mat rix, rather than the traditional 6 x 6 symmetric mass matrix. The symmetrie s of the 12 x 12 matrix are such that it has 6 pairs of real eigenvalues. A lthough the standard "see-saw" mechanism remains valid, and indeed the eige nvalues obtained are identical to the standard ones, the correct descriptio n of diagonalization and mixing is more complicated. The analogs of the CKM matrix for the light and the heavy neutrinos are nonunitary, enriching the opportunities for CP violation in the full neutrino sector. (C) 2000 Elsev ier Science B.V. All rights reserved.