Minimal mass matrices for Dirac neutrinos

We consider the possibility of neutrinos being Dirac particles and studyminimal mass matrices with as much zero entries as possible. We find that up to5 zero entries are allowed. Those matrices predict one vanishing mass state, CPconservation and U_{e3} either zero or proportional to R, where R is the ratioof the solar and atmospheric \Delta m^2. Matrices containing 4 zeros can beclassified in categories predicting U_{e3} = 0, U_{e3} \neq 0 but no CPviolation or |U_{e3}| \neq 0 and possible CP violation. Some cases allow to setconstraints on the neutrino masses. The characteristic value of U_{e3} capableof distinguishing some of the cases with non-trivial phenomenologicalconsequences is about R/2 \sin 2 \theta_{12}. Matrices containing 3 and lesszero entries imply (with a few exceptions) no correlation for the observables.We outline models leading to the textures based on the Froggatt-Nielsenmechanism or the non-Abelian discrete symmetry D_4 \times Z_2.Comment: 32 pages, 3 figures. Comments and references added. To appear in JHE