Minimal Mass Matrices for Dirac Neutrinos

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We consider the possibility of neutrinos being Dirac particles and study minimal mass matrices with as much zero entries as possible. We find that up to 5 zero entries are allowed. Those matrices predict one vanishing mass state, CP conservation and Uₑ₃ either zero or proportional to R, where R is the ratio of the solar and atmospheric Δm². Matrices containing 4 zeros can be classified in categories predicting Uₑ₃ = 0, Uₑ₃ ≠ 0 but no CP violation or |Uₑ₃| ≠ 0 and possible CP violation. Some cases allow to set constraints on the neutrino masses. The characteristic value of Uₑ₃ capable of distinguishing some of the cases with non-trivial phenomenological consequences is about R/2 2 θ₁₂. Matrices containing 3 and less zero entries imply (with a few exceptions) no correlation for the observables. We outline models leading to the textures based on the Froggatt-Nielsen mechanism or the non-Abelian discrete symmetry D₄ × Z₂.