In the most minimal seesaw model with two heavy right-handed neutrinos, we generalize the Frampton-Glashow-Yanagida Ansatz for the $3\times 2$ Dirac neutrino mass matrix and show that the determinant of the $3\times 3$ light Majorana neutrino mass matrix M always vanishes. Parametrizing M in terms of three neutrino masses, three lepton mixing angles, and three $\mathrm{CP}$-violating phases, we examine all its possible one-zero textures with one vanishing mass eigenvalue. We find that three one-zero patterns of M with $m_1=0\mathrm{}$ and four one-zero patterns of M with $m_3=0\mathrm{}$ are compatible with current neutrino oscillation data. The implications of these phenomenological Ansätze on the neutrino mass spectrum and the neutrinoless double beta decay are also discussed.

• Received 22 September 2003

DOI:https://doi.org/10.1103/PhysRevD.69.013006