The singular seesaw mechanism with hierarchical Dirac neutrino mass

The singular seesaw mechanism can naturally explain the atmospheric neutrino deficit by maximal oscillations between v(mu L) and v(mu R). This mechanism can also induce three different scales of the neutrino mass squared differences, which can explain the neutrino deficits of three independent experiments (solar, atmospheric, and LSND) by neutrino oscillations. In this paper we show that realistic mixing angles among the neutrinos can be obtained by introducing a hierarchy in the Dirac neutrino mass. Ia the case where the Majorana neutrino mass matrix has rank 2, the solar neutrino deficit is explained by vacuum oscillations between v(e) and v(tau). We also consider the case where the Majorana neutrino mass matrix has rank 1. In this case, the matter enhanced Mikheyev-Smirnov-Wolfenstein solar neutrino solution is preferred as the solution of the solar neutrino deficit.