Four Zero Neutrino Yukawa Textures in the Minimal Seesaw Framework

We investigate, within the Type I seesaw framework, the physical implications of zero textures in the Yukawa couplings which generate the neutrino Dirac mass matrix $m_D$. It is shown that four is the maximal number of texture zeroes compatible with the observed leptonic mixing and the assumption that no neutrino mass vanishes. We classify all allowed four-zero textures of $m_D$ into two categories with three classes each. We show that the different classes, in general, admit CP violation both at low and high energies. We further present the constraints obtained for low energy physics in each case. The r\^ ole of these zero textures in establishing a connection between leptogenesis and low energy data is analysed in detail. It is shown that it is possible in all cases to completely specify the parameters relevant for leptogenesis in terms of light neutrino masses and leptonic mixing together with the unknown heavy neutrino masses