Texture-zero model for the lepton mass matrices

Abstract

We suggest a simple model, based on the type-I seesaw mechanism, for the lepton mass matrices. The model hinges on an Abelian symmetry which leads to mass matrices with some vanishing matrix elements. The model predicts one massless neutrino and $M_{e\mu} = 0$ ($M$ is the effective light-neutrino Majorana mass matrix). We show that these predictions perfectly agree with the present experimental data if the neutrino mass spectrum is inverted, i.e. if $m_3 = 0$, provided the Dirac phase $\delta$ is very close to maximal ($\pm \pi / 2$). In the case of a normal neutrino mass spectrum, i.e. when $m_1 = 0$, the agreement of our model with the data is less than optimal---the reactor mixing angle $\theta_{13}$ is too small in our model. Minimal leptogenesis is not an option in our model due to the vanishing elements in the Yukawa-coupling matrices.