A discrete symmetry group for maximal atmospheric neutrino mixing

Abstract

We propose a discrete non-abelian symmetry group which enforces maximal atmospheric neutrino mixing, while $\theta_{13} = 0$ and the solar mixing angle $\theta_{12}$ remains undetermined; without finetuning, $\theta_{12}$ will be large but non-maximal. Our extension of the Standard Model has three right-handed neutrino singlets $\nu_R$ and implements the seesaw mechanism. Furthermore, we have an enlarged scalar sector with three Higgs doublets and two scalar gauge singlets; the latter have masses and vacuum expectation values of the order of the seesaw scale. Lepton mixing stems exclusively from the $\nu_R$ Majorana mass matrix, where non-diagonal elements are generated by the vacuum expectation values of the scalar singlets. The model predicts a neutrino mass spectrum with $m_3 > m_2 > m_1$ and the effective Majorana mass of neutrinoless $\beta\beta$ decay is equal to $m_1 m_2 / m_3$.