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 $m_1{m}_2/m_3$.

Comments: 9 pages, no figures, plain LaTeX; new section added and misprints corrected, version to be published in Phys. Lett. B