An A_5 Model of Four Lepton Generations

Abstract

We study the lepton sector of a four generations model based on the discrete flavor group $A_5$ (the even permutation of five objects). The best features of the three family $A_4$ model survive, including the tribimaximal pattern of three generation neutrino mixings. At leading order the three light neutrino mass relations of $m_{ν_1} = m_{ν_3}$ and $m_{ν_2} = 0$ are predicted. The splitting of the neutrino masses can be naturally obtained as a result of the breaking of $A_{5}$ down to $A_4$ and a degenerate spectrum is preferred in our model. In our $A_5$ model, the electron mass is zero at tree level, but calculable through quantum corrections.