Generating the Neutrino Mixing Matrix with Family Symmetries

A lepton family symmetry may provide an explanation for the existence of maximal and minimal mixing angles present in the best fit neutrino mixing matrix. Most models of family symmetries presented in the literature either cannot be extensions of the Standard Model, or have complicated aspects, such as an extended Higgs sector or explicit symmetry breaking. To find out whether there are any simpler predictive models, I conducted a systematic search to find the minimal extension of the Standard Model that can explain the mixing matrix form. I found that in the minimal extensions that include family symmetries all the mixing matrices are ruled out by experiment. However, Abelian symmetry models that have more Higgs doublets than the Standard Model can ensure that θ₁₃ = 0, but no Abelian symmetry produce maximal atmospheric mixing.