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I construct predictive models of neutrino mass and mixing that have fewerparameters, both in the lepton sector and overall, than the default seesawmodel. The predictions are theta13=0 and one massless neutrino, with the modelshaving a Z4 or Z2 symmetry and just one extra degree of freedom: one realsinglet Higgs field. It has been shown that models with an unbroken familysymmetry, and with no Higgs fields other than the Standard Model Higgs doubletproduce masses and mixing matrices that have been ruled out by experiment.Therefore, this article investigates the predictions of models with Abelianfamily symmetries that involve Higgs singlets, doublets and triplets, in thehope that they may produce the maximal and minimal mixing angles seen in thebest fit neutrino mixing matrix. I demonstrate that these models can onlyproduce mixing angles that are zero, maximal or unconfined by the symmetry. Themaximal mixing angles do not correspond to physical mixing, so an Abeliansymmetry can, at best, ensure that theta13=0, while leaving the solar andatmospheric mixing angles as free parameters. To generate more features of thebest-fit mixing matrix a model with a non-Abelian symmetry and a complicatedHiggs sector would have to be used.Comment: 16 pages, no figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Abelian family symmetries and the simplest models that give<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>θ</mml:mi><mml:mn>13</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math>in the neutrino mixing matrix

Abelian family symmetries and the simplest models that giveθ13=0in the neutrino mixing matrix