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Abstract

We study the intimate connection between neutrinos and simple abelian gauge symmetries U(1)', starting from the observation that the full global symmetry group of the Standard Model, G = U(1)(B-L) x U(1)(L_e-L_mu) x U(1)(L_mu-L_tau), can be promoted to a local symmetry group by introducing three right-handed neutrinos---automatically making neutrinos massive. The unflavored part U(1)(B-L) is linked to the Dirac vs. Majorana nature of neutrinos; we discuss the B-L landscape---including lepton-number-violating Dirac neutrinos---and implications for neutrinos, the baryon asymmetry, and experiments. Flavored subgroups U(1)' < G can shed light on the peculiar leptonic mixing pattern and mass ordering; we show how normal, inverted, and quasi-degenerate mass hierarchy can arise from a U(1)' in a simple and testable manner. We furthermore present all U(1)' < G that can enforce viable texture zeros in the neutrino mass matrices. Beyond G, symmetries U(1)(DM) in the dark matter sector can give rise to naturally light sterile neutrinos, which provide a new portal between visible and dark sector, and also resolve some longstanding anomalies in neutrino experiments. Further topics under consideration are the mixing of vector bosons with the Z boson, as well as the Stückelberg mechanism. The latter raises the question why the photon should be massless---or stable for that matter!