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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×U(1)Le−Lμ ×U(1)Lμ−Lτ , 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 leptonnumber- 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!