Neutrino hierarchies from a gauge symmetry

Abstract

We consider the phenomenology of the gauged Abelian symmetry $B+3({L}_{e}\ensuremath{-}{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}})$. Right-handed neutrinos necessary to cancel triangle anomalies are used in a type-I seesaw scheme to create active neutrino masses. Breaking the $B+3({L}_{e}\ensuremath{-}{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}})$ symmetry spontaneously below the seesaw scale generates low-energy neutrino mass matrices with the approximate symmetries ${L}_{e}$ (leading to normal hierarchy) or ${L}_{e}\ensuremath{-}{L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ (inverted hierarchy). For the latter we need to introduce a ${\mathbb{Z}}_{2}$ symmetry which decouples one of the right-handed neutrinos. If exact, this ${\mathbb{Z}}_{2}$ leads to a Majorana dark matter candidate that interacts with the standard model via the ${Z}^{\ensuremath{'}}$ and a scalar $s$ originating from spontaneous breaking of the new symmetry. The measured relic abundance of the dark matter particle can be obtained around the scalar and ${Z}^{\ensuremath{'}}$ resonances, while direct detection experiments are mainly sensitive to scalar exchange, which is induced by mass mixing of $s$ with the standard Higgs.