Gauged lepton number, Dirac neutrinos, dark matter, and muon g − 2

Abstract

Lepton number is promoted to an U(1)L gauge symmetry in a simple extension of the standard model. The spontaneous breaking of U(1)L by three units allows a conserved Z3L lepton symmetry to remain, guaranteeing that neutrinos are Dirac fermions, which acquire naturally small masses from a previously proposed mechanism. Dark matter appears as a singlet scalar, with dark symmetry Z3D derivable from Z3L. Muon g−2 may be explained.