Gauged Lepton Number, Dirac Neutrinos, Dark Matter, and Muon $g-2$

TL;DR

This paper proposes a gauge extension of the Standard Model with a new lepton number symmetry, resulting in Dirac neutrinos, a dark matter candidate, and a potential explanation for the muon g-2 anomaly.

Contribution

It introduces a gauged lepton number symmetry that leads to Dirac neutrinos, a stable dark matter candidate, and addresses the muon g-2 discrepancy.

Findings

Neutrinos are naturally Dirac fermions due to the symmetry breaking.

Dark matter is realized as a singlet scalar with a residual $Z_3^D$ symmetry.

The model can account for the muon g-2 anomaly.

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 $Z_3^L$ 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 $Z_3^D$ derivable from $Z_3^L$. Muon $g-2$ may be explained.