Gauged $L_e-L_{\mu}-L_{\tau}$ symmetry, fourth generation, neutrino mass and dark matter

TL;DR

This paper develops models with gauged $L_e-L_-L_ au$ symmetry, exploring anomaly cancellation, neutrino mass hierarchies, and dark matter candidates, including a light scalar field produced via freeze-in, and discusses implications for muon and electron g-2 anomalies.

Contribution

The paper introduces two anomaly-free models with gauged leptonic symmetries, linking neutrino mass hierarchies and dark matter to new gauge sectors and scalar fields.

Findings

Gauged $L_e-L_-L_ au$ can produce normal neutrino mass hierarchy.

A light scalar $$ can serve as freeze-in dark matter with a lifetime exceeding the universe's age.

Models can potentially explain muon and electron g-2 anomalies.

Abstract

We present two models where the familiar leptonic symmetry $L_e-L_\mu-L_\tau$ is a gauge symmetry. We show how anomaly cancellation constrains the allowed theories, with one of them requiring a fourth sequential chiral standard model fermion generation and a second one with three generations, requiring gauging of $(L_e-L_\mu-L_\tau)-(B_1-B_2-B_3)$ with $B_a$ representing the baryon number of the $a$th generation quarks. Unlike global $L_e-L_\mu-L_\tau$ models which always leads to inverted mass hierarchy for neutrinos, the gauged version can lead to normal hierarchy. We show how to construct realistic models in both the cases and discuss the dark matter candidate in both. In our model, the breaking of $U(1)_{L_e-L_\mu-L_\tau}$ is responsible for neutrino mass via type-I mechanism whereas the real part of $U(1)_{L_e-L_\mu-L_\tau}$ breaking scalar field (called $\phi$ here) plays the role of freeze-in dark matter candidate. Since $\phi$ is unstable, for it to qualify as dark matter, its lifetime must be larger than the age of the Universe, implying that the relic of $\phi$ is generated through freeze-in mechanism and its mass must be less than an MeV. We also discuss the possibility of explaining both muon and electron $(g-2)$ while being consistent with the dark matter relic density and lifetime constraints.