FIMP and Muon ($g-2$) in a U$(1)_{L_{\mu}-L_{\tau}}$ Model

TL;DR

This paper proposes a U(1)$_{L_{}-L_{ au}}$ extension of the Standard Model featuring a scalar FIMP dark matter candidate, a new gauge boson explaining muon ($g-2$), and a neutrino mass mechanism consistent with observed neutrino mixing.

Contribution

It introduces a novel U(1)$_{L_{}-L_{ au}}$ model with a scalar FIMP DM, a gauge boson addressing muon ($g-2$), and a neutrino mass structure, integrating multiple phenomena.

Findings

Scalar FIMP DM can satisfy relic density constraints.

The $Z_{ au}$ gauge boson explains muon ($g-2$) anomaly.

Model accommodates small neutrino masses and mixing patterns.

Abstract

The tightening of the constraints on the standard thermal WIMP scenario has forced physicists to propose alternative dark matter (DM) models. One of the most popular alternate explanations of the origin of DM is the non-thermal production of DM via freeze-in. In this scenario the DM never attains thermal equilibrium with the thermal soup because of its feeble coupling strength ($\sim 10^{-12}$) with the other particles in the thermal bath and is generally called the Feebly Interacting Massive Particle (FIMP). In this work, we present a gauged U(1)$_{L_{\mu}-L_{\tau}}$ extension of the Standard Model (SM) which has a scalar FIMP DM candidate and can consistently explain the DM relic density bound. In addition, the spontaneous breaking of the U(1)$_{L_{\mu}-L_{\tau}}$ gauge symmetry gives an extra massive neutral gauge boson $Z_{\mu\tau}$ which can explain the muon ($g-2$) data through its additional one-loop contribution to the process. Lastly, presence of three right-handed neutrinos enable the model to successfully explain the small neutrino masses via the Type-I seesaw mechanism. The presence of the spontaneously broken U(1)$_{L_{\mu}-L_{\tau}}$ gives a particular structure to the light neutrino mass matrix which can explain the peculiar mixing pattern of the light neutrinos.