Let there be Light Dark Matter: The gauged $U(1)_{L_\mu-L_\tau}$ case

TL;DR

This paper investigates a light vector-like fermion dark matter candidate within a gauged $U(1)_{L___ au}$ model, identifying parameter regions that satisfy relic abundance, explain the muon g-2 anomaly, and evade experimental constraints.

Contribution

It extends the minimal $U(1)_{L___ au}$ model by including a light fermion and explores viable parameter spaces that reconcile dark matter and muon g-2 anomalies.

Findings

Standard benchmark $M_V=3 m___ au$ is ruled out for unit charges.

Near-resonance region $M_V  2 m___ au$ can explain relic abundance and muon g-2.

A second parameter window exists in the few-GeV range with small charge hierarchies.

Abstract

As experimental null results increase the pressure on heavy weakly interacting massive particles (WIMPs) as an explanation of thermal dark matter (DM), it seems timely to explore previously overlooked regions of the WIMP parameter space. In this work we extend the minimal gauged $U(1)_{L_\mu-L_\tau}$ model studied in \cite{Bauer:2018onh} by a light (MeV-scale) vector-like fermion $\chi$. Taking into account constraints from cosmology, direct and indirect detection we find that the standard benchmark of $M_V=3 m_\chi$ for DM coupled to a vector mediator is firmly ruled out for unit DM charges. However, exploring the near-resonance region $M_V\gtrsim 2 m_\chi$ we find that this model can simultaneously explain the DM relic abundance $\Omega h^2 =0.12$ and the $(g-2)_\mu$ anomaly. Allowing for small charge hierarchies of $\lesssim\mathcal{O}(10)$, we identify a second window of parameter space in the few-GeV region, where $\chi$ can account for the full DM relic density.