$U(1)_{L_\mu-L_\tau}$ for Light Dark Matter, $g_\mu-2$, the $511$ keV excess and the Hubble Tension

TL;DR

This paper proposes a $U(1)_{L_-}$ gauge model with a light Dirac dark matter particle that can simultaneously address the muon g-2 anomaly, the Hubble tension, and the 511 keV photon excess, while remaining consistent with current constraints.

Contribution

It introduces a new gauge symmetry and parameter space that unify explanations for multiple astrophysical and particle physics anomalies.

Findings

Identifies a parameter space with $m_X \u2248 20$ MeV and $g_X \u2248 5 imes 10^{-4}$ that explains several anomalies.

Demonstrates the model's consistency with existing experimental and astrophysical constraints.

Suggests future experiments can test this model.

Abstract

In this paper we introduce a light Dirac particle $\psi$ as thermal dark matter candidate in a $U(1)_{L_{\mu}-L_{\tau}}$ model. Together with the new gauge boson $X$, we find a possible parameter space with $m_X \simeq 20$ MeV, $U(1)_{L_{\mu}-L_{\tau}}$ coupling $g_X \simeq 5 \cdot 10^{-4}$ and $m_\psi \gtrsim m_X/2$ where the $(g-2)_\mu$ anomaly, dark matter, the Hubble tension, and (part of) the excess of $511$ keV photons from the region near the galactic center can be explained simultaneously. This model is safe from current experimental and astrophysical constraints, but can be probed by the next generation of neutrino experiments as well as low-energy $e^+e^-$ colliders.