Dark matter and muon $(g-2)$ in local $U(1)_{L_\mu-L_\tau}$-extended Ma Model

TL;DR

This paper explores how a local $U(1)_{L__}$-extended Ma model with a light gauge boson can explain dark matter relic density and muon g-2 anomaly simultaneously, highlighting the role of enhanced annihilation cross sections.

Contribution

It demonstrates that correct dark matter relic density can be achieved in the model despite small gauge coupling, due to cross section enhancement from mass ratios.

Findings

Dark matter relic density is achievable for $M_1  10-100$ GeV.

Enhanced annihilation cross section due to $M_1^4/m_{Z'}^4$ ratio.

Model can accommodate muon g-2 anomaly within experimental constraints.

Abstract

We consider right-handed neutrino dark matter $N_1$ in local $U(1)_{L_\mu-L_\tau}$-extended Ma model. With the light $U(1)_{\mu-\tau}$ gauge boson ($m_{Z'} \sim {\cal O}(100)$ MeV) and small $U(1)_{\mu-\tau}$ gauge coupling ($g_{Z'}\sim 10^{-4}-10^{-3}$) which can accommodate the muon $(g-2)$ anomaly and is still allowed by other experimental constraints, we show that we can get correct relic density of dark matter for wide range of dark matter mass ($M_1 \sim 10-100$ GeV), although the gauge coupling constant $g_{Z'}$ is small. This is due to the fact that the annihilation cross section of dark matter pair is enhanced by $M_1^4/m_{Z'}^4$ in the processes $N_1 N_1 \to Z' Z'$ or $N_1 N_1 \to Z' H_2$. We also consider the constraints from direct detection, collider searches.