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

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 ($m_{Z^{\prime }}\sim \mathcal{O}(100)$ MeV) and small $U(1{)}_{\mu -\tau }$ gauge coupling ($g_{Z^{\prime }}\sim 10^{-4}-10^{-3}$) 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 $g_{Z^{\prime }}$ is small. This is due to the fact that the annihilation cross section of dark matter pair is enhanced by $M_1^4/m_{Z^{\prime }}^4$ in the processes $N_1{N}_1\to Z^{\prime }{Z}^{\prime }$ or $N_1{N}_1\to Z^{\prime }{H}_2$. We also consider the constraints from direct detection, collider searches.

11 pages, 3 figures

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