In this talk we consider right-handed neutrino dark matter N 1 in local U(1) L µ −L τ -extended Ma model. With the light U(1) µ−τ gauge boson (m Z ∼ O(100) MeV) and small U(1) µ−τ gauge coupling (g Z ∼ 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 ∼ 10 − 100 GeV), although the gauge coupling constant g Z is small. This is

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... e to the fact that the annihilation cross section of dark matter pair is enhanced by M 4 1 /m 4 Z in the processes N 1 N 1 → Z Z or N 1 N 1 → Z H 2 . We also consider the constraints from direct detection, collider searches.