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In this paper, we study the phenomenology of a Dirac dark matter in the$L_\mu-L_\tau$ model and investigate the neutrino oscillation in the dark halo.Since dark matter couples to the muon neutrino and the tau neutrino withopposite sign couplings, it contributes effective potentials, $\pm A_\chi$, tothe evolution equation of the neutrino flavor transition amplitude, which canbe significant for high energy neutrino oscillations in a dense dark matterenvironment. We discuss neutrino masses, lepton mixing angles, Dirac CP phase,and neutrino oscillation probabilities in the dark halo using full numericalcalculations. Results show that neutrinos can endure very different mattereffects. When the potential $A_\chi$ becomes ultra-large, three neutrinoflavors decouple from each other.

Neutrino oscillation in dark matter with $L_\mu-L_\tau$