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We propose a model with $U(1)_{B-L}$ gauge symmetry and several new fermionsin no conflict with anomaly cancellation where the neutrino masses are given bythe vacuum expectation value of Higgs triplet induced at the one-loop level.The new fermions are odd under discrete $Z_2$ symmetry and the lightest onebecomes dark matter candidate. We find that the mass of dark matter istypically $O(1)$-$O(10)$ GeV. Then relic density of the dark matter isdiscussed.

Loop induced type-II seesaw model and GeV dark matter with $U(1)_{B-L}$ gauge symmetry