Alternative minimal U(1) B − L

We provide a minimal alternative gauged U(1)${}_{B-L}$ model in which three right-handed neutrinos with charges of $(5,-4,-4)$ and only one $B-L$ Higgs field with charge 1 are introduced. Consistent active neutrino masses and mixings can be obtained if the $Z_2$ symmetry on two of the right-handed neutrinos is introduced. It predicts two heavy degenerate right-handed neutrinos, which may realize resonant leptogenesis scenario, and one relatively light sterile neutrino, which is a good dark matter candidate.