A radiative seesaw model with higher order terms under an alternative $U(1)_{B-L}$

We propose a model based on an alternative $U(1)_{B-L}$ gauge symmetry with 5 dimensional operators in the Lagrangian, and we construct the neutrino masses at one-loop level, and discuss lepton flavor violations, dark matter, and the effective number of neutrino species due to two massless particles in our model. Then we search allowed region to satisfy the current experimental data of neutrino oscillation and lepton flavor violations without conflict of several constraints such as stability of dark matter and the effective number of neutrino species, depending on normal hierarchy and inverted one.