Radiative Linear Seesaw model, Dark Matter and $U(1)_{B-L}$

In this paper we propose a radiated linear seesaw model where the naturally small term $\mu_{L}$ are generated at one-loop level and its soft-breaking of lepton number symmetry attributes to the spontaneous breaking(SSB) of B-L gauge symmetry. The value of $B-L$ charges for new particles are assigned to satisfy the anomalies cancelation. It is founded that some new particles may have exotic values of $B-L$ charge such that there exists residual $Z_{2}\times Z_{2}^{\prime}$ symmetry even after SSB of $B-L$ gauge symmetry. The $Z_{2}\times Z_{2}^{\prime}$ discrete symmetry stabilizes the these particles as dark matter candidates. In the model, two classes of inert fermions and scalars with different $B-L$ charges are introduced, leading to two-component dark matter candidates. The lepton flavor violation processes, the relic density of dark matter, the direct detection of dark matter and the phenomenology at LHC are investigated.