Scalar Dark Matter and Radiative Dirac neutrino mass in an extended $U(1)_{B-L}$ model

We explore a gauged $U(1)_{B-L}$ extension of standard model with inclusion of three right-handed neutrinos of exotic $B-L$ charges to cancel the gauge anomaly. Non-trivial transformation of new particles under $B-L$ symmetry forbids the neutrino mass at tree level and hence a small Dirac mass can be generated radiatively at one loop with a doublet fermion and singlet scalar. We also discuss the phenomenology of a scalar dark matter, which can be obtained from the mixing of neutral CP even component of a doublet and real singlet scalar. An adhoc $Z_2$ symmetry is required in the current framework to stabilize the dark matter candidate. Presence of new particles with $Z_2$ odd charges and small mass splitting, makes the phenomenology more interesting by governing the relic density with co-annihilation processes. We explore the spin-independent direct detection constraints on dark matter via the scalar mediation. The new particle spectrum not only opens up new window for dark matter study but also satisfy the constraints from lepton flavor violating decay of $\mu \rightarrow e \gamma$.