Singlet scalar Dark matter in $U(1)_{B-L}$ models without right-handed neutrinos

We investigate the phenomenology of singlet scalar dark matter in a simple $B-L$ gauge extension of the Standard Model where the dark matter particle is charged under the $U(1)_{B-L}$ symmetry. The non-trivial gauge anomalies are cancelled with the introduction of three exotic fermions with $B-L$ charges as $-4,-4,5$, instead of right-handed neutrinos $\nu_{Ri}~(i=1,2,3)$ with $B-L=-1$ in conventional $U(1)_{B-L}$ model. Without the need of any ad-hoc discrete symmetry, the $B-L$ charge plays a crucial role in stabilizing the dark matter. We make a comprehensive study of dark matter phenomenology in the scalar and gauge portals separately. In the gauge-mediated regime, we invoke the LEP-II constraints and dilepton limits of ATLAS on the gauge parameters. A massless physical Goldstone plays a vital role in the scalar-portal dark matter observables, becomes a unique feature of the model. We show the mechanism of generating the light neutrino mass at one-loop level where the dark matter singlet runs in the loop. We shed light on the semi-annihilation and finally, we comment on indirect signals in this framework.