FIMP dark matter candidate(s) in a $B-L$ model with inverse seesaw mechanism

The non-thermal dark matter (DM) production via the so-called freeze-in mechanism provides a simple alternative to the standard thermal WIMP scenario. In this work, we consider a popular $U(1)_{B-L}$ extension of the standard model (SM) in the context of inverse seesaw mechanism which has at least one (fermionic) FIMP DM candidate. Due to the added $\mathbb{Z}_{2}$ symmetry, a SM gauge singlet fermion, with mass of order keV, is stable and can be a warm DM candidate. Also, the same $\mathbb{Z}_{2}$ symmetry helps the lightest right-handed neutrino, with mass of order GeV, to be a stable or long-lived particle by making a corresponding Yukawa coupling very small. This provides a possibility of a two component DM scenario as well. Firstly, in the absence of a GeV DM component (i.e., without tuning its corresponding Yukawa coupling to be very small), we consider only a keV DM as a single component DM, which is produced by the freeze-in mechanism via the decay of the extra $Z'$ gauge boson associated to $U(1)_{B-L}$ and can consistently explain the DM relic density measurements. In contrast with most of the existing literature, we have found a reasonable DM production from the annihilation processes. After numerically studying the DM production, we show the dependence of the DM relic density as a function of its relevant free parameters. We use these results to obtain the parameter space regions that are compatible with the DM relic density bound. Secondly, we study a two component DM scenario and emphasize that the current DM relic density bound can be satisfied for a wide range of parameter space.