Minimal inverse seesaw accompanied by Dirac fermionic dark matter

We present a minimal inverse seesaw mechanism by resorting to a $U(1)_{B-L}$ gauge symmetry. In order to cancel the gauge anomalies, we introduce seven neutral fermions among which four participate in the inverse seesaw to induce two nonzero neutrino mass eigenvalues, two forms a stable Dirac fermion to become a dark matter, while the last one keeps massless but decouples early. In this inverse seesaw, two neutral fermions are the usual right-handed neutrinos while the other two have a small Majorana mass term. An additional seesaw mechanism for generating these small Majorana masses also explains the cosmic baryon asymmetry in association with the sphaleron processes.