Double type II seesaw mechanism accompanied by Dirac fermionic dark matter

In the type II seesaw mechanism, the neutrino mass generation could be tested experimentally if the Higgs triplet is at the TeV scale and has a small cubic coupling to the standard model Higgs doublet. We show such small triplet-doublet coupling and the cosmic baryon asymmetry can be simultaneously induced by an additional seesaw mechanism involving a U(1)(B-L) gauge symmetry. Meanwhile, three right-handed neutrinos for canceling the gauge anomalies can form a stable Dirac fermionic dark matter besides an acceptably massless fermion.