  A TeV-scale Higgs doublet with a small mixing to the standard model Higgs
doublet can have the sizable Yukawa couplings to several right-handed neutrinos
and the standard model lepton doublets. This provides a testable Dirac neutrino
mass generation. We further consider a seesaw mechanism involving a
$U(1)_{B-L}^{}$ gauge symmetry, which predicts the existence of two
right-handed neutrinos and a stable Dirac fermionic dark matter, to
simultaneously explain the small mixing between the two Higgs doublets and the
generation of the cosmic baryon asymmetry.
