Dirac Leptogenesis with a Non-anomalous $U(1)^{\prime}$ Family Symmetry
  We propose a model for Dirac leptogenesis based on a non-anomalous
$U(1)^{\prime}$ gauged family symmetry. The anomaly cancellation conditions are
satisfied with no new chiral fermions other than the three right-handed
neutrinos, giving rise to stringent constraints among the charges. Realistic
masses and mixing angles are obtained for all fermions. The model predicts
neutrinos of the Dirac type with naturally suppressed masses. Dirac
leptogenesis is achieved through the decay of the flavon fields. The cascade
decays of the vector-like heavy fermions in the Froggatt-Nielsen mechanism play
a crucial role in the separation of the primodial lepton numbers. We find that
a large region of parameter space of the model gives rise to a sufficient
cosmological baryon number asymmetry through Dirac leptogenesis.
