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We propose a minimal extension of the Standard Model in which neutrinos are Dirac particles and their tiny masses are explained without requiring tiny Yukawa couplings. A second Higgs doublet with a tiny vacuum expectation value provides neutrino masses while simultaneously improving the naturalness of the model by allowing a heavier Standard Model-like Higgs boson consistent with electroweak precision data. The model predicts a mu to e gamma rate potentially detectable in the current round of experiments, as well as distinctive signatures in the production and decay of the charged Higgs H+ of the second doublet which can be tested at future colliders. Neutrinoless double beta decay is absent.

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