Abstract
We present a version of the Type II seesaw mechanism for parametrically small Dirac neutrino masses. Our model starts from an $\mathrm{SU}(2{)}_{\mathrm{L}}\ensuremath{\bigotimes}\mathrm{SU}(2{)}^{\ensuremath{'}}\ensuremath{\bigotimes}\mathrm{U}(1{)}_{\mathrm{X}}$ gauge extension of the Standard Model involving a sector of mirror fermions. A bidoublet scalar with a very small vacuum expectation value connects the SM leptons with their mirror counterparts, and we can identify the mirror neutrino with the right-handed neutrino. Similar to the conventional Type II seesaw, our particle spectrum features singly and doubly charged scalars. The strong $CP$ problem is solved by a discrete exchange symmetry between the two sectors that forces the contributions of quarks and mirror quarks to the strong $CP$ phase to cancel each other. We discuss the low-energy phenomenology, comment on the cosmological implications of this scenario, and indicate how to realize successful Dirac leptogenesis.
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