$U(1)_χ$ and Seesaw Dirac Neutrinos

Abstract: In the context of $SO(10) \to SU(5) \times U(1)_\chi$, it is shown how seesaw Dirac neutrinos may be obtained. In this framework, $U(1)$ lepton number is conserved, with which self-interaction dark matter with a light scalar dilepton mediator may be implemented. In addition, $U(1)$ baryon number may be broken to $(-1)^{3B}$, thereby generating a baryon asymmetry of the Universe. The axionic solution to the strong $CP$ problem may also be incorporated.