Complete supersymmetric SO(10) model

A complete supersymmetric SO(10) model is constructed, which is the most general one consistent with R, discrete, and U(1) flavor symmetries. At the supersymmetric level there are many degenerate vacua, one of which is phenomenologically successful. This vacuum has VEV’s which align in certain definite directions in SO(10) group space, such as the B-L direction. Although this desired vacuum is not proven to be the global minimum of the entire theory, including supersymmetry breaking, it is separated from vacua where the VEV’s point in different group directions by a large potential barrier. This desired vacuum simultaneously leads to three major features of the theory. (1) SO(10) is broken at the scale ${\mathit{v}}_{10}$ to SU(5), which breaks at ${\mathit{M}}_{\mathit{G}}$ to the standard model gauge group. Beneath ${\mathit{M}}_{\mathit{G}}$ the only light gauge nonsinglet fields are those of the minimal supersymmetric standard model, so that the successful prediction for the weak mixing angle is retained. (2) The alignment of the VEV’s leads to a natural mass separation of the weak Higgs doublets from their colored partners via a mechanism which is closely related to the issue of the proton decay rate. Also, the generation of the μ term is studied. (3) A set of particles acquire mass at the highest perturbative scale of the theory, M and at ${\mathit{v}}_{10}$. When they are integrated out, they lead to just four flavor operators for quark and charged lepton masses, and two more for neutrino masses. These flavor operators lead to many quark and lepton mass and mixing angle relations which involve pure SO(10) group theory numerical Clebsch factors. The family hierarchies result from the ratio of scales ${\mathit{v}}_{10}$/M, ${\mathit{M}}_{\mathit{G}}$/${\mathit{v}}_{10}$, and ${\mathit{M}}_{\mathit{G}}$/M. While the theory is by no means unique, it is complete, and hence illustrates the close connection between several important features of the theory.