Implications of Higgs discovery for the strong CP problem and unification

A Z(2) symmetry that extends the weak interaction, SU(2)(L) SU(2)(L) xSU(2), and the Higgs sector, H(2) H(2, 1) + H(1, 2), yields a Standard Model quartic coupling that vanishes at scale v = H >> H. Near v, theories either have a prime sector, or possess Left-Right (LR) symmetry with SU(2) = SU(2)(R). If the Z(2) symmetry incorporates spacetime parity, these theories can solve the strong CP problem. The LR theories have all quark and lepton masses arising from operators of dimension 5 or more, requiring Froggatt-Nielsen structures. Two-loop contributions to theta are estimated and typically lead to a neutron electric dipole moment of order 10(-27)e cm that can be observed in future experiments. Minimal models, with gauge group SU(3) x SU(2)(L) x SU(2)(L) x U(1)(B-L), have precise gauge coupling unification for v = 10(10 +/- 1) GeV, successfully correlating gauge unification with the observed Higgs mass of 125 GeV. With SU(3) x U(1)(B-L) embedded in SU(4), the central value of the unification scale is reduced from 10(16-17) GeV to below 10(16) GeV, improving the likelihood of proton decay discovery. Unified theories based on SO(10) x CP are constructed that have H + H in a 16 or 144 and generate higher-dimensional flavor operators, while maintaining perturbative gauge couplings.