Implications of Higgs Discovery for the Strong CP Problem and Unification

Abstract

A $Z_2$ symmetry that extends the weak interaction, $SU(2{)}_L\to SU(2{)}_L\times SU(2{)}^{\prime }$, and the Higgs sector, $H(2)\to H(2,1)+H^{\prime }(1,2)$, yields a Standard Model quartic coupling that vanishes at scale $v^{\prime }=<H^{\prime }>\gg <H>$. Near $v^{\prime }$, theories either have a "prime" sector, or possess "Left-Right" (LR) symmetry with $SU(2{)}^{\prime }=SU(2{)}_R$. 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 $\bar{\theta }$ 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 $SU(3)\times SU(2{)}_L\times SU(2{)}_L\times U(1{)}_{B-L}$, have precise gauge coupling unification for $v^{\prime }=10^{10\pm 1}$ GeV, successfully correlating gauge unification with the observed Higgs mass of $125$ GeV. With $SU(3)\times U(1{)}_{B-L}$ 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 $SO(10)\times CP$ are constructed that have $H+H^{\prime }$ in a $16$ or $144$ and generate higher-dimensional flavor operators, while maintaining perturbative gauge couplings.

Comments: 36 pages, 5 figures