Implications of Higgs Discovery for the Strong CP Problem and Unification

Understand

A $Z_2$ symmetry that extends the weak interaction, $SU(2)_L \rightarrow SU(2)_L \times SU(2)'$, and the Higgs sector, $H(2) \rightarrow H(2,1) + H'(1,2)$, yields a Standard Model quartic coupling that vanishes at scale $v' = <H'>~\gg~<H>$.

• Near $v'$, theories either have a &#34;prime&#34; sector, or possess &#34;Left-Right&#34; (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.