Higgs Parity, Strong CP, and Dark Matter

Abstract: An exact spacetime parity replicates the $SU(2) \times U(1)$ electroweak interaction, the Higgs boson $H$, and the matter of the Standard Model. This "Higgs Parity" and the mirror electroweak symmetry are spontaneously broken at scale $v' = \left\langle{H'} \right\rangle \gg \left\langle{H}\right\rangle$, yielding the Standard Model below $v'$ with a quartic coupling that essentially vanishes at $v'$: $\lambda_{SM}(v') \sim 10^{-3}$. The strong CP problem is solved as Higgs parity forces the masses of mirror quarks and ordinary quarks to have opposite phases. Dark matter is composed of mirror electrons, $e'$, stabilized by unbroken mirror electromagnetism. These interact with Standard Model particles via kinetic mixing between the photon and the mirror photon, which arises at four-loop level and is a firm prediction of the theory. Physics below $v'$, including the mass and interaction of $e'$ dark matter, is described by $\textit{one fewer parameter}$ than in the Standard Model. The allowed range of $m_{e'}$ is determined by uncertainties in $(\alpha_s, m_t, m_h)$, so that future precision measurements of these will be correlated with the direct detection rate of $e'$ dark matter, which, together with the neutron electric dipole moment, will probe the entire parameter space.