Natural Suppression of Strong<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>- and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>-Invariance Violations and Calculable Mixing Angles in SU (2) ⊗ U (1)

Abstract

Permutation symmetry is imposed on an $\mathrm{SU}{(2)}_{L}\ensuremath{\bigotimes}\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{CP}$-invariant Lagrangian with six quarks. The mixing angles of the $b$ and $t$ are determined: $b$ decays predominantly to $u$ and a meson containing $b$ should have a lifetime ${\ensuremath{\tau}}_{B}\ensuremath{\approx}{10}^{\ensuremath{-}11}$ sec or less. A phase in the gauge couplings of $b$ and $t$ causes nonconservation of $\mathrm{CP}$ in ${K}_{L}$ decays that is naturally small. No violations of $P$ and $T$ invariance are induced into the strong interactions by $\ensuremath{\varphi}=\mathrm{arg}(\mathrm{Det}M)$ at the tree level. One-loop corrections yield an upper bound of $\ensuremath{\varphi}&lt;{10}^{\ensuremath{-}10}(\frac{{m}_{s}}{{m}_{b}}){(\frac{{m}_{t}}{{m}_{b}})}^{2}$.