One-loop-generatedCPviolation in SU(2) ⊗ U(1) ⊗ U(1)′ gauge theories and their extensions

Abstract

We study the possibility that $\mathrm{CP}$ violation may arise from the one-loop corrections to the fermion mass matrices in two gauge models. First, in an $\mathrm{SU}{(2)}_{L}\ensuremath{\bigotimes}\mathrm{U}(1)$ model with six quarks, we show that it is possible to forbid the $\mathrm{CP}$ violation in the zeroth order by the addition of an extra U(1) group. Owing to the spontaneous breaking of the symmetry, however, $\mathrm{CP}$ violation arises from the one-loop radiative corrections. Despite the success of this model for generating $\mathrm{CP}$ violation at the one-loop level, the magnitude of this violation turns out to be too small to account for the experimental data. Next, this model is generalized and extended to include two more SU(2) groups, and it is shown that, in this case, $\mathrm{CP}$ violation generated by the one-loop radiative corrections is calculated to be compatible with the experiment. Some general consequences are discussed.