Is the Weinberg model of CP violation really excluded?

Abstract

We give an updated analysis on various {ital CP}-violating effects in the Weinberg three-Higgs-doublet model of {ital CP} violation. Because of the improved estimate of the {eta}-{eta}{prime} mixing and of the {ital K}-{eta}{sub 0} transition, the sign of {epsilon}{prime}/{epsilon} is predicted to be the same as that of the chiral suppression of {ital CP}-odd {ital K}{r arrow}2{pi} amplitudes (owing to the presence of tadpole contributions) and is most likely to be positive, contrary to previous calculations. The neutron electric dipole moment {ital d}{sub {ital n}} due to neutral-Higgs-boson exchange at the one-loop level is reexamined and is found to be below the present experimental limit for reasonable Higgs-boson mass. However, the Weinberg's three-gluon operator arising from charged-Higgs-boson exchange will produce an excessive {ital d}{sub {ital n}} even if the charged Higgs bosons are uncomfortably light. We conclude that the Weinberg {ital CP}-violation model is {ital not} necessarily inconsistent with experiment of measuring {epsilon}{prime}/{epsilon}, but it tends to give too large a value of {ital d}{sub {ital n}}.