Ruling out the Weinberg Model of Spontaneous CP Violation

Abstract

There have been many declarations of the death of the Weinberg model of spontaneous CP violation. Previous studies, before the recent measurements of $\epsilon'/\epsilon$, indicated that the model could not accommodate the experimental values on $\epsilon$ in $K^0-\bar K^0$ mixing, the neutron electric dipole moment (EDM), the branching ratio of $b\to s \gamma$ and the upper limit on $\epsilon'/\epsilon$. We point out that these studies were based on optimistic estimates of the uncertainties in the calculations and that when more realistic estimates of these errors are used the Weinberg model cannot be conclusively ruled out from these considerations alone. Here we use these realistic error estimates to analyze the present situation of the Weinberg model. The latest results from Belle and BaBar on $\sin 2 \beta$ allow the small values of this parameter which occur naturally in the Weinberg model. However, in this model, the recently measured value of $\Re(\epsilon'/\epsilon) = (1.92\pm 0.25)\times 10^{-3}$ cannot be made compatible with the branching ratio $B(b\to s \gamma) = (3.15\pm0.54)\times 10^{-4}$. As a result we conclude that the Weinberg model is now confidently and conservatively ruled out.