There have been many declarations of the death of the Weinberg model of spontaneous $\mathrm{CP}$ violation. However, these studies relied on the assumption of unrealistically small errors in the theoretical uncertainties in the calculations of the relevant observables, and a realistic estimate of the errors shows that the Weinberg model cannot be ruled out on the basis used in the past—the experimental values on $\epsilon$ in $K^0-K^0$ mixing, the neutron electric dipole moment (EDM), the branching ratio of $\overrightarrow{b}s\gamma ,$ and the earlier upper limit on ${\epsilon }^{\prime }/\epsilon .$ In this paper we use these realistic estimates of the theoretical uncertainty, together with the recent experimental results to study the consistency of the Weinberg model of $\mathrm{CP}$ violation with the data. 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 $\mathrm{Re}({\epsilon }^{\prime }/\epsilon )=(1.92\mathrm{}\pm 0.25)\times {10}^{-3}$ cannot be made compatible with the branching ratio $B\left(\overrightarrow{b}s\gamma \right)=(3.15\mathrm{}\pm 0.54)\times {10}^{-4}.$ As a result we conclude that the Weinberg model is now confidently and conservatively ruled out.

• Received 14 September 1999

DOI:https://doi.org/10.1103/PhysRevD.63.096005