We propose a model of soft $\mathrm{CP}$ violation that evades the strong $\mathrm{CP}$ problem and can describe observed $\mathrm{CP}$ violation in the neutral kaon sector, both direct and indirect. Our model requires two “duark” mesons carrying quark number two that have complex ( $\mathrm{CP}$-violating) bare masses and are coupled to quark pairs. Aside from the existence of these potentially observable new particles with masses of several hundred GeV, we predict a flat unitarity triangle (i.e., no observable direct $\mathrm{CP}$ violation in the $B$-meson sector) and a possibly anomalous branching ratio for the decay mode $K^{+}\to {\pi }^{+}+\overline{\nu }\nu$.

• Received 2 March 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.011801