Dispersive contribution toK0−K¯0transition and Higgs-boson-exchange model ofCPviolation

Dispersive ${\pi }^0$, $\eta$, and ${\eta }^{\prime }$ pole contributions to $\mathrm{CP}$-violating $K^0-{\overline{K}}^0$ transition are analyzed for the Higgs-boson-exchange model of $\mathrm{CP}$ violation and are found to produce $\frac{{\epsilon }_m}{\xi }$ much larger than the box-diagram contributions, independent of $\mathrm{CP}$-violating $\Delta S=1\mathrm{}$ matrix elements. The penguin-type $\mathrm{CP}$-violating $\Delta S=2\mathrm{}$ transition due to one-gluon exchange, not analyzed previously, is found to be negligible. This indicates that barring accidental cancellation of the low-energy and high-energy dispersive contributions, the Higgs-boson-exchange model of $\mathrm{CP}$ violation can still be acceptable with present data on $\frac{{\epsilon }^{\prime }}{\epsilon }$.