$\overrightarrow{K}\pi \pi$ and a light scalar meson

We explore the $\Delta I=\frac{1}{2}$ rule and ${\epsilon }^{\prime }/\epsilon$ in $\overrightarrow{K}\pi \pi$ transitions using a Dyson-Schwinger equation model. Exploiting the feature that quantum chromodynamics penguin operators direct $K_S^0$ transitions through $0^{++}$ intermediate states, we observe an enhancement of $\overrightarrow{K}\pi {\pi }_{I=0\mathrm{}}$ transitions from the contribution of a putative light $\sigma$-meson. This mechanism also affects ${\epsilon }^{\prime }/\epsilon .$