Are "Penguins" Black-and-White?

Abstract

Contributions of low energy "eye" and "figure-eight" quark diagrams to the $K \rightarrow \pi$ weak transitions are studied in a hadron- level phenomenological approach. It is shown that these contributions may be estimated by considering meson-cloud effects. If all intermediate mesons under consideration are degenerate only the "eye" (low-energy penguin) diagram is nonvanishing. When allowance is made for smaller mass of pseudoscalar mesons, the contribution of "figure-eight" diagrams turns out to enhance the $\Delta I = \frac{1}{2}$ (suppress the $\Delta I = \frac{3}{2}$) amplitudes naturally. The overall long-distance-induced enhancement of the ratio of the $\Delta I = \frac{1}{2}$ amplitudes over the $\Delta I = \frac{3}{2}$ amplitudes is estimated at around 4-8.