CP Violation and $\Delta I=1/2$ Enhancement for $K\to \pi \pi$, $K\to \pi \pi \gamma$ Weak Decays

Abstract

Data indicate that $\Delta I=1/2$ transitions account for 4.5-4.7% of both CP conserving and CP violating $K\to 2\pi$ decays, as well as CP conserving radiative $K\to \pi \pi \gamma$ processes. Observed $K\to \pi \pi \gamma /\pi \pi$ branching ratios are shown to scale near $\alpha /\pi$ or $\alpha /2\pi$. The $K_L$-$K_S$ mixing angle $\varphi$ and the semileptonic weak-rate asymmetry $\delta$ are reviewed, and theory is shown to be consistent with data. Also, $K\to 2\pi$ $\Delta I=1/2$ dominance is studied in the context of the chiral constituent quark model, displaying again excellent agreement with data. Finally, indirect and direct kaon CP violation are successfully described in the framework of photon-mediated loop graphs. This suggests that kaon CPV can be understood via second-order weak transitions, radiatively corrected.

Comments: Plain LaTeX, 12 pages, 4 EPS figures. PACS numbers: 11.30.Er, 12.15.Lk, 13.20.Eb, 13.40.Ks. Version 2: 14 pages, improved presentation, introductory and concluding remarks as well as references added; accepted for publication in Mod. Phys. Lett. A (2004)