Progress in $K\to\pi\pi$ Decays

TL;DR

This paper reviews recent progress in understanding $K o\pi o\pi$ decays, focusing on connecting short-distance calculations with long-distance matrix elements and analyzing the $\Delta I=1/2$ rule in the chiral limit.

Contribution

It introduces a systematic method to connect short-distance evolution with long-distance matrix elements, accounting for scheme dependence, and presents results for the $\Delta I=1/2$ rule.

Findings

Successful connection of short- and long-distance calculations.

Results for the $\Delta I=1/2$ rule in the chiral limit.

Enhanced understanding of $K o\pi o\pi$ decay mechanisms.

Abstract

Recent work by J.~Prades and myself on $K\to\pi\pi$ is described. The first part describes our method to connect in a systematic fashion the short-distance evolution with long-distance matrix-element calculations taking the scheme dependence of the short-distance evolution into account correctly. In the second part I show the results we obtain for the $\Delta I=1/2$ rule in the chiral limit.