Towards a quantitative understanding of the Delta I=1/2 rule

TL;DR

This paper reviews a strategy to quantify the charm quark's influence on the $
$ rule, finding significant long-distance effects that contribute to the rule but are insufficient to fully explain experimental observations.

Contribution

It introduces a method combining Chiral Perturbation Theory and quenched lattice QCD to analyze the charm quark's role in the $
$ rule, highlighting long-distance contributions.

Findings

Large $
$ enhancement observed, but not enough to match experimental data.

Long-distance effects are significant and unrelated to penguin contractions.

Results suggest the charm quark's mass influences the $
$ rule beyond short-distance operators.

Abstract

A recently proposed strategy to quantify the role of the charm quark mass in the $\Delta I=1/2$ rule is reviewed. Results for the low-energy couplings of the $\Delta S=1$ chiral effective Hamiltonian in a theory with a light charm quark (GIM limit) are obtained through a matching of three-point correlation functions computed in Chiral Perturbation Theory and in quenched lattice QCD. We observe a large $\Delta I=1/2$ enhancement, which is not large enough to explain the experimental result, but suggests significant long-distance contributions to the physical $\Delta I=1/2$ which are unrelated to penguin contractions or operators.