# Non-perturbative renormalization in kaon decays

## TL;DR

This paper applies a non-perturbative renormalization method to kaon decay operators, addressing the $ ext{Δ}I=1/2$ rule and operator mixing, with implications for understanding kaon decay dynamics.

## Contribution

It demonstrates the use of the MPSTV non-perturbative method for kaon decay operators, providing new insights into longstanding issues like the $ ext{Δ}I=1/2$ rule.

## Key findings

- Reappraisal of the $ ext{Δ}I=1/2$ rule using non-perturbative techniques
- Analysis of operator mixing and its effects on $B_K$
- Discussion of power-divergent subtractions in kaon decays

## Abstract

We discuss the application of the MPSTV non-perturbative method \cite{NPM} to the operators relevant to kaon decays. This enables us to reappraise the long-standing question of the $\Delta I=1/2$ rule, which involves power-divergent subtractions that cannot be evaluated in perturbation theory. We also study the mixing with dimension-six operators and discuss its implications to the chiral behaviour of the $B_K$ parameter.