Models of Low Energy Effective Theory applied to Kaon Non-leptonic Decays and Other Matrix Elements

TL;DR

This paper discusses a method for computing non-leptonic matrix elements in kaon decays by integrating long and short distance effects, highlighting the matching procedure and recent results on the $ riangle I=1/2$ rule.

Contribution

It introduces a consistent approach to include both long and short distance contributions in non-leptonic matrix element calculations, addressing scheme dependences and applying it to kaon decay phenomena.

Findings

Results for the $ riangle I=1/2$ rule

Calculations of $B_6$ parameter

Comparison of low-energy models

Abstract

In this talk I describe work on computing non-leptonic matrix elements consistently with both long and short distance contributions included. On the simpler example of the $\pi^+$-$\pi^0$ mass difference I explain in detail the matching procedure and the difference between various low-energy models. I then explain the new difficulties in non-leptonic Kaon decays and how the matching here can in principle be done in the same way when scheme dependences are correctly accounted for. In the end I summarize the results J. Prades and I obtain for the $\Delta I=1/2$ rule and $B_6$.