CP violation and Kaon weak matrix elements from Lattice QCD

TL;DR

This paper reviews recent lattice QCD calculations of kaon weak matrix elements crucial for understanding CP violation, highlighting progress in computing $ ext{Re}(rac{ ext{epsilon}'}{ ext{epsilon}})$ and discussing uncertainties in $B_K$ and beyond standard model effects.

Contribution

It presents the first realistic lattice computation of $ ext{epsilon}'/ ext{epsilon}$ with physical kinematics and analyzes the sources of discrepancies in neutral kaon mixing matrix elements.

Findings

Progress in computing $ ext{epsilon}'/ ext{epsilon}$ with physical kinematics.

Analysis of the error budget for $B_K$, especially perturbative errors.

Discussion of discrepancies in neutral kaon mixing matrix elements beyond the standard model.

Abstract

In this short review, I present the recent lattice computations of kaon weak matrix elements relevant to $K \to \pi\pi$ decays and neutral kaon mixing. These matrix elements are key to the theoretical determination of the CP violation parameters $\epsilon$ and $\epsilon'$ . Impressive progress have been achieved recently, in particular the first realistic computation of $\epsilon'/\epsilon$ with physical kinematics has been reported in [1]. The novelty is the $\Delta I = 1/2$ channel, whereas the $\Delta I = 3/2$ contribution is now computed at several values of the lattice spacing and extrapolated to the continuum limit. I will also present the status of $B_K$ and discuss its error budget, with a particular emphasis on the perturbative error. Finally I will review the matrix elements of neutral kaon mixing beyond the standard model and will argue that the discrepancy observed by different collaborations could be explained by the renormalisation procedure of the relevant four-quark operators.