$\varepsilon'/\varepsilon$ in the Standard Model and Beyond: 2021

TL;DR

This paper reviews the current theoretical understanding of the $ ext{ extepsilon}'/ ext{ extepsilon}$ ratio in the Standard Model, compares different calculation approaches, and discusses potential new physics contributions and their correlations with other observables.

Contribution

It provides a comprehensive comparison of three main approaches to calculating $ ext{ extepsilon}'/ ext{ extepsilon}$ and discusses recent developments in analyzing new physics effects within effective field theories.

Findings

Significant differences exist between Lattice QCD, Dual QCD, and Chiral Perturbation Theory calculations.

There remains room for new physics contributions to $ ext{ extepsilon}'/ ext{ extepsilon}$.

Recent technological developments enable better analysis of $ ext{ extepsilon}'/ ext{ extepsilon}$ and related observables.

Abstract

The present status of the ratio $\varepsilon'/\varepsilon$ in the Standard Model (SM) is summarized. In particular we stress the differences between three approaches that attempt to calculate $\varepsilon'/\varepsilon$ within the SM: Lattice QCD, Dual QCD and Chiral Perturbation Theory. As presently there is still a significant room left for new physics (NP) contributions, we summarize the present status of the technology that has been recently developed with the goal to analyze $\varepsilon'/\varepsilon$ and its correlations with other observables within the Weak Effective Theory (WET) and the Standard Model Effective Field Theory (SMEFT). We also make a few comments on the interpretation of the main dynamics behind the $\Delta I=1/2$ rule in $K\to\pi\pi$ decays.