The $\epsilon'/\epsilon$-Story: 1976-2021

TL;DR

This paper reviews the history and current status of the $ ext{ε'}/ ext{ε}$ ratio, a key measure of direct CP violation in kaon decays, highlighting the challenges in theoretical calculations and the uncertainties affecting new physics interpretations.

Contribution

It provides a historical overview and personal insights into the development of $ ext{ε'}/ ext{ε}$ calculations and discusses the persistent non-perturbative uncertainties impacting the interpretation of experimental data.

Findings

Significant non-perturbative uncertainties remain in $ ext{ε'}/ ext{ε}$ calculations.

The short-distance effects are well-controlled, but hadronic effects dominate the uncertainty.

The room for new physics contributions is still highly uncertain due to theoretical challenges.

Abstract

The ratio $\epsilon'/\epsilon$ measures the size of the direct CP violation in $K_L\to\pi\pi$ decays $(\epsilon^\prime)$ relative to the indirect one described by $\epsilon$ and is very sensitive to new sources of CP violation. As such it played a prominent role in particle physics already for 45 years. Due to the smallness of $\epsilon'/\epsilon$ its measurement required heroic efforts in the 1980s and the 1990s on both sides of the Atlantic with final results presented by NA48 and KTeV collaborations 20 years ago. Unfortunately, even 45 years after the first calculation of $\epsilon'/\epsilon$ we do not know to which degree the Standard Model agrees with this data and how large is the room left for new physics contributions to this ratio. This is due to significant non-perturbative (hadronic) uncertainties accompanied by partial cancellation between the QCD penguin contributions and electroweak penguin contributions. While the significant control over the short distance perturbative effects has been achieved already in the early 1990s, with several improvements since then, different views on the non-perturbative contributions to $\epsilon'/\epsilon$ have been expressed by different authors over last thirty years. In fact even today the uncertainty in the room left for NP contributions to $\epsilon'/\epsilon$ is very significant. My own work on $\epsilon'/\epsilon$ started in 1983 and involved both perturbative and non-perturbative calculations. This writing is a non-technical recollection of the steps which led to the present status of $\epsilon'/\epsilon$ including several historical remarks not known to everybody. The present status of the $\Delta I=1/2$ rule is also summarized. This story is dedicated to Jean-Marc Gerard on the occasion of the 35th anniversary of our collaboration and his 64th birthday.