The $ε'/ε$-Story: 1976-2021

Abstract

The ratio ε /ε measures the size of the direct CP violation in K L → ππ decays (ε ) relative to the indirect one described by ε 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 smallnes of ε /ε 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 at the beginning of this millennium. Unfortunately, even 45 years after the first calculation of ε /ε we do not know to which degree the Standard Model agrees with this data and how large is the room left for new physics (NP) contributions to this ratio. This is due to significant nonperturbative (hadronic) uncertainties accompanied by partial cancellation between the QCD penguin contributions and electroweak penguin contributions. In addition to the calculation of hadronic matrix elements of the relevant operators including isospin breaking effects and QED corrections, it is crucial to evaluate accurately the Wilson coefficients of the relevant operators. While the significant control over the latter short distance effects has been achived already in the early 1990s, with several improvements since then, different views on the non-perturbative contributions to ε /ε have been expressed by different authors over last thirty years. In fact even at the dawn of the 2020s the uncertainty in the room left for NP contributions to ε /ε is still very significant, which I find to be very exciting.My own work on ε /ε started in 1983 and involved both perturbative and nonperturbative calculations. This writing is a non-technical recollection of the steps which led to the present status of ε /ε including several historical remarks not known to everybody. The present status of the ∆I = 1/2 rule is also summarized.This story is dedicated to my great ε /ε-collaborator Jean-Marc Gérard on the occasion of the 35th anniversary of our collaboration and his 64th birthday.

BSM Master Formula for $\varepsilon'/\varepsilon$ in the WET Basis at NLO in QCD

“…A similar result is found using ChPT [7], but as discussed in [1] it is a numerical coincidence in view of the smaller estimate of EWP contributions by these authors relative to LQCD, and a different estimate of isospin-breaking corrections. In any case, while this estimate is fully compatible with the experimental value in (1), the large uncertainty related primarily to QCDP contributions does not exclude the modifications of ε ′ ε by NP as large as 10 −3 .…”

“…It is very sensitive to new sources of CP violation. As such it played a prominent role in particle physics already for 45 years [1]. However, due to large hadronic uncertainties in the evaluation of ε ′ ε no consensus between theorists has been reached on its value within the Standard Model (SM).…”

“…In fact as argued on the basis of the DQCD approach [6] in [1,11] the values of ε ′ ε in the SM in the ballpark of 5 × 10 −4 are still possible. This situation motivated various authors already for many years to perform analyses of ε ′ ε in various extensions of the SM with the goal to identify which models could allow for significant contributions to ε ′ ε taking existing constraints from other processes into account.…”

“…Moreover, for this matching the most convenient WET basis is the one introduced in [18], the so-called JMS basis. 1 In particular, for this basis the tree-level matching of SMEFT on to WET [18] and the corresponding one-loop matching [20,21] are known. Therefore it is evident that a master formula for ε ′ ε written in terms of WCs in the JMS basis would be more useful for BSM analyses than the one that uses BMU basis at the electroweak scale.…”

General non-leptonic $ΔF=1$ WET at the NLO in QCD

“…In fact, as argued on the basis of the large-N c QCD in Ref. [61], the values of ε ′ ε in the SM in the ballpark of 5 × 10 −4 are still possible.…”