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We reanalyse the ratio $varepsilon/varepsilon$ in the Standard Model (SM) using most recent hadronic matrix elements from the RBC-UKQCD collaboration in combination with most important NNLO QCD corrections to electroweak penguin contributions and the isospin-breaking corrections. We illustrate the importance of the latter by using their latest estimate from chiral perturbation theory (ChPT) based on the $octet$ approximation for lowest-lying mesons and a very recent estimate in the $nonet$ scheme that takes into account the contribution of $eta_0$. We find $(varepsilon/varepsilon)^{(8)}_text{SM} = (17.4 pm 6.1) times 10^{-4}$ and $(varepsilon/varepsilon)^{(9)}_text{SM} = (13.9 pm 5.2) times 10^{-4}$, respectively. Despite a very good agreement with the measured value $(varepsilon/varepsilon)_text{exp} = (16.6 pm 2.3) times 10^{-4}$, the large error in $(varepsilon/varepsilon)_text{SM}$ still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for $(varepsilon/varepsilon)_text{BSM}$ valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters $B_6^{(1/2)}(mu)$ and $B_8^{(3/2)}(mu)$ at the $mu$-scales used by the RBC-UKQCD collaboration and at lower scales $mathcal{O}(1,text{GeV})$ used by ChPT and DQCD. We present semi-analytic formulae for $(varepsilon/varepsilon)_text{SM}$ in terms of these parameters and $hat{Omega}_text{eff}$ that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the $mathcal{O}(alpha_text{em})$ contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at $mathcal{O}(alpha_text{em})$ in the present analyses of $varepsilon/varepsilon$.
For direct CP-violation in $Ktopipi$ decays, the usual isospin-breaking effects at the percent level are amplified by the dynamics behind the $Delta I=1/2$ rule and conventionally encoded in $Omega_{rm IB}$ parameters. The updated prediction $Omega_{
Estimates of the CP violating observable $varepsilon/varepsilon$ have gained some attention in the past few years. Depending on the long-distance treatment used, they exhibit up to $2.9sigma$ deviation from the experimentally measured value. Such a d
We present for the first time a model-independent anatomy of the ratio $varepsilon/varepsilon$ in the context of the $Delta S = 1$ effective theory with operators invariant under QCD and QED and in the context of the Standard Model Effective Field Th
We present for the first time a master formula for $varepsilon/varepsilon$, the ratio probing direct CP violation in $K to pipi$ decays, valid in any theory beyond the Standard Model (BSM). The formula makes use of hadronic matrix elements of BSM ope
Following the recent analysis done in collaboration with Jason Aebischer and Christoph Bobeth, I summarize the optimal, in our view, strategy for the present evaluation of the ratio $varepsilon/varepsilon$ in the Standard Model (SM). In particular, I