ε^′/ ε in the Standard Model at the Dawn of the 2020s

We reanalyse the ratio ε^′/ ε 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 η. We find (ε′/ε)SM(8)=(17.4±6.1)×10-4 and (ε′/ε)SM(9)=(13.9±5.2)×10-4, respectively. Despite a very good agreement with the measured value (ε′/ε)exp=(16.6±2.3)×10-4, the large error in (ε′/ε)SM still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for (ε′/ε)BSM valid in any extension beyond the SM without additional light degrees of freedom. We provide new values of the penguin parameters B6(1/2)(μ) and B8(3/2)(μ) at the μ-scales used by the RBC-UKQCD collaboration and at lower scales O(1GeV) used by ChPT and Dual QCD (DQCD). We present semi-analytic formulae for (ε′/ε)SM in terms of these parameters and Ω ^ _eff that summarizes isospin-breaking corrections to this ratio. We stress the importance of lattice calculations of the O(α_em) contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at O(α_em) in the present analyses of ε^′/ ε.