[Formula: see text] in the Standard Model at the Dawn of the 2020s

We reanalyse the ratio e ' / e 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 0 . We find ( e ' / e ) SM ( 8 ) = ( 17.4 ± 6.1 ) × 10 - 4 and ( e ' / e ) SM ( 9 ) = ( 13.9 ± 5.2 ) × 10 - 4 , respectively. Despite a very good agreement with the measured value ( e ' / e ) exp = ( 16.6 ± 2.3 ) × 10 - 4 , the large error in ( e ' / e ) SM still leaves room for significant new physics (BSM) contributions to this ratio. We update the 2018 master formula for ( e ' / e ) 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 ) ( μ ) and B 8 ( 3 / 2 ) ( μ ) at the μ -scales used by the RBC-UKQCD collaboration and at lower scales O ( 1 GeV ) used by ChPT and Dual QCD (DQCD). We present semi-analytic formulae for ( e ' / e ) 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 e ' / e .