Abstract
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 η0 . 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(1 GeV) 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(αem) contributions to the hadronic matrix elements necessary for the removal of renormalization scheme dependence at O(αem) in the present analyses of ε'/ε .