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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 $Omega_{rm IB}^{(8)}=(15.9pm 8.2)times 10^{-2}$ of the Chiral Perturbation Theory for the strong isospin-breaking due to $pi_3-eta_8$ mixing confirms such a tendency but is quite sensitive to the theoretical input value of the low-energy constant corresponding to the flavour-singlet $eta_0$ exchange contribution in this truncated octet scheme. We rather exploit the phenomenological $eta_8-eta_0$ mixing as a probe for the non-negligible flavour-singlet component of the physical $eta$ pole to find $Omega_{rm IB}^{(9)}=(35pm7)times 10^{-2}$ in a complete nonet scheme. A large central value in the nonet scheme is thus substituted for a large uncertainty in the octet one. Including the experimental $pi^+-pi^0$ mass difference as the dominant electromagnetic isospin-breaking, we obtain for the effective parameter entering the ratio $epsilon/epsilon$ an improved result $hatOmega_{rm eff}^{(9)}=(29pm7)times 10^{-2}$ to be compared with $hatOmega_{rm eff}^{(8)}=(17pm9)times 10^{-2}$ used in recent analyses of $epsilon/epsilon$. Accordingly, we get a reduction from $(epsilon/epsilon)_{rm SM}^{(8)}=(17.4pm 6.1)times 10^{-4}$ to $(epsilon/epsilon)_{rm SM}^{(9)}=(13.9pm 5.2)times 10^{-4}$ and thereby an effective suppression of $(epsilon/epsilon)_{rm SM}$ by isospin-breaking corrections as large as $40%$ relative to the recent RBC-UKQCD value.
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
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
Motivated by the recent findings that the ratio $varepsilon/varepsilon$ in the Standard Model (SM) appears to be significantly below the data we investigate whether the necessary enhancement of this ratio can be obtained in 331 models, in which new p
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
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