Isospin-breaking in š/: impact of 0 at the dawn of the 2020s

For direct CP-violation in K ->pi pi 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 IB parameters. The updated prediction Omega IB(8) (15.9 +/- 8.2)x10-2 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 IB(9)=(35 +/- 7)x10-2 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 Omega eff(9)=(29 +/- 7)x10-2 to be compared with Omega eff(8)=(17 +/- 9)x10-2 used in recent analyses of epsilon '/epsilon. Accordingly, we get a reduction from (epsilon '/epsilon)SM(8)=(17.4 +/- 6.1)x10-4 to (epsilon '/epsilon)SM(9)=(13.9 +/- 5.2)x10-4 and thereby an effective suppression of (epsilon '/epsilon)SM by isospin-breaking corrections as large as 40% relative to the recent RBC-UKQCD value.