Additional isospin-breaking effects in ϵ′/ϵ

In the analysis of ϵ′/ϵ it has been traditional to consider the isospin-breaking effects arising from electroweak-penguin contributions and from π0–η,η′ mixing, yet additional isospin-violating effects exist. In particular, we study the isospin violation which arises from the u–d quark mass difference in the hadronization of the gluonic penguin operator, engendering contributions of an effective ΔI=3/2 character. Using chiral perturbation theory and the factorization approximation for the hadronic matrix elements, we find within a specific model for the low-energy constants that we can readily accommodate an increase in ϵ′/ϵ by a factor of two.